# Événements

## Colloque des sciences mathématiques du Québec - Simone Brugiapaglia, Université Concordia

le vendredi 10 février 2023

The Mathematical Foundations of Deep Learning: From Rating Impossibility to Practical Existence Theorems

Deep learning is having a profound impact on industry and scientific research. Yet, while this paradigm continues to show impressive performance in a wide variety of applications, its mathematical foundations are far from being well established. In this talk, I will present recent developments in this area by illustrating two case studies.

First, motivated by applications in cognitive science, I will present “rating impossibility" theorems. They identify frameworks where deep learning is provably unable to generalize outside the training set for the seemingly simple task of learning identity effects, i.e. classifying whether pairs of objects are identical or not.

Second, motivated by applications in scientific computing, I will illustrate “practical existence" theorems. They combine universal approximation results for deep neural networks with compressed sensing and high-dimensional polynomial approximation theory. As a result, they yield sufficient conditions on the network architecture, the training strategy, and the number of samples able to guarantee accurate approximation of smooth functions of many variables.

Time permitting, I will also discuss work in progress and open questions.

Date: 10 février 2023

Lieu: Centre de recherches mathématiques, Pavillon André-Aisenstadt, Université de Montréal, Salle 5340

## Colloque des sciences mathématiques du Québec - Arul Shankar, Université de Toronto

le vendredi 27 janvier 2023

The distribution of Selmer groups of elliptic curves

The Goldfeld and Katz--Sarnak conjectures predict that 50% of elliptic curves have rank 0, that 50% have rank 1, and that the average rank of elliptic curves is 1/2 (the remaining 0% of elliptic curves not interfering in the average). Successive works of Brumer, Heath-Brown, and Young, have approached this problem by studying the central values of the L functions of elliptic curves. In this talk, we will take an algebraic approach, in which we study the ranks of elliptic curves via studying their Selmer groups.

Poonen and Stoll developed a beautiful model for the behaviours of p-Selmer groups of elliptic curves, and gave heuristics for all moments of the sizes of these groups.
In this talk, I will describe joint work with Manjul Bhargava and Ashvin Swaminathan, in which we prove that the second moment of the size of the 2-Selmer groups of elliptic curves is bounded above by 15 (which is the constant predicted by Poonen--Stoll).

La conférence ne sera pas diffusée via Zoom.

Date: Le 27 janvier 2023

Lieu: Université McGill, Pavillon Burnside, salle 1205

## Colloque des sciences mathématiques du Québec - Jaroslav Nešetřil, Université Charles, Prague

le vendredi 20 janvier 2023

Ramsey Theory, Sparsity and Limits (Combinatorics and Model Theory)

Several combinatorial problems are treated in the context of model theory.  We survey three such instances which were investigated recently, coming  from  Ramsey theory, sparsity of graphs and limits of sequences of structures. These are diverse areas but share some properties where the connection to  model theory is non-trivial and interesting. It also presents several open  problems of interest to both combinatorics and model theory.

Date: 20 janvier, 2023, 3:30 pm

Lieu: Pavillon André Aisenstadt, Salle 5340, 2920, chemin de la tour, Montréal

## Colloque des sciences mathématiques du Québec - Joshua Zahl, UBC

le vendredi 13 janvier 2023

Sticky Kakeya sets, and the sticky Kakeya conjecture

A Kakeya set is a compact subset of Rn that contains a unit line segment pointing in every direction. The Kakeya conjecture asserts that such sets must have dimension n. This conjecture is closely related to several open problems in harmonic analysis, and it sits at the base of a hierarchy of increasingly difficult questions about the behavior of the Fourier transform in Euclidean space.

There is a special class of Kakeya sets, called sticky Kakeya sets. Sticky Kakeya sets exhibit an approximate self-similarity at many scales, and sets of this type played an important role in Katz, Łaba, and Tao's groundbreaking 1999 work on the Kakeya problem. In this talk, I will discuss a special case of the Kakeya conjecture, which asserts that sticky Kakeya sets must have dimension n. I will discuss the proof of this conjecture in dimension 3. This is joint work with Hong Wang.

Date: 13 janvier 2023, 15h30

Lieu: Pavillon André Aisenstadt, Salle 5340, 2920, chemin de la tour, Montréal

## SUMM 2023

le vendredi 6 janvier 2023

Les Séminaires Universitaires en Mathématiques à Montréal (SUMM) est un organisme formé par de jeunes étudiant.e.s au premier cycle en mathématiques venant de toutes les universités montréalaises. Son objectif principal est de créer un environnement propice aux échanges d'idées et d'intérêts, ainsi que de permettre aux étudiant.e.s de faire de nouvelles rencontres.

La fin de semaine des SUMM s'adresse aux étudiant.e.s de premier cycle, en mathématiques ou en un autre domaine scientifique connexe. Elle se tiendra du 6 au 8 janvier 2023.

La fin de semaine sera composée de deux jours de présentations données par des étudiant.e.s au baccalauréat et par des professeur.e.s invité.e.s sur un éventail de sujets pouvant aller des coins les plus obscurs de la physique mathématique aux applications les plus extraordinaires de l’intelligence artificielle, en passant par la richesse de la philosophie et de l’histoire des mathématiques.

Durant les SUMM, les étudiant.e.s peuvent donner une conférence ou tout simplement venir écouter les présentations de leurs pairs. C'est une occasion de partager la passion des mathématiques dans un environnement stimulant et gratifiant, en discutant avec d’autres étudiant.e.s passioné.e.s toute la fin de semaine.

Au plaisir de vous y voir !

## Colloque des sciences mathématiques du Québec - Yuri Bakhtin, New York University

le vendredi 9 décembre 2022

Ergodic theory of the stochastic Burgers equation

I am interested in stationary distributions for the Burgers equation with random forcing. I will first consider an oversimplified random dynamical system to illustrate the power of a general approach based on the so-called pullback procedure. For the Burgers equation, which is a basic evolutionary stochastic PDE of Hamilton-Jacobi type related to fluid dynamics, growth models, and the KPZ equation, one can realize this approach via studying long-term properties of random Lagrangian action minimizers and directed polymer measures in random environments. The compact space case was studied in 2000's. This talk is based on my work on the noncompact case, joint with Eric Cator, Kostya Khanin, Liying Li.

Date: 9 décembre 2022, 15h30

Lieu: Pavillon André Aisenstadt, Salle 5340, 2920, chemin de la tour, Montréal

## Colloque des sciences mathématiques du Québec - Amnon Besser, Université Ben Gurion

le vendredi 2 décembre 2022

p-adic methods for solving Diophantine equations

The problem of finding rational or integer solutions to polynomial equations is one of the oldest problems in mathematics and is one of the key driving forces in the development of Number Theory.  In the last 15 years new methods were developed that can sometimes effectively solve this problem. These methods attempt to find the solutions inside the larger set of solutions of the same equation in the field of p-adic numbers as the vanishing set of some computable function. When these methods work they give the rational solutions to arbitrarily large p-adic precision, which usually suffices to rigorously recover the full set of solutions.

I will survey the new methods, originating from the work of Kim and from the more recent work of Lawrence and Venkatesh. I will then explain my work with Muller and Srinivasan that uses a p-adic version of the notion of norms on line bundles and associated heights, as used for example in arithmetic dynamics, to give a new approach to some Kim type results.

Date: 2 décembre 2022, 15h30

Lieu: Université Concordia, Library Building, 9th floor, room LB 921-4

## Colloque des sciences mathématiques du Québec - Rebecca Steorts, Université Duke

le vendredi 25 novembre 2022

(Almost) all of Entity Resolution

Whether the goal is to estimate the number of people that live in a congressional district, to estimate the number of individuals that have died in an armed conflict, or to disambiguate individual authors using bibliographic data, all these applications have a common theme — integrating information from multiple sources. Before such questions can be answered, databases must be cleaned and integrated in a systematic and accurate way, commonly known as record linkage, de-duplication, or entity resolution. In this article, we review motivational applications and seminal papers that have led to the growth of this area. Specifically, we review the foundational work that began in the 1940’s and 50’s that have led to modern probabilistic record linkage. We review clustering approaches to entity resolution, semi- and fully supervised methods, and canonicalization, which are being used throughout industry and academia in applications such as human rights, official statistics, medicine, citation networks, among others. Finally, we discuss current research topics of practical importance. This is joint work with Olivier Binette.

Date: 25 novembre, 2022

Pour obtenir le lien Zoom: https://forms.gle/8cqLPYuXwiqdVU1L8

## Colloque des sciences mathématiques du Québec - Robin Neumayer, Carnegie Mellon

le vendredi 18 novembre 2022

Quantitative Stability in the Calculus of Variations

Among all subsets of Euclidean space with a fixed volume, balls have the smallest perimeter. Furthermore, any set with nearly minimal perimeter is geometrically close, in a quantitative sense, to a ball. This latter statement reflects the quantitative stability of balls with respect to the perimeter functional. We will discuss recent advances in quantitative stability and applications in various contexts. The talk includes joint work with several collaborators and will be accessible to a broad research audience.

Date: 18 novembre 2022, 15h30

Lieu: Pavillon André Aisenstadt, Salle 5340, 2920, chemin de la tour, Montréal

## Colloque des sciences mathématiques du Québec - Jan Vonk, Université Leiden

le vendredi 11 novembre 2022

An equation of Diophantus

This is the story of an old equation of Diophantus, which will take us on an excursion along a branch of number theory that stretches over a large part of the subject's history. It will be our motivation for a friendly introduction to some modern developments on torsion and ranks of elliptic curves.

Date: 11 novembre 2022, 15h30

Lieu: Pavillon André Aisenstadt, Salle 5340, 2920, chemin de la tour, Montréal

## Colloque des sciences mathématiques du Québec - Jacob Bernstein, Johns Hopkins University

le vendredi 4 novembre 2022

Complexity of Submanifolds and Colding-Minicozzi Entropy

Given a submanifold of Euclidean space, Colding and Minicozzi defined its entropy to be the supremum of the Gaussian weighted surface areas of all of its translations and dilations. While initially introduced to study singularities of mean curvature flow, it has proven to be an interesting geometric measure of complexity. In this talk I will survey some of the recent progress made on studying the Colding-Minicozzi entropy of hypersurfaces. In particular, I will discuss a series of work by Lu Wang and myself showing closed hypersurfaces with small entropy are simple in various senses.

Date: 4 novembre 2022, 15h30

Lieu: Pavillon André Aisenstadt, Salle 5340, 2920, chemin de la tour, Montréal

## Colloque des sciences mathématiques du Québec - Derek Bingham, Simon Fraser University

le vendredi 28 octobre 2022

Computer Model Emulation using Deep Gaussian Processes

Computer models are often used to explore physical systems. Increasingly, there are cases where the model is fast, the code is not readily accessible to scientists, but a large suite of model evaluations is available. In these cases, an “emulator” is used to stand in for the computer model. This work was motivated by a simulator for the chirp mass of binary black hole mergers where no output is observed for large portions of the input space and more than 106 simulator evaluations are available. This poses two problems: (i) the need to address the discontinuity when observing no chirp mass; and (ii) performing statistical inference with a large number of simulator evaluations. The traditional approach for emulation is to use a stationary Gaussian process (GP) because it provides a foundation for uncertainty quantification for deterministic systems. We explore the impact of the choices when setting up the deep GP on posterior inference, apply the proposed approach to the real application and propose a sequential design approach for identifying new simulations.

Date: 28 octobre 2022, 15h30

Place: HEC, salle Hélène-Desmarais, chemin de la Côte-Sainte-Catherine

## Colloque des sciences mathématiques du Québec - Yevgeny Liokumovich, Université de Toronto

le vendredi 14 octobre 2022

### New isoperimetric inequalities and their applications to systolic geometry and minimal surfaces (Prix André Aisenstadt 2022)

I will describe two new isoperimetric inequalities for k-dimensional submanifolds of R^n or a Banach space. As a consequence of one we obtain a new systolic inequality that was conjectured by Larry Guth. As a consequence of another, we obtain an asymptotic formula for volumes of minimal submanifolds that was conjectured by Mikhail Gromov. The talk is based on joint works with Boris Lishak, Alexander Nabutovsky and Regina Rotman; Fernando Marques and Andre Neves; Larry Guth.

Date: 14 octobre 2022, 15h30

Lieu: Pavillon André Aisenstadt, Salle 1355, 2920, chemin de la tour, Montréal

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## Colloque des sciences mathématiques du Québec - Balint Virag, University of Toronto

le vendredi 7 octobre 2022

Random plane geometry - a gentle introduction

Consider Z2, and assign a random length of 1 or 2 to each edge based on independent fair coin tosses. The resulting random geometry, first passage percloation, is conjectured to have a scaling limit.

Most random plane geometric models (including hidden geometries) should have the same scaling limit.

I will explain the basics of the limiting geometry, the "directed landscape", the central object in the class of models named after Kardar, Parisi and Zhang.

Date: 7 octobre 2022, 15h30

Lieu: Pavillon André Aisenstadt, Salle 6214, 2920, chemin de la tour, Montréal

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## Colloque des sciences mathématiques du Québec - Pengfei Li, University of Waterloo

le vendredi 30 septembre 2022

(Prix SSC) Full likelihood inference for abundance from capture-recapture data: semiparametric efficiency and EM-algorithm

Capture-recapture experiments are widely used to collect data needed to estimate the abundance of a closed population.  To account for heterogeneity in the capture probabilities, Huggins (1989) and Alho (1990) proposed a semiparametric model in which the capture probabilities are modelled parametrically and the distribution of individual characteristics is left unspecified.  A conditional likelihood method was then proposed to obtain point estimates and Wald-type confidence intervals for the abundance.  Empirical studies show that the small-sample distribution of the maximum conditional likelihood estimator is strongly skewed to the right, which may produce Wald-type confidence intervals with lower limits that are less than the number of captured individuals or even negative.

In this talk, we present a full likelihood approach based on Huggins and Alho's model.  We show that the null distribution of the empirical likelihood ratio for the abundance is asymptotically chi-square with one degree of freedom, and the maximum empirical likelihood estimator achieves semiparametric efficiency.  We further propose an expectation–maximization algorithm to numerically calculate the proposed point estimate and empirical likelihood ratio function.  Simulation studies show that the empirical-likelihood-based method is superior to the conditional-likelihood-based method: its confidence interval has much better coverage, and the maximum empirical likelihood estimator has a smaller mean square error.

Date: 30 septembre 2022, 15h30

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## Colloque des sciences mathématiques du Québec - Anush Tserunyan, McGill

le vendredi 23 septembre 2022

A story about pointwise ergodic theorems

Pointwise ergodic theorems provide a bridge between the global behaviour of the dynamical system and the local combinatorial statistics of the system at a point. Such theorem have been proven in different contexts, but typically for actions of semigroups on a probability space. Dating back to Birkhoff (1931), the first known pointwise ergodic theorem states that for a measure-preserving ergodic transformation T on a probability space, the mean of a function (its global average) can be approximated by taking local averages of the function at a point x over finite sets in the forward-orbit of x, namely {x, Tx, ..., T^n x}. Almost a century later, we revisit Birkhoff's theorem and turn it backwards, showing that the averages along trees of possible pasts also approximate the global average. This backward theorem for a single transformation surprisingly has applications to actions of free groups, which we will also discuss. This is joint work with Jenna Zomback.

Date: 23 septembre 2022, 15h30

Lieu: Pavillon André Aisenstadt, Salle 5340, 2920, chemin de la tour, Montréal

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## Colloque des sciences mathématiques du Québec - Chandrashekhar Khare, UCLA

le vendredi 16 septembre 2022

Modularity of Galois representations, from Ramanujan to Serre's conjecture and beyond

Ramanujan made a series of influential conjectures in his 1916 paper "On some arithmetical functions" on what is now called the Ramanujan τ\tauτ function. A congruence Ramanujan observed for τ(n)\tau(n)τ(n) modulo 691 in the paper led to Serre and Swinnerton-Dyer developing a geometric theory of mod ppp modular forms. It was in the context of the theory of mod ppp modular forms that Serre made his modularity conjecture, which was initially formulated in a letter of Serre to Tate in 1973.

I will describe the path from Ramanujan's work in 1916, to the formulation of a first version of Serre's conjecture in 1973, to its resolution in 2009 by Jean-Pierre Wintenberger and myself. I will also try to indicate why this subject is very much alive and, in spite of all the progress, still in its infancy.

Date: 16 septembre 2022, 15h30

Lieu: Pavillon André Aisenstadt, Salle 5340, 2920, chemin de la tour, Montréal

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## Colloque des sciences mathématiques du Québec - Véronique Bazier-Matte, Université Laval

le vendredi 2 septembre 2022

Algèbres amassées et théorie des noeuds

Les algèbres amassées sont des algèbres de polynômes de Laurent dont les générateurs s’obtiennent par un processus récursif appelé mutation. On commence avec une graine, paire formée d’un ensemble de n variables, appelé amas, et d’un graphe orienté à n points. La mutation d’une graine remplace une variable à la fois et modifie le graphe, donnant ainsi une nouvelle graine. L’algèbre amassée est engendrée par toutes les variables obtenues par mutations successives, qu’on appelle variables amassées.

Les algèbres amassées ont été définies il y a 20 ans, et depuis, des liens entre elles et divers champs de recherche ont été découverts. Récemment, avec mon collaborateur, nous avons établi un lien entre la théorie des noeuds et les algèbres amassées. Cet exposé introduira d'abord les algèbres amassées puis présentera la connection entre ces dernières et le polynôme d'Alexander d'un noeud.

Date : 2 septembre, 2022, 3:30 pm

Lieu : Pavillon André Ainsenstadt, room 6214/6254, Université de Montréal

## École découverte de l'ISM: Mutations

le lundi 4 juillet 2022

L'objectif de cette école de découverte de l'ISM est d'explorer différents thèmes de la théorie de la représentation à travers le prisme des mutations.

UQAM, Montréal
4-8 juillet, 2022

## École découverte de l’ISM : La Géométrie et la combinatoire des variétés de Hessenberg

le lundi 6 juin 2022

Des développements relativement nouveaux relient la géométrie des variétés de Hessenberg et des fonctions symétriques et leur combinatoire associée. Ils ont montré que la géométrie (équivariante) et la topologie des variétés de Hessenberg sont intimement liées à un problème profond non résolu dans la théorie des fonctions symétriques (et quasi-symétriques) appelé la conjecture de Stanley-Stembridge.

Le sujet des variétés de Hessenberg se situe à l’intersection fructueuse de la géométrie algébrique, de la combinatoire et de la théorie des représentations géométriques. Une contribution fondamentale dans ce domaine, il y a plus de dix ans, a été la construction par Julianna Tymoczko d’une action du groupe symétrique sur les anneaux de cohomologie des variétés de Hessenberg semi-simples régulières. L’action de Tymoczko a fourni le premier lien entre les variétés de Hessenberg et les fonctions symétriques, car les représentations des groupes symétriques donnent lieu à des fonctions symétriques via la carte caractéristique de Frobenius.

Le second lien a été développé via la notion de fonction symétrique chromatique d’un graphe, introduite par Richard Stanley en 1995 comme une généralisation du polynôme chromatique classique d’un graphe. La conjecture de Stanley-Stembridge concerne la structure des fonctions symétriques chromatiques d’une famille spéciale de graphes ; elle affirme que les fonctions symétriques chromatiques de ces graphes sont des combinaisons linéaires non négatives de fonctions symétriques élémentaires. Cette conjecture est encore ouverte.

Une relation étroite entre les fonctions symétriques chromatiques et les variétés de Hessenberg a été découverte par John Shareshian et Michelle Wachs, qui ont associé un graphe à chaque variété régulière semi-simple de Hessenberg et formulé une conjecture reliant la fonction symétrique chromatique du graphe à la fonction symétrique associée à la variété de Hessenberg via l’action de Tymoczko. Leur conjecture a depuis été prouvée, et il y a lieu d’espérer que d’autres progrès sur la conjecture de Stanley-Stembridge pourront être réalisés en comprenant mieux la relation entre ces deux domaines.

L’école d’été est destinée aux étudiants aux cycles supérieurs spécialisés en géométrie ou en combinatoire, et l’objectif est d’introduire les théories des variétés de Hessenberg et des fonctions symétriques de manière à ce qu’un étudiant puisse avoir accès aux développements passionnants qui lient ces domaines.

## 24e Colloque panquébécois des étudiants de l'ISM

le vendredi 27 mai 2022

Le XXIVe colloque panquébécois de l’Institut des Sciences Mathématiques (ISM) aura lieu en présentiel sur le campus de l'Université Laval du 27 au 29 mai 2022. Organisé chaque année, ce colloque rassemble les étudiant·e·s aux cycles supérieurs en mathématiques du Québec pendant une fin de semaine.

Les participant·e·s sont invité·e·s à donner une présentation d'une durée de 20 minutes sur un sujet à caractère mathématique de leur choix. De plus, quatre conférences plénières seront données par des professeur·e·s et une autre conférence plénière sera donnée par le·a récipiendaire du prix Carl Herz décerné par l'ISM. L'événement sera également parsemé d'activités sociales et de surprises en tout genre afin de permettre aux participant·e·s de tisser des liens.

## Colloque des sciences mathématiques du Québec - Isabelle Gallagher, École normale supérieure

le vendredi 20 mai 2022

Mathematical analysis of dilute gases: derivation of the Boltzmann equation, fluctuations and large deviations

he evolution of a gas can be described by different models depending on the observation scale. A natural question, raised by Hilbert in his sixth problem, is whether these models provide consistent predictions. In particular, for rarefied gases, it is expected that continuum laws of kinetic theory can be obtained directly from molecular dynamics governed by the fundamental principles of mechanics. In the case of hard sphere gases, Lanford showed  in 1975 that the Boltzmann equation emerges as the law of large numbers in the low density limit, at least for very short times. The goal of this talk is to explain the heuristics of his proof and present recent progress in the understanding of this limiting process.

Date: 20 mai 2022, 15h30

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## Colloque des sciences mathématiques du Québec - Slawomir Solecki, Cornell University

le vendredi 6 mai 2022

Generic measure preserving transformations and descriptive set theory

The behavior of a measure preserving transformation, even a generic one, is highly non-uniform. In contrast to this observation, a different picture of a very uniform behavior of the closed group generated by a generic measure preserving transformation has emerged. This picture included substantial evidence that pointed to these groups being all topologically isomorphic to a single group, namely, L0---the non-locally compact, topological group of all Lebesgue measurable functions from [0,1] to the circle. In fact, Glasner and Weiss asked if this was the case.

We will describe the background touched on above, including the connections with Descriptive Set Theory. Further, we will indicate a proof of the following theorem that answers the Glasner--Weiss question in the negative: for a generic measure preserving transformation T, the closed group generated by T is not topologically isomorphic to L0.

Date: 6 mai 2022, 15h30

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## Colloque des sciences mathématiques du Québec - Forrest Crawford, Yale

le vendredi 29 avril 2022

COVID-19 transmission models in the real world: models, data, and policy

Simple mathematical models of COVID-19 transmission gained prominence in the early days of the pandemic. These models provided researchers and policymakers with qualitative insight into the dynamics of transmission and quantitative predictions of disease incidence.  More sophisticated models incorporated new information about the natural history of COVID-19 disease and the interaction of infected individuals with the healthcare system, to predict diagnosed cases, hospitalization, ventilator usage, and death. Models also provided intuition for discussions about outbreaks, vaccination, and the effects of non-pharmaceutical interventions like social distancing guidelines and stay-at-home orders. But as the pandemic progressed, complex real-world interventions took effect, people everywhere changed their behavior, and the usefulness of simple mathematical models of COVID-19 transmission diminished.  This challenge forced researchers to think more broadly about empirical data sources that could help predictive models regain their utility for guiding public policy. In this presentation, I will describe my view of the successes and failures of population-level transmission models in the context of the COVID-19 pandemic.  I will outline the evolution of a project to predict COVID-19 incidence in the state of Connecticut, from development of a transmission model to engagement with public health policymakers and initiation of a new data collection effort. I argue that a new data source – passive measurement of close interpersonal contact via mobile device location data – is a promising way to overcome many of the shortcomings of traditional transmission models.  I conclude with a summary of the impact this work has had on the COVID-19 response in Connecticut and beyond.

Date: 29 avril 2022, 15h30

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## Colloque des sciences mathématiques du Québec - Joel Kamnitzer, University of Toronto

le vendredi 22 avril 2022

Cactus groups and monodromy

The cactus group is a cousin of the braid group and shares many of its beautiful properties.  It is the fundamental group of the moduli space of points on RP1.  It also acts on many collections of combinatorial objects.  I will explain how we use the cactus group to understand monodromy of eigenvectors for Gaudin algebras.

Cette conférence aura lieu en mode hybride (en salle et par Zoom)

Date: 22 avril 2022, 15h30

Lieu: Pavillon André Ainsenstadt, salle 6214/6254, Université de Montréal

Pour le lien Zoom: S'inscrire

## Colloque des sciences mathématiques du Québec - Pierre Cardaliaguet, Université Paris-Dauphine

le vendredi 15 avril 2022

Some aspects of mean games

Mean Field Game is the study of the dynamical behavior of a large number of agents in interaction. For instance, it can model be the dynamics of a crowd, or the production of a renewable resource by a large amount of producers. The analysis of these models, first introduced in the economic literature under the terminology of “heterogenous agent models, has known a spectacular development with the pioneering woks of Lasry and Lions and of Caines, Huang and Malhamé. The aim of the talk will be to illustrate the theory through a few models and present some of the main results and open questions.

Date: 15 avril 2022, 15h00

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## Colloque des sciences mathématiques du Québec - Robert Raussendorf, UBC

le vendredi 8 avril 2022

Hidden Variable Model for Universal Quantum Computation with Magic States on Qubits

We show that every quantum computation can be described by a probabilistic update of a probability distribution on a finite phase space. Negativity in a quasiprobability function is not required in states or operations, which is a very unusual feature. Nonetheless, our result is consistent with Gleason’s Theorem and the Pusey-Barrett- Rudolph theorem.

The reason I have chosen this subject for my talk is two-fold: (i) It gives the audience a glimpse of the quest to understand the quantum mechanical cause for speed-up in quantum computation, which is one of the central questions on the theory side of the field, and (ii) Maybe there can be feedback from the audience. The structures underlying the above probabilistic model are the so-called Lambda-polytopes, which are highly symmetric objects.  At present we only know very few general facts about them. Help with analysing them would be appreciated!

Joint work with Michael Zurel and Cihan Okay,

Journal reference: Phys. Rev. Lett. 125, 260404 (2020)

Date: 8 avril 2022, 15h30 pm

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## Colloque des sciences mathématiques du Québec - Sibylle Schroll, University of Cologne

le vendredi 1 avril 2022

Gentle algebras, surfaces and a glimpse of homological mirror symmetry

Derived categories are in general not easy to parse. However, in certain cases, combinatorial models give a good picture of these categories. One such case are the bounded derived categories of gentle algebras which can be represented in terms of curves and crossings of curves on surfaces. In this talk, we will give the construction of these surface models and briefly explain how they are connected to the homological mirror symmetry programme. We will show how a combination of surface combinatorics and representation theory can give new insights into the associated categories.

Date: 1er avril 2022, 14h00

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## Colloque des sciences mathématiques du Québec - Heather Macbeth, Fordham University

le vendredi 25 mars 2022

Making mathematics computer-checkable

In the last thirty years, computer proof verification became a mature technology, with successes including the checking of the Four-Colour Theorem, the Odd Order Theorem, and Hales' proof of the Kepler Conjecture.  Recent advances such as the "Liquid Tensor Experiment" verifying a recent theorem of Scholze have provided further momentum, as likewise have promising experiments integrating this technology with machine learning.

I will briefly describe some of these developments.  I will then try to describe, more generally, what it *feels* like to carry out research-level computer verifications of mathematics proofs: the level of expression one has access to, the ways one finds oneself interrogating and reorganizing a paper proof, the kinds of arguments which are more tedious (or less tedious!) than on paper.

Date: 25 mars 2022, 15h30

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## Colloque des sciences mathématiques du Québec - Bernard Derrida, École normale supérieure

le vendredi 18 mars 2022

The importance of large deviations in non-equilibrium systems

Statistical Physics allowed to unify, at the end of the 19th century, Newton's mechanics and thermodynamics. It gave a way to predict the amplitude of fluctuations around the physical laws which were known at that time. Einstein, in his very first works, showed that the measurement of these fluctuations allowed to estimate the size of atoms. His reasoning, which was at the origin of the linear response theory, applied to the black body gave one of the first evidences of the duality wave-particle in Quantum Mechanics. Statistical Physics gives also a framework to predict large deviations for systems at equilibrium. In the last two decades, major efforts were devoted to extend our understanding of the statistical laws of fluctuations and large deviations to non-equilibrium systems. This talk will try to present some of the recent progresses.

Date: 18 mars 2022, 15h30

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## Activités de la journée internationale des mathématiques au Centre de recherches mathématiques (CRM)

le lundi 14 mars 2022

Bonne journée internationale des mathématiques 2022 sous le thème « Les mathématiques unissent »! Vous pouvez assister à la couverture en ligne de 48 heures (le 14 mars partout sur la planète) et visiter les meilleures photos du défi de photos

Voici deux évènements organisés par le CRM.

1. Conférence grand public virtuelle par Francis Su (Harvey-Mudd College):

Mathematics for Human Flourishing

Détails et inscription

En particulier, Francis Su a développé une amitié avec un prisonnier, Christopher, dans une prison à sécurité maximale aux États-Unis et ce prisonnier s’éveille aux mathématiques.

2. Cette conférence est précédée par le lancement d’un recueil de brèves (tool kit) de l’UNESCO dont le CRM a été maitre d'oeuvre « Mathematics for Action: Supporting Science Based Decision » à 18:30 HAE. On peut consulter le recueil à: recueil

Le lancement canadien se tiendra le lundi 14 mars 2022, 18:30-19:15 HAE en mode hybride. Voir programme et inscription

## Colloque des sciences mathématiques du Québec - Evgeny Gorskiy, UC Davis

le vendredi 11 mars 2022

Algebra, geometry and combinatorics of link homology

Khovanov and Rozansky defined in 2005 a triply graded link homology theory which generalizes HOMFLY-PT polynomial. In this talk, I will outline some known results and structures in Khovanov-Rozansky homology, describe its connection to q,t-Catalan combinatorics and present several geometric models for some classes of links.

Date: 11 mars 2022, 15h30

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## Colloque des sciences mathématiques du Québec - Stanislav Volgushev - University of Toronto

le vendredi 18 février 2022

Structure learning for Extremal graphical models

Extremal graphical models are sparse statistical models for multivariate extreme events.  The underlying graph encodes conditional independencies and enables a visual interpretation of the complex extremal dependence structure.  For the important case of tree models, we provide a data-driven methodology for learning the graphical structure.  We show that sample versions of the extremal correlation and a new summary statistic, which we call the extremal variogram, can be used as weights for a minimum spanning tree to consistently recover the true underlying tree.  Remarkably, this implies that extremal tree models can be learned in a completely non-parametric fashion by using simple summary statistics and without the need to assume discrete distributions, existence of densities, or parametric models for marginal or bivariate distributions.  Extensions to more general graphs are also discussed.

Date: 18 février 2022, 15h30

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## Colloque des sciences mathématiques du Québec - Ryan Hynd, University of Pennsylvania

le vendredi 11 février 2022

Sticky particle dynamics

I will discuss the time evolution of a collection of particles that interact primarily through perfectly inelastic collisions.  I will explain why this problem is tractable if the particles are constrained to lie on a line versus if they are allowed to move freely in space.  In particular, I'll also describe an equation at the heart of this difficulty which some researchers believe has been solved and others do not.  This topic has motivations in astronomy and connections with optimal mass transportation which I will touch upon if time permits.

Date: 11 février 2022, 15h30

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## Colloque des sciences mathématiques du Québec - Sarah Zerbes, ETH Zürich

le vendredi 4 février 2022

Euler Systems and the Birch--Swinnerton-Dyer conjecture

L-functions are one of the central objects of study in number theory. There are many beautiful theorems and many more open conjectures linking their values to arithmetic problems. The most famous example is the conjecture of Birch and Swinnerton-Dyer, which is one of the Clay Millenium Prize Problems. I will discuss this conjecture and some related open problems, and I will describe some recent progress on these conjectures, using tools called "Euler systems".

Date: 4 février 2022, 12h00

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## Colloque des sciences mathématiques du Québec - Gilles Stupfler, ENSAI

le vendredi 28 janvier 2022

Risk assessment, heavy tails, and asymmetric least squares techniques

Statistical risk assessment, in particular in finance and insurance, requires estimating simple indicators to summarize the risk incurred in a given situation.  Of most interest is to infer extreme levels of risk so as to be able to manage high-impact rare events such as extreme climate episodes or stock market crashes.  A standard procedure in this context, whether in the academic, industrial or regulatory circles, is to estimate a well-chosen single quantile (or Value-at-Risk).  One drawback of quantiles is that they only take into account the frequency of an extreme event, and in particular do not give an idea of what the typical magnitude of such an event would be.  Another issue is that they do not induce a coherent risk measure, which is a serious concern in actuarial and financial applications. In this talk, after giving a leisurely tour of extreme quantile estimation, I will explain how, starting from the formulation of a quantile as the solution of an optimization problem, one may come up with two alternative families of risk measures, called expectiles and extremiles, in order to address these two drawbacks.  I will give a broad overview of their properties, as well as of their estimation at extreme levels in heavy-tailed models, and explain why they constitute sensible alternatives for risk assessment using real data applications.  This is based on joint work with Abdelaati Daouia, Irène Gijbels, Stéphane Girard, Simone Padoan and Antoine Usseglio-Carleve.

Date: 28 janvier 2022, 15h30

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## Colloque des sciences mathématiques du Québec - Allen Knutson, Cornell University

le vendredi 21 janvier 2022

The commuting variety and generic pipe dreams

Nobody knows whether the scheme "pairs of commuting nxn matrices" is reduced. I'll show how this scheme relates to matrix Schubert varieties, and give a formula for its equivariant cohomology class (and that of many other varieties) using "generic pipe dreams" that I'll introduce. These interpolate between ordinary and bumpless pipe dreams. With those, I'll rederive both formulae (ordinary and bumpless) for double Schubert polynomials. This work is joint with Paul Zinn-Justin.

Date: 21 janvier 2022, 14h00

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## Colloque des sciences mathématiques du Québec - Eva Miranda, Polytechnic University of Catalonia

le vendredi 14 janvier 2022

Looking at hydrodynamics through a contact mirror: From Euler to Turing and beyond

What physical systems can be non-computational? (Roger Penrose, 1989).  Is hydrodynamics capable of calculations? (Cris Moore, 1991). Can a mechanical system (including the trajectory of a fluid) simulate a universal Turing machine? (Terence Tao, 2017).

The movement of an incompressible fluid without viscosity is governed by Euler equations. Its viscid analogue is given by the Navier-Stokes equations whose regularity is one of the open problems in the list of problems for the Millenium bythe Clay Foundation. The trajectories of a fluid are complex. Can we measure its levels of complexity (computational, logical and dynamical)?

In this talk, we will address these questions. In particular, we will show how to construct a 3-dimensional Euler flow which is Turing complete. Undecidability of fluid paths is then a consequence of the classical undecidability of the halting problem proved by Alan Turing back in 1936. This is another manifestation of complexity in hydrodynamics which is very different from the theory of chaos.

Our solution of Euler equations corresponds to a stationary solution or Beltrami field. To address this problem, we will use a mirror [5] reflecting Beltrami fields as Reeb vector fields of a contact structure. Thus, our solutions import techniques from geometry to solve a problem in fluid dynamics. But how general are Euler flows? Can we represent any dynamics as an Euler flow? We will address this universality problem using the Beltrami/Reeb mirror again and Gromov's h-principle. We will also consider the non-stationary case. These universality features illustrate the complexity of Euler flows. However, this construction is not "physical" in the sense that the associated metric is not the euclidean metric. We will  announce an euclidean construction and its implications to complexity and undecidability.

These constructions  [1,2,3,4] are motivated by Tao's approach to the problem of Navier-Stokes  [7,8,9] which we will also explain.

[1] R. Cardona, E. Miranda, D. Peralta-Salas, F. Presas. Universality of Euler flows and flexibility of Reeb embeddings. https://arxiv.org/abs/1911.01963.

[2] R. Cardona, E. Miranda, D. Peralta-Salas, F. Presas. Constructing Turing complete Euler flows in dimension 3. Proc. Natl. Acad. Sci. 118 (2021) e2026818118.

[3] R. Cardona, E. Miranda, D. Peralta-Salas. Turing universality of the incompressible Euler equations and a conjecture of Moore. Int. Math. Res. Notices, , 2021;, rnab233, https://doi.org/10.109/imrn/rnab233

[4] R. Cardona, E. Miranda, D. Peralta-Salas. Computability and Beltrami fields in Euclidean space. https://arxiv.org/abs/2111.03559

[5] J. Etnyre, R. Ghrist. Contact topology and hydrodynamics I. Beltrami fields and the Seifert conjecture. Nonlinearity 13 (2000) 441–458.

[6] C. Moore. Generalized shifts: unpredictability and undecidability in dynamical systems. Nonlinearity 4 (1991) 199–230.

[7] T. Tao. On the universality of potential well dynamics. Dyn. PDE 14 (2017) 219–238.

[8] T. Tao. On the universality of the incompressible Euler equation on compact manifolds. Discrete Cont. Dyn. Sys. A 38 (2018) 1553–1565.

[9] T. Tao. Searching for singularities in the Navier-Stokes equations. Nature Rev. Phys. 1 (2019) 418–419.

Date: 14 janvier 2022, 11h00

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## Colloque des sciences mathématiques du Québec - Yen-Tsung Huang, Institute of Statistical Science, Academia Sinica

le vendredi 17 décembre 2021

Nonparametric causal mediation in a time-to-event setting

A causal mediation model with multiple time-to-event mediators is exemplified by the natural course of human disease marked by sequential milestones with a time-to-event nature.  For example, from hepatitis B infection to death, patients may experience intermediate events such as liver cirrhosis and liver cancer.  The sequential events of hepatitis, cirrhosis, cancer, and death are susceptible to right censoring; moreover, the latter events may preclude the former events.  Casting the natural course of human diseases in the framework of causal mediation modeling, we establish a model with intermediate and terminal events as the mediators and outcomes, respectively.  We define the interventional analog of path-specific effects (iPSEs) as the effect of an exposure on a terminal event mediated (or not mediated) by any combination of intermediate events without parametric models.  The expression of a counting process-based counterfactual hazard is derived under the sequential ignorability assumption.  We employ composite nonparametric likelihood estimation to obtain maximum likelihood estimators for the counterfactual hazard and iPSEs.  Our proposed estimators achieve asymptotic unbiasedness, uniform consistency, and weak convergence.  Applying the proposed method, we show that hepatitis B induced mortality is mostly mediated through liver cancer and/or cirrhosis whereas hepatitis C induced mortality may be through extrahepatic diseases.

Date: 17 décembre 2021, 10h00

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## Colloque des sciences mathématiques du Québec - Samit Dasgupta, Duke University

le vendredi 10 décembre 2021

Stark's Conjectures and Hilbert's 12th Problem

In this talk we will discuss two central problems in algebraic number theory and their interconnections: explicit class field theory and the special values of L-functions.  The goal of explicit class field theory is to describe the abelian extensions of a ground number field via analytic means intrinsic to the ground field; this question lies at the core of Hilbert's 12th Problem.  Meanwhile, there is an abundance of conjectures on the values of L-functions at certain special points.  Of these, Stark's Conjecture has relevance toward explicit class field theory.  I will describe two recent joint results with Mahesh Kakde on these topics.  The first is a proof of the Brumer-Stark conjecture away from p=2. This conjecture states the existence of certain canonical elements in abelian extensions of totally real fields.  The second is a proof of an exact formula for Brumer-Stark units that has been developed over the last 15 years.  We show that these units together with other easily written explicit elements generate the maximal abelian extension of a totally real field, thereby giving a p-adic solution to the question of explicit class field theory for these fields.

Date: 10 décembre 2021, 14h00

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## Colloque des sciences mathématiques du Québec - Valentino Tosatti, McGill

le vendredi 3 décembre 2021

K3 surfaces: geometry and dynamics

K3 surfaces are a class of compact complex manifolds that enjoys many special properties and play an important role in several areas of mathematics. In this colloquium I will discuss a new interplay between complex geometry and analysis on K3 surfaces equipped with their Calabi-Yau metrics, and dynamics of holomorphic diffeomorphisms of these surfaces, that Simion Filip and I have been investigating recently.

Date: 3 décembre 2021, 15h30

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## Colloque des sciences mathématiques du Québec - Simon Bonner, Western

le vendredi 26 novembre 2021

Adventures with Partial Identifications in Studies of Marked Individuals

Monitoring marked individuals is a common strategy in studies of wild animals (referred to as mark-recapture or capture-recapture experiments) and hard to track human populations (referred to as multi-list methods or multiple-systems estimation).  A standard assumption of these techniques is that individuals can be identified uniquely and without error, but this can be violated in many ways.  In some cases, it may not be possible to identify individuals uniquely because of the study design or the choice of marks.  Other times, errors may occur so that individuals are incorrectly identified.  I will discuss work with my collaborators over the past 10 years developing methods to account for problems that arise when are only individuals are only partially identified.  I will present theoretical aspects of this research, including an introduction to the latent multinomial model and algebraic statistics, and also describe applications to studies of species ranging from the golden mantella (an endangered frog endemic to Madagascar measuring only 20 mm) to the whale shark (the largest known species of sh measuring up to 19 m).

Date: 26 novembre 2021, 15h30

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## Colloque des sciences mathématiques du Québec - Tristan Collins, MIT

le vendredi 19 novembre 2021

Exploring string vacua through geometric transitions

A fundamental problem in string theory is the multitude of distinct geometries which give rise to consistent solutions of the vacuum equations of motion. One possible resolution of this "vacuum degeneracy" problem is the "fantasy" that the moduli space of string vacua is connected through the process of "geometric transitions". I will discuss some geometric problems associated to this fantasy and their applications.

Date: 19 novembre 2021, 15h30

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## Colloque des sciences mathématiques du Québec - Gabor Lugosi, UPF and BSE

le vendredi 12 novembre 2021

Estimating the mean of a random vector

One of the most basic problems in statistics is the estimation of the mean of a random vector, based on independent observations.  This problem has received renewed attention in the last few years, both from statistical and computational points of view.  In this talk, we review some recent results on the statistical performance of mean estimators that allow heavy tails and adversarial contamination in the data.  In particular, we are interested in estimators that have a near-optimal error in all directions in which the variance of the one dimensional marginal of the random vector is not too small.  The material of this talk is based on a series of joint papers with Shahar Mendelson.

Date: 12 novembre 2021, 15h30

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Lieu: HYBRIDE

Cette conférence aura lieu en mode hybride avec un nombre limité de 21 participants sur place. Pour réserver votre place sur la base de premier arrivé, premier servi, veuillez utiliser le lien ci-dessous. /

Sur place : CRM - Pavillon André Aisenstadt: Salle/ Room 5340

Le passeport vaccinal et une pièce d’identité seront exigés

## Colloque des sciences mathématiques du Québec - Louise Poirier, Université de Montréal

le vendredi 5 novembre 2021

Les mathématiques ont une histoire et une géographie

La présentation se divise en deux temps.  Dans un premier temps, les principaux résultats de notre étude sur le « portrait mathématique » des étudiants du Québec effectué dans le cadre du projet En avant math! (projet conjoint CRM-CIRANO soutenu par le Ministère des finances) seront présentés.  Ce rapport se fonde d’une part sur les résultats des tests internationaux TIMS et PISA pour les élèves québécois du primaire et du secondaire et d’autre part, sur la situation des mathématiques dans les universités québécoises dégagée des données du Bureau de coopération interuniversitaire (BCI) ( évolution des inscriptions étudiantes et portrait des étudiants tant en genre qu’en statut). Les données du BCI montrent que l'étudiant typique inscrit en maths dans les universités québécoises est citoyen canadien, blanc et masculin. Et le nombre total d'inscrits baisse à chaque année (sauf, peut-être au doctorat). Où sont les filles? Où sont les étudiants issus de l'immigration récente? Et pourtant aux tests PISA et TIMMS les élèves issus de l'immigration performent mieux au Canada que les élèves canadiens (c'est l'inverse pour la moyenne des pays de l'OCDE).

Puis, dans un deuxième temps, à la lumière des résultats du portrait des étudiants, nous discuterons des enjeux sociaux pour des mathématiques plus inclusives. Une recherche collaborative avec les communautés inuit du Nunavik viendra illustrer nos propos.

Date: 5 novembre 2021, 15h30

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## Colloque des sciences mathématiques du Québec - Tiffany Timbers, University of British Columbia

le vendredi 29 octobre 2021

Opinionated practices for teaching reproducibility: motivation, guided instruction and pratice

In the data science courses at the University of British Columbia, we define data science as the study, development and practice of reproducible and auditable processes to obtain insight from data. While reproducibility is core to our definition, most data science learners enter the field with other aspects of data science in mind, for example predictive modelling, which is often one of the most interesting topic to novices. This fact, along with the highly technical nature of the industry standard reproducibility tools currently employed in data science, present out-ofthe gate challenges in teaching reproducibility in the data science classroom. Put simply, students are not as intrinsically motivated to learn this topic, and it is not an easy one for them to learn. What can a data science educator do? Over several iterations of teaching courses focused on reproducible data science tools and workflows, we have found that providing extra motivation, guided instruction and lots of practice are key to effectively teaching this challenging, yet important subject. Here we present examples of how we deeply motivate, effectively guide and provide ample practice opportunities to data science students to effectively engage them in learning about this topic.

Date: 29 octobre 2021, 15h30

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## Colloque des sciences mathématiques du Québec - Giulio Tiozzo, University of Toronto

le vendredi 15 octobre 2021

Entropy along the Mandelbrot set

The notion of topological entropy, arising from information theory, is a fundamental tool to understand the complexity of a dynamical system.  When the dynamical system varies in a family, the natural question arises of how the entropy changes with the parameter.

In the last decade, W.  Thurston introduced these ideas in the context of complex dynamics by defining the "core entropy" of a quadratic polynomials as the entropy of a certain forward-invariant set of the Julia set (the Hubbard tree).

As we shall see, the core entropy is a purely topological/combinatorial quantity which nonetheless captures the richness of the fractal structure of the Mandelbrot set.  In particular, we will relate the variation of such a function to the geometry of the Mandelbrot set.  We will also prove that the core entropy on the space of polynomials of a given degree varies continuously, answering a question of Thurston.

Finally, we will provide a new interpretation of core entropy in terms of measured laminations and discuss its finer regularity properties such as its Holder exponent.

Date: 15 octobre 2021, 15h30

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## Colloque des sciences mathématiques du Québec - Jennifer Hill, NYU Steinhardt

le vendredi 24 septembre 2021

Deep down, everyone wants to be causal

Most researchers in the social, behavioral, and health sciences are taught to be extremely cautious in making causal claims.  However, causal inference is a necessary goal in research for addressing many of the most pressing questions around policy and practice.  In the past decade, causal methodologists have increasingly been using and touting the benefits of more complicated machine learning algorithms to estimate causal effects.  These methods can take some of the guesswork out of analyses, decrease the opportunity for “p-hacking,” and may be better suited for more fine-tuned tasks such as identifying varying treatment effects and generalizing results from one population to another.  However, should these more advanced methods change our fundamental views about how difficult it is to infer causality? In this talk I will discuss some potential advantages and disadvantages of using machine learning for causal inference and emphasize ways that we can all be more transparent in our inferences and honest about their limitations.

Date: 24 septembre 2021, 15h00

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## École d'été de combinatoire algébrique

le lundi 21 juin 2021

21 au 25 juin 2021
Intégralement en ligne

L'objectif de cette école est de faire progresser les connaissances et l'enthousiasme des participants envers la combinatoire algébrique. Grâce à des présentations de haut niveau, les étudiants apprendront de multiples aspects combinatoires liés à la théorie des représentations. Chaque jour, un chercheur postdoctoral présentera un sujet de recherche lié aux cours d'introduction.

Le calcul de Schubert, les fonctions symétriques, les algèbres amassées, les treillis de Tamari, la combinatoire des frises et la catégorie amassée sont non seulement des façons d'étudier la théorie de la représentation, mais ces sujet sont de plus tous liés entre eux. Les algèbres amassées, introduites par Sergey Fomin et Andrei Zelevinsky peuvent, d'une part, être étudiée au travers des frises d'un point de vue combinatoire et au travers de la catégorie amassée d'un point de vue algébrique. D'autre part, elles ont une correspondance avec les cellules double de Bruhat. Dans le cas de la variété de drapeaux et des grassmaniennes, la décomposition en cellules de Bruhat donne lieu à la décomposition en cellules de Schubert. Celles-ci peuvent être obtenues via le calcul de Schubert. Les polynômes de Schubbert sont une généralisation des fonctions de Schur: des fonctions symétriques. Via les complexes de sous-mots, l'étude des variétés de Schubert est liée à l'étude des treillis de Tamari. Ces derniers correspondent au graphe d'échange de certaines algèbres amassées.

Enfin, notre but est de promouvoir la visibilité et l’accomplissement des femmes en mathématiques. Bien que l’école soit ouverte à tous les participantes et participants, seules des femmes donneront des exposés. Il nous semble important de donner l’occasion aux étudiantes et aux étudiants de côtoyer des mathématiciennes accomplies, car elles sont sous-représentées parmi les professeurs de mathématiques dans les universités.

## Réduire l'écart: lutter contre les inégalités mathématiques dans l'éducation autochtone

le lundi 21 juin 2021

Réduire l'écart: lutter contre les inégalités mathématiques dans l'éducation autochtone

Lundi 21 juin 2021, Journée nationale des peuples autochtones
16 h - 17 h, heure de l'Est

CONFÉRENCIÈRE: Melania Alvarez (Pacific Institute for the Mathematical Sciences)

Cette conférence sera prononcée en anglais.

RÉSUMÉ :
Afin de réduire positivement l'écart d'éducation entre les communautés autochtones et le reste de la population, il faut une intervention continue et à long terme pour le changement. En abandonnant la philosophie d'attentes réduites, les mathématicien.ne.s et les éducateur.trice.s de l'Ouest canadien ont lancé une variété de programmes intéressants et stimulants. Notre première étape a été d'établir des partenariats avec des aînés et des écoles dirigées par des communautés autochtones, ainsi qu'avec des écoles publiques urbaines à forte concentration d'élèves à risque et d'étudiants autochtones. Grâce à leur contribution et à leur soutien, divers programmes de sensibilisation ont été mis en œuvre, qui seront décrits dans cette conférence.

Visitez aussi la page du Comité Équité, diversité et inclusion au CRM

## École d’été virtuelle de McGill en analyse des données en santé

le lundi 31 mai 2021

31 mai au 3 juin 2021

L’école sera composée de quatre journées de cours ciblant surtout des étudiantes et étudiants avancés de premier cycle et à la maîtrise qui aimeraient poursuivre des études universitaires et apprendre davantage sur les sujets actuels de la statistique qu’ils n’auraient pas vus lors de leur formation.

## 23e Colloque panquébécois des étudiants de l'ISM

le samedi 22 mai 2021

Le XXIIIe colloque panquébécois de l’Institut des Sciences Mathématiques (ISM) aura lieu en ligne du 22 au 23 mai 2021. Organisé chaque année, ce colloque réunit les étudiant·e·s aux cycles supérieurs en mathématiques du Québec pour une fin de semaine.

Les participant·e·s sont invité·e·s à donner des présentations de 20 minutes sur le sujet en mathématiques de leur choix. De plus, quatre conférences plénières données par des professeur·e·s auront lieu au cours de la fin de semaine. La conférence comprendra également une conférence du récipiendaire du prix Carl Herz décerné par l’ISM.

## Colloque des sciences mathématiques du Québec - Eva Bayer-Fluckiger, École Polytechnique Fédérale de Lausanne

le vendredi 30 avril 2021

Knots, polynomials and signatures
After a historical introduction to knot theory, the talk will be centered around two knot invariants, the Alexander polynomial and the signature. The aim is to introduce a finite abelian group that controls their relationship, and to illustrate this by several examples. Using Seifert matrices, the geometric questions are translated into arithmetic ones.

Date: 30 avril 2021, 15h00

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## Colloque des sciences mathématiques du Québec - Adrian Lewis, Cornell University

le vendredi 23 avril 2021

Date: 23 avril 2021, 15h00

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## Colloque des sciences mathématiques du Québec - Kilian Raschel, Université de Tours

le vendredi 16 avril 2021

Reflected Brownian motion in a wedge: from probability theory to Galois theory of difference equations
We consider a reflected Brownian motion in a two-dimensional wedge. Under standard assumptions on the parameters of the model (opening of the wedge, angles of the reflections on the axes, drift), we study the algebraic and differential nature of the Laplace transform of its stationary distribution. We derive necessary and sufficient conditions for this Laplace transform to be rational, algebraic, differentially finite or more generally differentially algebraic. These conditions are explicit linear dependencies among the angles involved in the definition of the model.

To prove these results, we start from a functional equation that the Laplace transform satisfies, to which we apply tools from diverse horizons. To establish differential algebraicity, a key ingredient is Tutte's invariant approach, which originates in enumerative combinatorics. To establish differential transcendence, we turn the functional equation into a difference equation and apply Galoisian results on the nature of the solutions to such equations.

This is a joint work with M. Bousquet-Mélou, A. Elvey Price, S. Franceschi and C. Hardouin (https://arxiv.org/abs/2101.01562).

Date: 16 avril 2021, 15h00

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## Colloque des sciences mathématiques du Québec - Jane Wang, Cornell University

le vendredi 9 avril 2021

Insect Flight from Newton's law to Neurons

Why do animals move the way they do? Bacteria, insects, birds, and fish share with us the necessity to move so as to live. Although each organism follows its own evolutionary course, it also obeys a set of common laws. At the very least, the movement of animals, like that of planets, is governed by Newton’s law: All things fall. On Earth, most things fall in air or water, and their motions are thus subject to the laws of hydrodynamics. Through trial and error, animals have found ways to interact with fluid so they can float, drift, swim, sail, glide, soar, and fly. This elementary struggle to escape the fate of falling shapes the development of motors, sensors, and mind. Perhaps we can deduce parts of their neural computations by understanding what animals must do so as not to fall.

We have been seeking mechanistic explanations of the complex movement of insect flight. Starting from the Navier-Stokes equations governing the unsteady aerodynamics of flapping flight, we worked to build a theoretical framework for computing flight and for studying the control of flight.  I will discuss our recent computational and experimental studies of the balancing act of dragonflies and fruit flies:  how a dragonfly recovers from falling upside-down and how a fly balances in air. In each case,  the physics of flight informs us about the neural feedback circuitries underlying their fast reflexes.

Date: 9 avril 2021, 15h00

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## Colloque des sciences mathématiques du Québec - François Dubois, Le CNAM

le vendredi 19 mars 2021

### ABCD asymptotic expansion for lattice Boltzmann schemes and application to compressible Navier Stokes equations

Après avoir rappelé divers éléments sur l'histoire de la construction des schémas de Boltzmann sur réseau, nous présentons notre approche "ABCD", fondée sur le fait que le schéma numérique est exact pour l'équation d'advection avec les vitesses du réseau.  Cette analyse asymptotique permet d'écrire aux différents ordres les équations aux dérivées partielles conservatives équivalentes au schéma.  Un réglage de paramètres permet dans les bons cas une approximation précise des équations des fluides compressibles.

Date: 19 mars 2021, 15h00

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## Journée internationale des mathématiques au CRM: Les mathématiques pour un monde meilleur

le vendredi 12 mars 2021

Avec sa thématique 2021 «Les mathématiques pour un monde meilleur», la Journée internationale des mathématiques de l’UNESCO vient souligner l'impact des sciences mathématiques pour faire face aux défis dans des domaines tels que l’intelligence artificielle, les modèles de prédiction, les changements climatiques, les dépistages, le partage équitable ainsi que pour améliorer la qualité de vie de bien des façons inattendues grâce aux connaissances combinées des scientifiques qui y travaillent. Le CRM a réuni des conférenciers-organisateurs hors pair qui explorent chacun à leur manière le thème de cette année.

http://www.crm.umontreal.ca/2021/JIM21/index.php

## Colloque des sciences mathématiques du Québec - Jay Breidt, Colorado State University

le vendredi 12 mars 2021

### Nonparametric Tests for Informative Selection in Complex Surveys

Informative selection, in which the distribution of response variables given that they are sampled is different from their distribution in the population, is pervasive in complex surveys.  Failing to take such informativeness into account can produce severe inferential errors, including biased and inconsistent estimation of population parameters.  While several parametric procedures exist to test for informative selection, these methods are limited in scope and their parametric assumptions are difficult to assess.  We consider two classes of nonparametric tests of informative selection.  The first class is motivated by classic nonparametric two-sample tests.  We compare weighted and unweighted empirical distribution functions and obtain tests for informative selection that are analogous to Kolmogorov-Smirnov and Cramer-von Mises.  For the second class of tests, we adapt a kernel-based learning method that compares distributions based on their maximum mean discrepancy.  The asymptotic distributions of the test statistics are established under the null hypothesis of noninformative selection.  Simulation results show that our tests have power competitive with existing parametric tests in a correctly specified parametric setting, and better than those tests under model misspecification.  A recreational angling application illustrates the methodology.

This is joint work with Teng Liu, Colorado State University.

Date: 12 mars 2021, 15h30

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## Les femmes en mathématiques à l'époque de la COVID

le lundi 8 mars 2021

Cet événement, qui se tiendra à l'occasion de la Journée internationale des femmes, vise à sensibiliser le public aux défis professionnels rencontrés par les femmes mathématiciennes pendant la pandémie.

Ce sera également l'occasion de réunir la communauté CRM pour honorer les réalisations des femmes en mathématiques.

Quatre mathématiciennes remarquables mettront en lumière leurs travaux récents, ainsi que les circonstances inhabituelles auxquelles elles ont dû faire face. Ces discussions seront suivies d'une table ronde informelle qui se tiendra en soirée, avec un accent sur le point de vue des jeunes mathématiciennes.

## Mathflix: Secrets of the Surface: The Mathematical Vision of Maryam Mirzakhani (sous-titré en français)

le vendredi 5 mars 2021

Filmé au Canada, en Iran et aux États-Unis, le très beau documentaire Secrets of the Surface : The Mathematical Vision of Maryam Mirzakhani examine la vie et l'œuvre mathématique de Maryam Mirzakhani, une immigrante iranienne aux États-Unis qui est devenue une superstar dans son domaine. En 2014, elle a été à la fois la première femme et la première Iranienne à recevoir la plus haute récompense en mathématiques, la médaille Fields.

Les contributions de Mirzakhani sont expliquées dans le film par des mathématiciens de premier plan et illustrées par des séquences animées. Ses collègues mathématiciens du monde entier, ainsi que d'anciens enseignants, camarades de classe et élèves de l'Iran d'aujourd'hui, expriment l'impact profond de ses réalisations. Elle est une véritable source d'inspiration.

Date/heure: Le 5 mars 2021, 19h30

Durée: 60 min

En ligne: https://webinaires.uqam.ca/mathflix

## Colloque des sciences mathématiques du Québec - Jean-Pierre Demailly, Université Grenoble Alpes

le vendredi 26 février 2021

Analytic solutions to algebraic equations, and a conjecture of Kobayashi
A projective algebraic variety is defined as the zero locus of a finite family of homogeneous polynomials.  Over the field of complex numbers, the geometry of such varieties is governed to a large extent by the sign, in a suitable sense, of the Ricci curvature form.  When this sign is negative, the variety is expected to exhibit certain hyperbolicity properties in the sense of Kobayashi - as well as further very deep number-theoretic properties that are mostly conjectural, in the arithmetic situation.  In particular, all entire holomorphic curves drawn on it should be contained in a proper algebraic subvariety: this is a famous conjecture of Green-Griffiths and Lang.  Following recent ideas of D.  Brotbek, we will try to explain here a rather elementary proof of a related conjecture of Kobayashi, stating that a general algebraic hypersurface of sufficiently high degree is hyperbolic, i.e. does not contain any entire holomorphic curve.

Date: 26 février 2021, 15h00

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## Colloque des sciences mathématiques du Québec - Larry Guth, MIT

le vendredi 19 février 2021

Local smoothing for the wave equation
The local smoothing problem asks about how much solutions to the wave equation can focus.  It was formulated by Chris Sogge in the early 90s.  Hong Wang, Ruixiang Zhang, and I recently proved the conjecture in two dimensions.  In the talk, we will build up some intuition about waves to motivate the conjecture, and then discuss some of the obstacles and some ideas from the proof.

Date: 19 février 2021, 15h30

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## Colloque des sciences mathématiques du Québec - Mikael Kuusela, Carnegie Mellon University

le vendredi 12 février 2021

Spatio-temporal methods for estimating subsurface ocean thermal response to tropical cyclones
Tropical cyclones (TCs), driven by heat exchange between the air and sea, pose a substantial risk to many communities around the world.  Accurate characterization of the subsurface ocean thermal response to TC passage is crucial for accurate TC intensity forecasts and for understanding the role TCs play in the global climate system, yet that characterization is complicated by the high-noise ocean environment, correlations inherent in spatio-temporal data, relative scarcity of in situ observations and the entanglement of the TC-induced signal with seasonal signals.  We present a general methodological framework that addresses these difficulties, integrating existing techniques in seasonal mean field estimation, Gaussian process modeling, and nonparametric regression into a functional ANOVA model.  Importantly, we improve upon past work by properly handling seasonality, providing rigorous uncertainty quantification, and treating time as a continuous variable, rather than producing estimates that are binned in time.  This functional ANOVA model is estimated using in situ subsurface temperature profiles from the Argo fleet of autonomous floats through a multi-step procedure, which (1) characterizes the upper ocean seasonal shift during the TC season; (2) models the variability in the temperature observations; (3) fits a thin plate spline using the variability estimates to account for heteroskedasticity and correlation between the observations.  This spline fit reveals the ocean thermal response to TC passage.  Through this framework, we obtain new scientific insights into the interaction between TCs and the ocean on a global scale, including a three-dimensional characterization of the near-surface and subsurface cooling along the TC storm track and the mixing-induced subsurface warming on the track's right side.  Joint work with Addison Hu, Ann Lee, Donata Giglio and Kimberly Wood.

Date: 12 février 2021, 15h30

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## Colloque des sciences mathématiques du Québec - Egor Shelukhin, Université de Montréal

le vendredi 5 février 2021

Symmetry, Barcodes, and Hamiltonian dynamics
In the early 60s Arnol'd has conjectured that Hamiltonian diffeomorphisms, the motions of classical mechanics, often possess more fixed points than required by classical topological considerations.  In the late 80s and early 90s Floer has developed a powerful theory to approach this conjecture, considering fixed points as critical points of a certain functional.  Recently, in joint work with L.  Polterovich, we observed that Floer theory filtered by the values of this functional fits into the framework of persistence modules and their barcodes, originating in data sciences.  I will review these developments and their applications, which arise from a natural time-symmetry of Hamiltonians.  This includes new constraints on one-parameter subgroups of Hamiltonian diffeomorphisms, as well as my recent solution of the Hofer-Zehnder periodic points conjecture.  The latter combines barcodes with equivariant cohomological operations in Floer theory recently introduced by Seidel to form a new method with further consequences.

Date: 5 février 2021, 15h00

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## Colloque des sciences mathématiques du Québec - Jonathan Wakefield, University of Washington

le vendredi 29 janvier 2021

Small Area Estimation in Low- and Middle-Income Countries
The under-five mortality rate (U5MR) is a key barometer of the health of a nation.  Unfortunately, many people living in low- and middle-income countries are not covered by civil registration systems.  This makes estimation of the U5MR, particularly at the subnational level, difficult.  In this talk, I will describe models that have been developed to produce the official United Nations (UN) subnational U5MR estimates in 22 countries.  Estimation is based on household surveys, which use stratified, two-stage cluster sampling.  I will describe a range of area- and unit-level models and describe the rationale for the modeling we carry out.  Data sparsity in time and space is a key challenge, and smoothing models are vital.  I will discuss the advantages and disadvantages of discrete and continuous spatial models, in the context of estimation at the scale at which health interventions are made.  Other issues that will be touched upon include: design-based versus model-based inference; adjustments for HIV epidemics; the inclusion of so-called indirect (summary birth history) data; reproducibility through software availability; benchmarking; how to deal with incomplete geographical data; and working with the UN to produce estimates.

Date: 29 janvier 2021, 15h00

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## Colloque des sciences mathématiques du Québec - Robert Haslhofer, University of Toronto

le vendredi 22 janvier 2021

Mean curvature flow through neck-singularities
A family of surfaces moves by mean curvature flow if the velocity at each point is given by the mean curvature vector.  Mean curvature flow first arose as a model of evolving interfaces and has been extensively studied over the last 40 years.  In this talk, I will give an introduction and overview for a general mathematical audience.  To gain some intuition we will first consider the one-dimensional case of evolving curves.  We will then discuss Huisken’s classical result that the flow of convex surfaces always converges to a round point.  On the other hand, if the initial surface is not convex we will see that the flow typically encounters singularities.  Getting a hold of these singularities is crucial for most striking applications in geometry, topology and physics.  Specifically, singularities can be either of neck-type or conical-type.  We will discuss examples from the 90s, which show, both experimentally and theoretically, that flow through conical singularities is utterly non-unique.  In the last part of the talk, I will report on recent work with Kyeongsu Choi, Or Hershkovits and Brian White, where we proved that mean curvature flow through neck-singularities is unique.  The key for this is a classification result for ancient asymptotically cylindrical flows that describes all possible blowup limits near a neck-singularity.  In particular, this confirms the mean-convex neighborhood conjecture.  Assuming Ilmanen’s multiplicity-one conjecture, we conclude that for embedded two-spheres mean curvature flow through singularities is well-posed.

Date: 22 janvier 2021, 15h00

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## SUMM 2021

le samedi 9 janvier 2021

Les Séminaires Universitaires en Mathématiques à Montréal (SUMM) est un organisme formé par de jeunes étudiant.e.s au premier cycle en mathématiques venant de toutes les universités montréalaises. Son objectif principal est de créer un environnement propice aux échanges d'idées et d'intérêts, ainsi que de permettre aux étudiant.e.s de faire de nouvelles rencontres. Pour la douzième édition, nous avons en plus comme objectif d’unir et de dynamiser la communauté étudiante au premier cycle en mathématiques à Montréal, au Québec et dans les provinces avoisinantes.

La fin de semaine des SUMM s'adresse aux étudiant.e.s de premier cycle, en mathématiques ou en un autre domaine scientifique connexe. Cette année, elle se tiendra les 9 et 10 janvier, en ligne à cause de la pandémie.

La fin de semaine commencera sera composée de deux jours de présentations données par des étudiant.e.s au baccalauréat et par des professeur.e.s invité.e.s sur des sujets allant des coins les plus obscurs de la physique mathématique aux applications les plus extraordinaires de l’intelligence artificielle, en passant par la richesse de la philosophie et de l’histoire des mathématiques.

Durant les SUMM, les étudiant.e.s peuvent donner une conférence ou tout simplement venir écouter les présentations de leurs pairs. C'est une occasion de partager la passion des mathématiques dans un environnement stimulant et gratifiant, en discutant avec d’autres étudiant.e.s passioné.e.s toute la fin de semaine.

Au plaisir de vous y voir!

## Colloque des sciences mathématiques du Québec - Frances Kirwan, Oxford

le vendredi 27 novembre 2020

Moduli of unstable objects in algebraic geometry

Moduli spaces arise naturally in classification problems in geometry. The study of the moduli spaces of nonsingular complex projective curves (or equivalently of compact Riemann surfaces) goes back to Riemann himself in the nineteenth century. The construction of the moduli spaces of stable curves of fixed genus is one of the classical applications of Mumford's geometric invariant theory (GIT), developed in the 1960s; many other moduli spaces of 'stable' objects can be constructed using GIT and in other ways. A projective curve is stable if it has only very mild singularities (nodes) and its automorphism group is finite; similarly in other contexts stable objects are usually better behaved than unstable ones.

The aim of this talk is to explain how recent methods from a version of GIT for non-reductive group actions can help us to classify singular curves in such a way that we can construct moduli spaces of unstable curves (of fixed type). More generally our aim is to use suitable 'stability conditions' to stratify other moduli stacks into locally closed strata with coarse moduli spaces. The talk is based on joint work with Gergely Berczi, Vicky Hoskins and Joshua Jackson.

Date: 27 novembre 2020, 15h00

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## Colloque des sciences mathématiques du Québec - Wieslawa Niziol, Sorbonne

le vendredi 20 novembre 2020

p-adic Hodge Theory is one of the most powerful tools in modern Arithmetic Geometry. In this talk, I will review p-adic Hodge Theory of algebraic varieties, present current developments in p-adic Hodge Theory of analytic varieties, and discuss some of its applications to problems in Number Theory.

Date: 20 novembre 2020, 15h00

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## Colloque des sciences mathématiques du Québec - Tamara Broderick, MIT

le vendredi 13 novembre 2020

Approximate Cross-Validation for Large Data and High Dimensions
The error or variability of statistical and machine learning algorithms is often assessed by repeatedly re-fitting a model with different weighted versions of the observed data. The ubiquitous tools of cross-validation (CV) and the bootstrap are examples of this technique. These methods are powerful in large part due to their model agnosticism but can be slow to run on modern, large data sets due to the need to repeatedly re-fit the model. We use a linear approximation to the dependence of the fitting procedure on the weights, producing results that can be faster than repeated re-fitting by orders of magnitude. This linear approximation is sometimes known as the "infinitesimal jackknife" (IJ) in the statistics literature, where it has mostly been used as a theoretical tool to prove asymptotic results. We provide explicit finite-sample error bounds for the infinitesimal jackknife in terms of a small number of simple, verifiable assumptions. Without further modification, though, we note that the IJ deteriorates in accuracy in high dimensions and incurs a running time roughly cubic in dimension. We additionally show, then, how dimensionality reduction can be used to successfully run the IJ in high dimensions when data is sparse or low rank. Simulated and real-data experiments support our theory.

Date: 13 novembre 2020, 15h30

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## Colloque des sciences mathématiques du Québec - Nicolas Bergeron, ENS, Paris

le vendredi 16 octobre 2020

Hyperplane arrangements and modular symbols
In his fantastic book « Elliptic functions according to Eisenstein and Kronecker, » Weil writes:  « As Eisenstein shows, his method for constructing  elliptic functions applies beautifully to the simpler case of the trigonometric functions. Moreover, this case provides […] the simplest proofs for a series of results, originally discovered by Euler. »  The results Weil alludes to are relations between product of trigonometric functions. I will first explain how these relations are quite surprisingly governed by relations between modular symbols (whose elementary theory I will sketch). I will then show how this story fits into a wider picture that relates the topological world of group homology of some linear groups to the algebraic world of trigonometric and elliptic functions. To conclude I will briefly describe  a number theoretical application.  This is based on a work-in-progress with Pierre Charollois, Luis Garcia and Akshay Venkatesh.

Date: 16 octobre 2020, 15h00

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## Colloque des sciences mathématiques du Québec - Phillip Griffiths, IAS, Princeton

le vendredi 9 octobre 2020

Hodge Theory and Moduli
The theory of moduli is an important and active area in algebraic geometry. For varieties of general type the existence of a moduli space  with a canonical completion  has been proved by Kollar/Shepard-Barron/Alexeev. Aside from the classical case of algebraic curves, very little is known about the structure of , especially it’s boundary. The period mapping from Hodge theory provides a tool for studying these issues.

In this talk, we will discuss some aspects of this topic with emphasis on I-surfaces, which provide one of the first examples where the theory has been worked out in some detail. Particular notice will me made of how the extension data in the limiting mixed Hodge structures that arise from singular surfaces on the boundary of moduli may be used to guide the desingularization of that boundary.

Date: 9 octobre 2020, 15h00

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## Colloque des sciences mathématiques du Québec - Paul McNicholas, McMaster University (Vidéoconférence)

le vendredi 2 octobre 2020

Data Science, Classification, Clustering and Three-Way Data
Data science is discussed along with some historical perspective.  Selected problems in classification are considered, either via specific datasets or general problem types.  In each case, the problem is introduced before one or more potential solutions are discussed and applied.  The problems discussed include data with outliers, longitudinal data, and three-way data.  The proposed approaches are generally mixture model-based.

Zoom: Si ce n’est déjà fait, pour recevoir le lien Zoom pour la série, veuillez vous inscrire à: http://crm.umontreal.ca/colloque-sciences-mathematiques-quebec/#csmq

## Colloque des sciences mathématiques du Québec - - Stefan Wager, Stanford

le vendredi 11 septembre 2020

Machine Learning for Causual Inference

Date: 11 septembre 2020, 16h00

## Colloque des sciences mathématiques du Québec - Morgan Craig, Université de Montréal

le vendredi 19 juin 2020

Quantitative approaches to understanding the immune response to SARS-CoV-2 infection
COVID-19 is typically characterized by a range of respiratory symptoms that, in severe cases, progress to acute respiratory distress syndrome (ARDS). These symptoms are also frequently accompanied by a range of inflammatory indications, particularly hyper-reactive and dysregulated inflammatory responses in the form of cytokine storms and severe immunopathology. Much remains to be uncovered about the mechanisms that lead to disparate outcomes in COVID-19. Here, quantitative approaches, especially mechanistic mathematical models, can be leveraged to improve our understanding of the immune response to SARS-CoV-2 infection. Building upon our prior work modelling the production of innate immune cell subsets and the viral dynamics of HIV and oncolytic viruses, we are developing a quantitative framework to interrogate open questions about the innate and adaptive immune reaction in COVID-19. In this talk, I will outline our recent work modelling SARS-CoV-2 viral dynamics and the ensuing immune response at both the tissue and systemic levels. A portion of this work is done as part of an international and multidisciplinary coalition working to establish a comprehensive tissue simulator (physicell.org/covid19 [1]), which I will also discuss in more detail.

Date: 19 juin 2020, 16h00

## Colloque des sciences mathématiques du Québec - Lai-Sang Young, NYU Courant (Vidéoconférence)

le vendredi 17 avril 2020

Observable events and typical trajectories in finite and infinite dimensional dynamical systems
The terms "observable events" and "typical trajectories" in the title should really be between quotation marks, because what is typical and/or observable is a matter of interpretation.  For dynamical systems on finite dimensional spaces, one often equates observable events with positive Lebesgue measure sets, and invariant distributions that reflect the large-time behaviors of positive Lebesgue measure sets of initial conditions (such as Liouville measure for Hamiltonian systems) are considered to be especially important.  I will begin by introducing these concepts for general dynamical systems -- including those with attractors -- describing a simple dynamical picture that one might hope to be true.  This picture does not always hold, unfortunately, but a small amount of random noise will bring it about.  In the second part of my talk I will consider infinite dimensional systems such as semi-flows arising from dissipative evolutionary PDEs.  I will discuss the extent to which the ideas above can be generalized to infinite dimensions, and propose a notion of "typical solutions".

Date / Heure: Vendredi, 17 avril 2020 - 16h00

https://umontreal.zoom.us/j/170851981?pwd=b1ZxMWM0Z3Q0d3I5ZHJUS0FUZEY5QT09
ID de la réunion: 170 851 981
Mot de passe: 942210

## ANNULÉ-Film: Secrets of the Surface. The Mathematical Vision of Maryam Mirzakhani

le dimanche 15 mars 2020

Filmé au Canada, en Iran et aux États-Unis, Secrets of the Surface : The Mathematical Vision of Maryam Mirzakhani examine la vie et l'œuvre mathématique de Maryam Mirzakhani, une immigrante iranienne aux États-Unis qui est devenue une superstar dans son domaine. En 2014, elle a été à la fois la première femme et la première Iranienne à recevoir la plus haute récompense en mathématiques, la médaille Fields.

Les contributions de Mirzakhani sont expliquées dans le film par des mathématiciens de premier plan et illustrées par des séquences animées. Ses collègues mathématiciens du monde entier, ainsi que d'anciens enseignants, camarades de classe et élèves de l'Iran d'aujourd'hui, expriment l'impact profond de ses réalisations. Le cheminement de ses études, son succès dans l'équipe iranienne des Olympiades de mathématiques et son brillant travail font de Mirzakhani un modèle idéal pour les filles qui envisagent une carrière dans les sciences et les mathématiques.

Quand
15/03/2020
17:00-19:00.

J.A. De Sève Cinema
Room / salle 125
J.W. McConnell Building
1400 De Maisonneuve W.
Sir George Williams Campus

Cet événement est gratuit.

## ANNULÉ-Colloque des sciences mathématiques du Québec - Almut Burchard, University of Toronto

le vendredi 13 mars 2020

Optimal shapes arising from pair interactions
In many physical and social situations, pair interactions determine how a large group of particles or individuals arranges itself in space under constraints on the overall mass, density, and geometry. Typical examples are capacitor problems (where the interaction is purely repulsive), and flocking (where the interaction tends to be attractive at large distances and repulsive as individuals get too close). Mathematically, this leads to non-local shape optimization problems, where a density interacts with itself by a pair potential. Under what conditions is there aggregation, and when do individuals disperse? Is the optimal shape always round? Can multiple flocks co-exist? I will discuss some toy models, symmetrization techniques, recent results, and open questions.

Date / Heure: Vendredi, 13 mars 2020 - 16h00

Lieu: CRM, Université de Montréal, Pavillon André-Aisenstadt, salle 1175

## Colloque des sciences mathématiques du Québec - Yang Feng, NYU

le vendredi 28 février 2020

Neyman-Pearson classification: parametrics and sample size requirement
The Neyman-Pearson (NP) paradigm in binary classification seeks classifiers that achieve a minimal type II error while enforcing the prioritized type I error controlled under some user-specified level alpha.  This paradigm serves naturally in applications such as severe disease diagnosis and spam detection, where people have clear priorities among the two error types.  Recently, Tong, Feng and Li (2018) proposed a nonparametric umbrella algorithm that adapts all scoring-type classification methods (e.g., logistic regression, support vector machines, random forest) to respect the given type I error (i.e., conditional probability of classifying a class 0 observation as class 1 under the 0-1 coding) upper bound alpha with high probability, without specific distributional assumptions on the features and the responses.  Universal the umbrella algorithm is, it demands an explicit minimum sample size requirement on class 0, which is often the more scarce class, such as in rare disease diagnosis applications.  In this work, we employ the parametric linear discriminant analysis (LDA) model and propose a new parametric thresholding algorithm, which does not need the minimum sample size requirements on class 0 observations and thus is suitable for small sample applications such as rare disease diagnosis.  Leveraging both the existing nonparametric and the newly proposed parametric thresholding rules, we propose four LDA-based NP classifiers, for both low- and high-dimensional settings.  On the theoretical front, we prove NP oracle inequalities for one proposed classifier, where the rate for excess type II error benefits from the explicit parametric model assumption.  Furthermore, as NP classifiers involve a sample splitting step of class 0 observations,  we construct a new adaptive sample splitting scheme that can be applied universally to NP classifiers, and this adaptive strategy reduces the type II error of these classifiers.  The proposed NP classifiers are implemented  in the R package nproc.

Date / Heure: Vendredi, 28 février 2020 - 16:00

Lieu: McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104

## Colloque des sciences mathématiques du Québec - Steve Kudla, University of Toronto

le vendredi 21 février 2020

Arithmetic Theta Series
I will recount a family history of theta series through several generations. Theta series for positive definite integral quadratic forms provide some of the most classical examples of elliptic modular forms and their Siegel modular variants. Analogous series were defined by Siegel and Maass for lattices with indefinite quadratic forms say with signature (p,q). These series are no longer holomorphic and depend on an additional variable in the Grassmannian of negative q-planes, i.e., the symmetric space for the orthogonal group O(p,q). Motivated by work of Hirzebruch and Zagier on the generating series for curves on Hilbert modular surfaces, Millson and I constructed a theory of theta series valued in the cohomology of certain locally symmetric spaces -- geometric theta series. More recently, a theory of arithmetic theta series has been emerging, theta series valued in the Chow groups or arithmetic Chow groups of the integral models of certain Shimura varieties.

Date / Heure: Vendredi, 21 février 2020 - 16:00

Lieu: McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104

## Colloque des sciences mathématiques du Québec - Eyal Z. Goren, McGill University

le vendredi 7 février 2020

Complex multiplication - old and new
The theory of complex multiplication is more than a century old; its origins date back to Klein, Hilbert, Kummer, Weber, Deuring and many others. It has been instrumental in the development of class field theory and algebraic number theory. Yet, more than a century later we find new theorems that are truly surprising. I will start with this historical perspective and try to position some of these new developments in the light of the André-Oort conjecture - a conjecture in the area of Shimura varieties that was recently resolved by Tsimerman, building on ideas of Edixhoven, Pila, Wilkie and Zannier. The resolution rests on the averaged Colmez conjecture, a conjecture that addresses the arithmetic complexity of abelian varieties with complex multiplication, which was proved by Andreatta-Howard-Madapusi Pera and the speaker, and, independently, by Yuan-Zhang.

Date / Heure: Vendredi, 7 février 2020 - 16:00

Lieu: McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104

## Colloque des sciences mathématiques du Québec - Ana-Maria Staicu, North Carolina State University

le vendredi 31 janvier 2020

Longitudinal functional regression: tests of significance
We consider longitudinal functional regression, where, for each subject, the response consists of multiple curves observed at different time visits. We discuss tests of significance in two general settings. First, when there are no additional covariates, we develop a hypothesis testing methodology for formally assessing that the mean function does not vary over time. Second, in the presence of other covariates, we propose a testing procedure to determine the significance of the covariate's time-varying effect formally. The methods account for the complex dependence structure of the response and are computationally efficient. Numerical studies confirm that the testing approaches have the correct size and are have a superior power relative to available competitors. We illustrate the methods on a real data application.

Date / Heure: Vendredi, 31 janvier 2020 - 16:00

Lieu: HEC Montréal, 3000, chemin de la Côte-Sainte-Catherine, salle Béton Grilli

## Colloque des sciences mathématiques du Québec - Olivier Lafitte, Unité Mixte Internationale – Centre de recherches mathématiques (UMI-CRM).

le vendredi 24 janvier 2020

Propagation des ondes et diffraction par un obstacle: résultats utilisant l’analyse microlocale

Date / Heure: Vendredi, 24 janvier 2020 - 16:00

Lieu: McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104

## Colloque des sciences mathématiques du Québec - Éva Tardos, Cornell University

le vendredi 17 janvier 2020

Learning in Games
Selfish behavior can often lead to suboptimal outcome for all participants, a phenomenon illustrated by many classical examples in game theory. Over the last decade we developed good understanding on how to quantify the impact of strategic user behavior on the overall performance in many games (including traffic routing as well as online auctions). In this talk we will focus on games where players use a form of learning that helps them adapt to the environment, and consider two closely related questions: What are broad classes of learning behaviors that guarantee high social welfare in games, and are these results robust to situations when game or the population of players is dynamically changing.

Date / Heure: Vendredi, 17 janvier 2020 - 14h00

Lieu: CRM, Université de Montréal, Pavillon André-Aisenstadt, salle 6214-6254

## SUMM 2020

le vendredi 10 janvier 2020

Les Séminaires Universitaires en Mathématiques à Montréal (SUMM) est un organisme formé par de jeunes étudiant.e.s au premier cycle en mathématiques venant de toutes les universités montréalaises. Son objectif principal est de créer un environnement propice aux échanges d'idées et d'intérêts, ainsi que de permettre aux étudiant.e.s de faire de nouvelles rencontres. Pour la onzième édition, nous avons en plus comme objectif d’unir et de dynamiser la communauté étudiante au premier cycle en mathématiques à Montréal, au Québec et dans les provinces avoisinantes.

La fin de semaine des SUMM s'adresse aux étudiant.e.s de premier cycle, en mathématiques ou en un autre domaine scientifique connexe. Cette année, elle se tiendra les 10, 11, et 12 janvier à l’Université du Québec à Montréal.

La fin de semaine commencera par une soirée vins et fromages et sera suivie par deux jours de présentations données par des étudiant.e.s au baccalauréat et par six professeur.e.s invité.e.s sur des sujets allant des coins les plus obscurs de la physique mathématique aux applications les plus extraordinaires de l’intelligence artificielle, en passant par la richesse de la philosophie et de l’histoire des mathématiques.

Durant les SUMM, les étudiant.e.s peuvent donner une conférence, participer au concours d’affiches ou tout simplement venir écouter les présentations de leurs pairs. C'est une occasion de partager la passion des mathématiques dans un environnement stimulant et gratifiant, en discutant avec d’autres étudiant.e.s passioné.e.s toute la fin de semaine, que ce soit entre deux présentations ou pendant les pauses du déjeuner, du dîner ou du souper en dégustant, par exemple, un merveilleux panini au poulet .

Au plaisir de vous y voir!

## Colloque des sciences mathématiques du Québec - Persi Diaconis, Stanford University

le vendredi 29 novembre 2019

Shuffling and Group Representations
Picture n cards, numbered 1,2,...,n face down, in order, in a row on the table. Each time, your left hand picks a random card, your right hand picks a random card and the two cards are transposed. It is clear that 'after a while' the cards get all mixed up. How long does this take? In joint work with Mehrdad Shahshahani we analyzed this problem using the character theory of the symmetric group. The methods work for general measures on general compact groups. They mix probability, analysis, combinatorics and group theory (we need real formulas for the representations). I will try to explain all of this(along with some motivation for studying such problems) 'in English'. The answer, when n=52, is 'about 400'.

Date / Heure: Vendredi, 29 novembre 2019 - 16:00

Lieu: McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104

## Colloque des sciences mathématiques du Québec - Donald Estep, Simon Fraser University

le vendredi 22 novembre 2019

Formulation and solution of stochastic inverse problems for science and engineering models
The stochastic inverse problem of determining probability structures on input parameters for a physics model corresponding to a given probability structure on the output of the model forms the core of scientific inference and engineering design. We describe a formulation and solution method for stochastic inverse problems that is based on functional analysis, differential geometry, and probability/measure theory. This approach yields a computationally tractable problem while avoiding alterations of the model like regularization and ad hoc assumptions about the probability structures. We present several examples, including a high-dimensional application to determination of parameter fields in storm surge models. We also describe work aimed at defining a notion of condition for stochastic inverse problems and tackling the related problem of designing sets of optimal observable quantities.

Date / Heure: Vendredi, 22 novembre 2019 - 16:00

Lieu: UQAM, Pavillon Président-Kennedy - 201, avenue du Président-Kennedy, salle PK-5115

## Colloque des sciences mathématiques du Québec - Yaniv Plan, University of British Columbia - Lauréat 2019 du Prix André-Aisenstadt

le vendredi 15 novembre 2019

The role of random models in compressive sensing and matrix completion
Random models lead to a precise and comprehensive theory of compressive sensing and matrix completion.  The number of random linear measurements needed to recover a sparse signal, or a low-rank matrix, or, more generally, a structured signal, are now well understood.  Indeed, this boils down to a question in random matrix theory:  How well conditioned is a random matrix restricted to a fixed subset of Rn?  We discuss recent work addressing this question in the sub-Gaussian case.  Nevertheless, a practitioner with a fixed data set will wonder:  Can they apply theory based on randomness?  Is there any hope to get the same guarantees?  We discuss these questions in compressive sensing and matrix completion, which, surprisingly, seem to have divergent answers.

Date / Heure: Vendredi, 15 novembre 2019 - 16:00

Lieu: CRM, Université de Montréal, Pavillon André-Aisenstadt, salle 1355

## Colloque des sciences mathématiques du Québec - Jaume Gomis, Lauréat 2019 du Prix CAP-CRM, Institut Périmètre de physique théorique

le vendredi 8 novembre 2019

Symmetries in topological quantum field theories
In this talk I will describe how to characterize symmetries of topological field theories and give a complete classification of symmetries in Abelian Topological Field Theories, uncovering a plethora of quantum symmetries in these theories and an intriguing connection to number theory.

Date / Heure: Vendredi, 8 novembre 2019 - 16:00

Lieu: CRM, Université de Montréal, Pavillon André-Aisenstadt, salle 1355

## Colloque des sciences mathématiques du Québec - Stephen Walker, University of Texas

le vendredi 1 novembre 2019

General Bayesian modeling
The work is motivated by the inflexibility of Bayesian modeling; in that only parameters of probability models are required to be connected with data. The idea is to generalize this by allowing arbitrary unknowns to be connected with data via loss functions. An updating process is then detailed which can be viewed as arising in at least a couple of ways - one being purely axiomatically driven.   The further exploration of replacing probability model based approaches to inference with loss functions is ongoing. Joint work with Chris Holmes, Pier Giovanni Bissiri and Simon Lyddon.

Date / Heure: Vendredi, 1 novembre 2019 - 16:00

Lieu: McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104

## Colloque des sciences mathématiques du Québec - Melanie Matchett Wood, UC Berkeley

le vendredi 25 octobre 2019

Coincidences in homological densities
For certain natural sequences of topological spaces, the kth homology group stabilizes once you go far enough out in the sequence of spaces. This phenomenon is called homological stability. Two classical examples of homological stability are the configuration space of n unordered distinct points in the plane, studied in the 60's by Arnold' and the space of (based) algebraic maps from CP1 to CP1 studied by Segal in the 70's. It turns out that the stable homology is the same in these two examples, and in this talk we explain that this is just the tip an iceberg--a subtle, but precise relationship between the values of stable of homology different sequences of spaces. To explain this relationship, which we discovered through an analogy to asymptotic counts in number theory, we introduce a new notion of homological density. This talk is on joint work with Benson Farb and Jesse Wolfson.

Date / Heure: Vendredi, 25 octobre 2019 - 16:00

Lieu: McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104

## Colloque des sciences mathématiques du Québec - Jacob Tsimerman, University of Toronto

le vendredi 18 octobre 2019

o-minimal GAGA and applications to Hodge theory
(Joint with B.Bakker and Y.Brunebarbe) One very fruitful way of studying complex algebraic varieties is by forgetting the underlying algebraic structure, and just thinking of them as complex analytic spaces.  To this end, it is a natural and fruitful question to ask how much the complex analytic structure remembers.  One very prominent result is Chows theorem, stating that any closed analytic subspace of projective space is in fact algebraic.  One notable consequence of this result is that a compact complex analytic space admits at most 1 algebraic structure - a result which is false in the non-compact case.  This was generalized and extended by Serre in his famous GAGA paper using the language of cohomology.  We explain how we can extend Chow's theorem and in fact all of GAGA to the non-compact case by working with complex analytic structures that are "tame" in the precise sense defined by o-minimality.  This leads to some very general "algebraization" theorems, and we give applications to Hodge theory.

Date / Heure: Vendredi, 18 octobre 2019 - 16:00

Lieu: McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104

## Colloque des sciences mathématiques du Québec - Ruth Misener, Imperial College

le vendredi 11 octobre 2019

Scoring positive semidefinite cutting planes for quadratic optimization via trained neural networks
Semidefinite programming relaxations complement polyhedral relaxations for quadratic optimization, but global optimization solvers built on polyhedral relaxations cannot fully exploit this advantage.  We develop linear outer-approximations of semidefinite constraints that can be effectively integrated into global solvers for nonconvex quadratic optimization.  The difference from previous work is that our proposed cuts are (i) sparser with respect to the number of nonzeros in the row and (ii) explicitly selected to improve the objective.  A neural network estimator is key to our cut selection strategy: ranking each cut based on objective improvement involves solving a semidefinite optimization problem, but this is an expensive proposition at each Branch&Cut node.  The neural network estimator, trained a priori of any instance to solve, takes the most time consuming computation offline by predicting the objective improvement for any cut.

Date / Heure: Vendredi, 11 octobre 2019 - 16:00

Lieu: McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104

## Colloque des sciences mathématiques du Québec - Johanna Nešlehová, McGill University - Lauréate 2019 du Prix CRM-SSC

le vendredi 4 octobre 2019

La queue, la tuile, le bris d’égalité et leur rôle dans les modèles de dépendance
La modélisation de la dépendance entre variables aléatoires est omniprésente en statistique. S’agissant d’événements rares à fort impact, tels que des orages violents, des inondations ou des vagues de chaleur, la question revêt une grande importance pour la gestion des risques et pose des défis théoriques. Une approche hautement flexible et prometteuse s’appuie sur la théorie des valeurs extrêmes, la modélisation par copules et l’inférence fondée sur les rangs. Je présenterai trois avancées récentes dans ce domaine. Nous nous intéresserons d’abord à la prise en compte de la dépendance en régime moyen, lorsque les modèles asymptotiques de valeurs extrêmes ne conviennent pas. Nous verrons ensuite quoi faire lorsque le nombre de variables est grand et comment une structure de modèle hiérarchique peut être apprise à partir de matrices de corrélation de rangs de grande taille. Enfin, je ne résisterai pas à l’envie de vous initier à l’univers complexe de l’inférence basée sur les rangs pour les données discrètes ou mixtes.

Date / Heure: Vendredi, 4 octobre 2019 - 16:00

Lieu: CRM, Université de Montréal, Pavillon André-Aisenstadt, salle 1355

## Colloque des sciences mathématiques du Québec - Nassif Ghoussoub, UBC - Lauréat 2019 du Prix CRM-Fields-PIMS

le jeudi 26 septembre 2019

From Monge optimal transports to optimal Skorokhod embeddings
The optimal transportation problem, which originated in the work of Gaspard Monge in 1781, provides a fundamental and quantitave way to measure the distance between probability distributions. It has led to many successful applications in PDEs, Geometry, Statistics and Probability Theory. Recently, and motivated by problems in Financial Mathematics, variations on this problem were introduced by requiring the transport plans to abide by certain "fairness rules," such as following martingale paths. One then specifies a stochastic state process and a costing procedure, and minimize the expected cost over stopping times with a given state distribution. Recent work has uncovered deep connections between this type of constrained optimal transportation problems, the celebrated Skorokhod embeddings of probability distributions in Brownian motion, and Hamilton-Jacobi variational inequalities.

Date / Heure: Jeudi, 26 septembre 2019 - 16:00

Lieu: CRM, Université de Montréal, Pav. Roger-Gaudry, 2900, boul. Édouard-Montpetit, salle M-415

## Colloque des sciences mathématiques du Québec - Alex Lubotzky, The Hebrew University of Jerusalem

le vendredi 20 septembre 2019

Date / Heure: Vendredi, 20 septembre 2019 - 16:00

Lieu: McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104

## Colloque des sciences mathématiques du Québec - Brent Pym, McGill University

le vendredi 13 septembre 2019

Multiple zeta values in deformation quantization
The subject of "deformation quantization" originated as a mathematical abstraction of the passage from classical to quantum mechanics: starting from a classical phase space (i.e. a Poisson manifold), we deform the ordinary multiplication of functions to produce a noncommutative ring, which serves as the algebra of quantum observables.  Over the years, the theory has evolved from its physical origins to take on a mathematical life of its own, with rich connections to representation theory, topology, graph theory, number theory and more.  I will give an introduction to the subject and explain how the quantization process is inextricably linked, via a formula of Kontsevich, to special values of the Riemann zeta function, and their generalizations known as multiple zeta values.

Date / Heure: Vendredi, 13 septembre 2019 - 16:00

Lieu: McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104

## Colloque des sciences mathématiques du Québec - Ciprian Manolescu, UCLA

le vendredi 30 août 2019

Khovanov homology, 3-manifolds, and 4-manifolds
Khovanov homology is an invariant of knots in R3. A major open problem is to extend its definition to knots in other three-manifolds, and to understand its relation to surfaces in 4-manifolds. I will discuss some partial progress in these directions, from different perspectives (gauge theory, representation theory, sheaf theory). In the process I will also review some of the topological applications of Khovanov homology.

Date / Heure: Vendredi, 30 août 2019 - 16:00

Venue: UQAM, Pavillon Sherbrooke, 201, rue Sherbrooke ouest, salle SH-3620

## École découverte de l'ISM: Progrès en basses dimensions

le mardi 27 août 2019

### 27 au 30 août 2019

Cette école découverte s’inspire des développements récents en topologie de basse dimension basés sur les travaux de Ciprian Manolescu qui tiendra la Chaire Aisenstadt pendant le programme du 50e anniversaire du CRM en topologie de basse dimension. Ainsi, l’école présentera les nouveaux développements en homologie Heegaard-Floer et en théorie de jauge ainsi que les développements liés à la célèbre réfutation de la conjecture de triangulation de Manolescu.

## École découverte de l'ISM: La dynamique des processus aléatoires

le lundi 10 juin 2019

### 10 au 14 juin 2019

L’analyse des processus stochastiques dynamiques (ou dépendants du temps) et leur comportement asymptotique est fondamentale tant dans les probabilités discrètes que continues. Dans certains cas, le comportement asymptotique du processus stochastique démontre des dynamiques intéressantes en soi. Par exemple, on peut observer ce phénomène dans le contexte de la propagation du front qui se produit de façon asymptotique dans le mouvement brownien ramifié. Dans d’autres cas, un comportement dynamique intéressant émerge des processus stochastiques dans la limite d’échelle. Des exemples incluent l’étude des marches aléatoires dans les environnements aléatoires (ce qui dans certains environnements convergent presque certainement vers un mouvement brownien, et dans d’autres à des processus de saut), ou l’étude de modèles de treillis en deux dimensions dans la statistique mécanique (dont beaucoup convergent, de façon démontrable ou conjecturale, à des évolutions Schramm-Loewner).

L’objectif de ce programme est de présenter une variété de sujets d’intérêt actuel dans l’étude des processus stochastiques dynamiques aux étudiants avancés de premier cycle et aux étudiants aux cycles supérieurs.

## 22e Colloque panquébécois des étudiant.e.s

le vendredi 17 mai 2019

Le XXIIe colloque panquébécois de l’Institut des Sciences Mathématiques (ISM) aura lieu à Montréal en du 17 mai au 20 mai 2019. Organisé chaque année, ce colloque réunit les étudiant·e·s aux cycles supérieurs en mathématiques du Québec pour une fin de semaine. Cette année, le colloque se tiendra à l'Université de Montréal.

Les participant·e·s pourront assister à quatre conférences plénières données par des professeur·e·s et pourront également présenter sur un pan des mathématiques de leur intérêt. Consultez la programmation pour plus de détails sur l'horaire de l'évènement.

L'inscription est de 20$. Ceci inclut un vin et fromage le vendredi soir, un souper le samedi ainsi que les déjeuners, dîners, pauses café tout au long de la fin de semaine. Les premier·ère·s participant·e·s inscrit·e·s recevront une tasse de l'ISM! Pour toute question, n'hésitez pas à nous contacter. ## Colloque des sciences mathématiques du Québec - Jungkai A. Chen, National Taiwan University le jeudi 16 mai 2019 Introduction to birational classification theory in dimension three and higher One of the main themes of algebraic geometry is to classify algebraic varieties and to study various geometric properties of each of the interesting classes. Classical theories of curves and surfaces give a beautiful framework of classification theory. Recent developments provide more details in the case of dimension three. We are going to introduce the three-dimensional story and share some expectations for even higher dimensions. Date / Heure: Vendredi, 16 mai 2019 - 16:00 Lieu: UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, salle PK-5115 ## Les 24 heures de science: Les mathématiques de la magie! le samedi 11 mai 2019 Vous avez toujours rêvé de concevoir vos propres tours de magie? Vous souhaitez savoir ce que les mathématiques peuvent vous apporter? L'Institut des sciences mathématiques vous invite à voir des tours de magie utilisant cartes, noeuds et mathématiques, mais surtout pas votre intuition... elle pourrait être trompeuse! Samedi 11 mai, 12h à 14h UQAM, Pavillon Président-Kennedy 201, ave du Président-Kennedy local PK-1630, Montréal ## Colloque des sciences mathématiques du Québec - Amanda Folsom, Amherst College le vendredi 10 mai 2019 Quantum Jacobi forms and applications Quantum modular forms were defined in 2010 by Zagier; they are somewhat analogous to ordinary modular forms, but they are defined on the rational numbers as opposed to the upper half complex plane, and have modified transformation properties. In 2016, Bringmann and the author defined the notion of a quantum Jacobi form, naturally marrying the concept of a quantum modular form with that of a Jacobi form (the theory of which was developed by Eichler and Zagier in the 1980s). We will discuss these intertwined topics, emphasizing recent developments and applications. In particular, we will discuss applications to combinatorics, topology (torus knots), and representation theory (VOAs). Date / Heure: Vendredi, 10 mai 2019 - 16:00 Lieu: McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104 ## Colloque des sciences mathématiques du Québec - Lenya Ryzhik, Stanford University le vendredi 3 mai 2019 The stochastic heat equation and KPZ in dimensions three and higher The stochastic heat equation and the KPZ equation appear as the macroscopic limits for a large class of probabilistic models, and the study of KPZ, in particular, led to many fascinating developments in probability over the last decade or so, from the regularity structures to integrable probability. We will discuss a small group of recent results on these equations in simple settings, of the PDE flavour, that fall in line with what one may call naive expectations by an applied mathematician. Date / Heure: Vendredi, 3 mai 2019 - 16:00 Lieu: McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104 ## Journée mathématique pour les étudiantes de cégep le samedi 27 avril 2019 L'ISM organise un atelier d’une demie journée (en anglais) à l’intention des jeunes femmes au cégep qui s’intéressent aux mathématiques et à la science. Nous proposons des exposés amusants et interactifs, une table ronde et une conférence plénière inspiratrice, tous donnés par des femmes qui étudient ou travaillent dans les domaines qui utilisent des mathématiques. L’objectif de l’événement est d’encourager les jeunes femmes à poursuivre leurs études en mathématiques et en sciences. L’événement servira également à encourager les étudiantes de cégep à faire des contacts pour faciliter la transition de cégep à l’université. L’activité, gratuite, est ouverte aux étudiantes de cégep, ainsi qu’à leurs parents et profs. Le lunch et des collations seront offerts. Nous demandons aux personnes intéressées de s’inscrire sur la page inscription avant le mercredi 24 avril 2019. ## Colloque des sciences mathématiques du Québec - Alan W. Reid, Rice University le vendredi 26 avril 2019 Distinguishing finitely presented groups by their finite quotients If G is a finitely generated group, let C(G) denote the set of finite quotients of G. This talk will survey work on the question of to what extent C(G) determines G up to isomorphism, culminating in a discussion of examples of Fuchsian and Kleinian groups that are determined by C(G) (amongst finitely generated residually finite groups). Date / Heure: Vendredi, 26 avril 2019 - 16:00 Lieu: McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104 ## Colloque des sciences mathématiques du Québec - Nicolas Bergeron, Institut de Mathématiques de Jussieu - Paris Rive Gauche le vendredi 12 avril 2019 Linking in torus bundles and Hecke L functions Torus bundles over the circle are among the simplest and cutest examples of 3-dimensional manifolds. After presenting some of these examples, using in particular animations realized by Jos Leys, I will consider periodic orbits in these fiber bundles over the circle. We will see that their linking numbers --- that are rational numbers by definition --- can be computed as certain special values of Hecke L-functions. Properly generalized this viewpoint makes it possible to give new topological proof of now classical rationality or integrality theorems of Klingen-Siegel and Deligne-Ribet. It also leads to interesting new "arithmetic lifts" that I will briefly explain. All this is extracted from an on going joint work with Pierre Charollois, Luis Garcia and Akshay Venkatesh. Date / Heure: Vendredi, 12 avril 2019 - 16:00 Lieu: McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104 ## Colloque des sciences mathématiques du Québec - Minhyong Kim, University of Oxford le vendredi 29 mars 2019 Principal Bundles in Diophantine Geometry Principal bundles and their moduli have been important in various aspects of physics and geometry for many decades. It is perhaps not so well-known that a substantial portion of the original motivation for studying them came from number theory, namely the study of Diophantine equations. I will describe a bit of this history and some recent developments. Date / Heure: Vendredi, 29 mars 2019 - 16:00 Lieu: McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104 ## Colloque des sciences mathématiques du Québec - Emmy Murphy, Northwestern University le vendredi 22 mars 2019 Flexibility in contact and symplectic geometry We discuss a number of h-principle phenomena which were recently discovered in the field of contact and symplectic geometry. In generality, an h-principle is a method for constructing global solutions to underdetermined PDEs on manifolds by systematically localizing boundary conditions. In symplectic and contact geometry, these strategies typically are well suited for general constructions and partial classifications. Some of the results we discuss are the characterization of smooth manifolds admitting contact structures, high dimensional overtwistedness, the symplectic classification of flexibile Stein manifolds, and the construction of exotic Lagrangians in Cn. Date / Heure: Vendredi, 22 mars 2019 - 16:00 Lieu: UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, salle PK-5115 ## Sommet étudiant de la statistique à Montréal le vendredi 15 mars 2019 Le Sommet de la statistique à Montréal (SÉSÀM) 2019 est un événement qui réunira au cours d’une journée d’activités et de séminaires les étudiants en statistique des universités québécoises. Avec des conférences plénières, des séminaires étudiants et un concours de conférences-éclairs, le SÉSÀM offrira une occasion privilégiée pour le partage et la discussion entre étudiant-es et avec des chercheurs de renom. Un dîner et un cocktail en soirée vous permettront d'échanger et d'élargir votre réseau, le tout dans une ambiance chaleureuse et décontractée. Le 15 mars 2019, c'est un rendez-vous à ne pas manquer! ## Colloque des sciences mathématiques du Québec - Shmuel Weinberger, University of Chicago le vendredi 15 mars 2019 Persistent homology as an invariant, rather than as an approximation Persistent homology is a very simple idea that was initially introduced as a way of understanding the underlying structure of an object from, perhaps noisy, samples of the object, and has been used as a tool in biology, material sciences, mapping and elsewhere. I will try to explain some of this, but perhaps also some more mathematical applications within geometric group theory. Then I'd like to pivot and study the part that traditionally has been thrown away, and show that this piece is relevant to approximation theory (a la Chebyshev), closed geodesics (a la Gromov), and to problems of quantitative topology (joint work with Ferry, Chambers, Dotter, and Manin). Date / Heure: Vendredi, 15 mars 2019 - 16:00 Lieu: McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104 ## Colloque des sciences mathématiques du Québec - Sarah Harrison, McGill University le vendredi 22 février 2019 Quantum Modularity in Topology in Physics I will discuss a set of inter-related phenomena in topology, physics, and number theory. A natural question in topology is the construction of homological invariants of 3-manifolds. These turn out to be related to certain special 3- dimensional quantum field theories in physics. Both of these scenarios exhibit a fascinating number theoretic phenomenon: quantum modularity. Quantum modular forms, introduced by Zagier, are functions defined only at rational numbers, and in the most general cases are neither analytic nor modular. It is still an open question to develop a general theory which encompasses their behavior. I will overview these relations and discuss recent advances which may shed light on some of these questions. Date / Heure: Vendredi, 22 février 2019 - 16:00 Lieu: McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104 ## Colloque des sciences mathématiques du Québec - Fanny Kassel, CNRS, Institut des Hautes Études Scientifiques le vendredi 15 février 2019 Discrete subgroups of Lie groups and geometric structure Discrete subgroups of Lie groups play a fundamental role in several areas of mathematics. Discrete subgroups of SL(2,R) are well understood, and classified by the geometry of the corresponding hyperbolic surfaces. On the other hand, discrete subgroups of SL(n,R) for n>2, beyond lattices, remain quite mysterious. While lattices in this setting are rigid, there also exist more flexible "thinner" discrete subgroups, which may have large and interesting deformation spaces (some of them with topological and geometric analogies to the Teichmüller space of a surface, giving rise to so-called "higher Teichmüller theory"). We will survey recent progress in constructing and understanding such discrete subgroups from a geometric and dynamical viewpoint. Date / Heure: Vendredi, 15 février 2019 - 16:00 Lieu: McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104 ## Colloque des sciences mathématiques du Québec - Viktor Ginzburg, University of California, Santa Cruz le vendredi 8 février 2019 Periodic orbits of Hamiltonian systems: the Conley conjecture and beyond One distinguishing feature of Hamiltonian dynamical systems is that such systems, with very few exceptions, tend to have numerous periodic orbits and these orbits carry a lot of information about the dynamics of the system. In 1984 Conley conjectured that a Hamiltonian diffeomorphism (i.e., the time-one map of a Hamiltonian flow) of a torus has infinitely many periodic points. This conjecture was proved by Hingston some twenty years later, in 2004. Similar results for Hamiltonian diffeomorphisms of surfaces of positive genus were also established by Franks and Handel. Of course, one can expect the Conley conjecture to hold for a much broader class of closed symplectic manifolds and this is indeed the case as has been proved by Gurel, Hein and the speaker. However, the conjecture is known to fail for some, even very simple, phase spaces such as the sphere. These spaces admit Hamiltonian diffeomorphisms with finitely many periodic orbits -- the so-called pseudo-rotations -- which are of particular interest in dynamics. In this talk, mainly based on joint work with Gurel, we will discuss the role of periodic orbits in Hamiltonian dynamics and the methods used to prove their existence, and examine the situations where the Conley conjecture does not hold. Date / Heure: Vendredi,8 février 2019 - 16:00 Lieu: UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, salle PK-5115 ## Colloque des sciences mathématiques du Québec - Mina Teicher, Bar-Ilan University le vendredi 1 février 2019 How does the brain works? We will go over the basic challenges for understanding the human brain, the role if mathematics and three examples , one in theoretical neuroscience and two in neuro medicine. Date / Heure: Vendredi, 1 février 2019 - 16:00 Lieu: McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104 ## Colloque des sciences mathématiques du Québec - Vadim Kaloshin (University of Maryland) le vendredi 25 janvier 2019 Conférence Nirenberg du CRM en analyse géométrique: Stochastic diffusive behavior at Kirkwood gaps One of the well known indications of instability in the Solar system is the presence of Kirkwood gaps in the Asteroid belt. The gaps correspond to resonance between their periods and the period of Jupiter. The most famous ones are period ratios 3:1, 5:2, 7:3. In the 1980s, J. Wisdom and, independently, A. Neishtadt discovered one mechanism of creation for the 3:1 Kirkwood gap. We propose another mechanism of instabilities, based on an a priori chaotic underlying dynamical structure. As an indication of chaos at the Kirkwood gaps, we show that the eccentricity of Asteroids behaves like a stochastic diffusion process. Along with the famous KAM theory this shows a mixed behavior at the Kirkwood gaps: regular and stochastic. This is a joint work with M. Guardia, P. Martin and P. Roldan. Date / Heure: Vendredi, 25 janvier 2019 - 16:00 Lieu: CRM, Université de Montréal, Pavillon André-Aisenstadt, salle 6254 ## Colloque des sciences mathématiques du Québec - Valentino Tosatti, Northwestern University le vendredi 18 janvier 2019 The boundary of the Kähler cone On any compact Kähler manifold the space of cohomology classes of all possible Kähler forms is an open convex cone inside a finite-dimensional vector space. I will discuss some recent advances in understanding the geometric and analytic properties of the classes on the boundary of this cone, and describe several applications. Date / Heure: Vendredi, 18 janvier 2019 - 16:00 Lieu: McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104 ## SUMM 2019 le vendredi 11 janvier 2019 Les Séminaires Universitaires en Mathématiques à Montréal (SUMM) sont un évènement organisé annuellement par des étudiants de premier cycle en mathématiques et ayant lieu dans l’une des quatre universités montréalaises. L’édition 2019 du SUMM se déroulera les 11, 12 et 13 janvier à l’Université de Montréal. ## Colloque des sciences mathématiques du Québec - Andreas Kyprianou, University of Bath le vendredi 11 janvier 2019 The mathematics of neutron transport We discuss the evolving mathematical view of the Neutron Transport Equation (NTE), which describes the flux of neutrons through inhomogeneous fissile materials. Neutron transport theory emerges in the rigorous mathematical literature in the mid-1950s. Its treatment as an integro-differential equation eventually settled in the applied mathematics literature through the theory of c_0-semigroup theory, thanks to the work of Robert Dautray, Louis Lions and collaborators. This paved the way for its spectral analysis which has played an important role in the design of nuclear reactors and nuclear medical equipment. We also look at the natural probabilistic approach to the NTE which has largely been left behind. Connections with methods of branching particle systems, quasi-stationarity for Markov processes and stochastic analysis all lead new ways of characterising solutions and spectral behaviour the NTE. In particular this, in turn, leads to the suggestion of completely new Monte-Carlo algorithms, which has genuine industrial impact. Date / Heure: Vendredi, 11 janvier 2019 - 16:00 Lieu: McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104 ## Colloque des sciences mathématiques du Québec - Peter Hintz, MIT le vendredi 7 décembre 2018 Stability problems in general relativity There exist several remarkable explicit solutions of Einstein's field equations of General Relativity. A fundamental problem (with implications even for experimental science) is to determine their properties upon perturbation of their initial conditions. I will describe two such solutions: Minkowski spacetime, which is a model for regions of the universe without matter or energy content; and the Kerr--de Sitter family of spacetimes describing (rotating) black holes. In recent work, in parts joint with A. Vasy, we prove global existence and obtain a precise asymptotic description of perturbations of these spacetimes. I will explain these results and indicate the role played by modern microlocal and spectral theoretic techniques in our proofs. Date / Heure: Vendredi, 7 décembre 2018 - 16:00 Lieu: UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, salle PK-5115 ## Colloque des sciences mathématiques du Québec - Marcin Sabok, McGill University le vendredi 30 novembre 2018 Completeness of the isomorphism problem for separable C*-algebras In logic and computer science one often studies the complexity of decision problems. In mathematical logic this leads to the program of study of relative complexity of isomorphism problems and determining various complexity classes. Broadly speaking, a problem p in a class C is complete in C if any other problem in C reduces to p. The isomorphism problem for separable C*-algebras has been studied since the 1960's and evolved into the Elliott program that classifies C*-algebras via their K-theoretic invariants. During the talk I will discuss the complexity of the isomorphism problem for separable C*-algebras and its completeness in the class of orbit equivalence relations. Date / Heure: Vendredi, 30 novembre 2018 - 16:00 Lieu: McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104 ## Colloque des sciences mathématiques du Québec - Svetlana Jitomirskaya, UC Irvine / Chaire Aisenstadt 2018 le vendredi 16 novembre 2018 Sharp arithmetic transitions for 1D quasiperiodic operators A very captivating question in solid state physics is to determine/understand the hierarchical structure of spectral features of operators describing 2D Bloch electrons in perpendicular magnetic fields, as related to the continued fraction expansion of the magnetic flux. In particular, the hierarchical behavior of the eigenfunctions of the almost Mathieu operators, despite significant numerical studies and even a discovery of Bethe Ansatz solutions has remained an important open challenge even at the physics level. I will present a complete solution of this problem in the exponential sense throughout the entire localization regime. Namely, I will describe the continued fraction driven hierarchy of local maxima, and a universal (also continued fraction expansion dependent) function that determines local behavior of all eigenfunctions around each maximum, thus giving a complete and precise description of the hierarchical structure. In the regime of Diophantine frequencies and phase resonances there is another universal function that governs the behavior around the local maxima, and a reflective-hierarchical structure of those, phenomena not even described in the physics literature. These results lead also to the proof of sharp arithmetic transitions between pure point and singular continuous spectrum, in both frequency and phase, as conjectured since 1994. This part of the talk is based on the papers joint with W. Liu. Within the singular continuous regime, it is natural to look for further, dimensional transitions. I will present a sharp arithmetic transition result in this regard that holds for the entire class of analytic quasiperiodic potentials, based on the joint work with S. Zhang. Date / Heure: Vendredi, 16 novembre 2018 - 16:00 Lieu: CRM, Université de Montréal, Pavillon André-Aisenstadt, salle 1140 ## Colloque des sciences mathématiques du Québec - Akshay Venkatesh, IAS le vendredi 9 novembre 2018 Period mappings and Diophantine equations I will give some friendly examples introducing the period mapping. This is an analytic mapping which controls many aspects of how algebraic varieties change in families. After that I will explain joint work with Brian Lawrence which shows that one can exploit transcendence properties of the period mapping to prove results about Diophantine equations. For example we give another proof of the Mordell conjecture (originally proved by Faltings): there are only finitely many rational points on an algebraic curve over Q whose genus is at least 2. Date / Heure: Vendredi, 9 novembre 2018 - 16:00 Lieu: McGill University, Burnside Hall , 805 O., rue Sherbrooke ATTENTION - SALLE 1B45 - ATTENTION ## Colloque des sciences mathématiques du Québec - Benjamin Rossman (University of Toronto - Lauréat 2018 du Prix André-Aisenstadt) le vendredi 2 novembre 2018 The complexity of detecting cliques and cycles in random graphs A strong form of the P ≠ NP conjecture holds that no algorithm faster than nO(k) solves the k-clique problem with high probability when the input is an Erdös–Rényi random graph with an appropriate edge density. Toward this conjecture, I will describe a line of work lower-bounding the average-case complexity of k-clique (and other subgraph isomorphism problems) in weak models of computation: namely, restricted classes of boolean circuits and formulas. Along the way I will discuss some of the history and current frontiers in Circuit Complexity.Joint work with Kenichi Kawarabayashi, Yuan Li and Alexander Razborov. Joint work with Ken-ichi Kawarabayashi, Yuan Li and Alexander Razborov. Date / Heure: Vendredi, 2 novembre 2018 - 16:00 Lieu: CRM, Université de Montréal, Pavillon André-Aisenstadt, salle 1355 ## Colloque des sciences mathématiques du Québec - David P. Ruelle (Institut des Hautes Études Scientifiques) le vendredi 26 octobre 2018 A generalized detailed balance relation The transition probabilities of reactions J -> K and K -> J in a thermal bath are related because of the time reversal symmetry of fundamental physical laws. The relation is known as detailed balance relation. We study the problems that arise in obtaining a rigorous proof of detailed balance, using deterministic rather than Markovian dynamics. J. Englands’ biological applications of detailed balance are briefly considered. Date / Heure: Vendredi, 26 octobre 2018 - 16:00 Lieu: CRM, Université de Montréal, Pavillon André-Aisenstadt, salle 6254 ## Colloque des sciences mathématiques du Québec - Ariel Zhitnitsky (UBC - Lauréat 2018 du Prix ACP-CRM) le vendredi 19 octobre 2018 Vacuum Energy of the Universe and nontrivial topological sectors in Quantum Field Theory I discuss a new scenario for early cosmology when the inflationary de Sitter phase emerges dynamically. This genuine quantum effect occurs as a result of dynamics of the topologically nontrivial sectors in a strongly coupled non-abelian gauge theory in an expanding universe. I argue that the key element for this idea to work is the presence of nontrivial holonomy in strongly coupled gauge theories. The effect is global in nature, non-analytical in coupling constant, and cannot be formulated in terms of a gradient expansion in an effective local field theory. I explain the basic ideas of this framework using a simplified 2D quantum field theory where precise computations can be carried out in theoretically controllable way. I move on to generalize the computations to 4D non-abelian gauge field theories. The last (and most important for cosmological applications) part of my talk is based on recent paper [arXiv:1709.09671]. Date / Heure: Vendredi, 19 octobre 2018 - 16:00 Lieu: CRM, Université de Montréal, Pavillon André-Aisenstadt, salle 1140 ## Colloque des sciences mathématiques du Québec - David Haziza (Univ. de Montréal - Lauréat 2018 du Prix CRM-SSC) le vendredi 12 octobre 2018 Robust estimation in the presence of influential units for skewed finite and infinite populations Many variables encountered in practice (e.g., economic variables) have skewed distributions. The latter provide a conducive ground for the presence of influential observations, which are those that have a drastic impact on the estimates if they were to be excluded from the sample. We examine the problem of influential observations in a classical statistic setting as well as in a finite population setting that includes two main frameworks: the design-based framework and the model-based framework. Within each setting, classical estimators may be highly unstable in the presence of influential units. We propose a robust estimator of the population mean based on the concept of conditional bias of a unit, which is a measure of influence. The idea is to reduce the impact of the sample units that have a large conditional bias. The proposed estimator depends on a cut-off value. We suggest selecting the cut-off value that minimizes the maximum absolute estimated conditional bias with respect to the robust estimator. The properties of the proposed estimator will be discussed. Finally, the results of a simulation study comparing the performance of several estimators in terms of bias and mean square error will be presented. Date / Heure: Vendredi 12 octobre 2018 - 16:00 Lieu: CRM, Université de Montréal, Pavillon André-Aisenstadt, salle 6254 ## Colloque des sciences mathématiques du Québec - Mireille Bousquet-Mélou (CNRS - Université de Bordeaux) le vendredi 5 octobre 2018 Counting lattice walks confined to cones The study of lattice walks confined to cones is a very lively topic in combinatorics and in probability theory, which has witnessed rich developments in the past 20 years. In a typical problem, one is given a finite set of allowed steps S in Zd, and a cone C in Rd. Clearly, there are |S|n walks of length n that start from the origin and take their steps in S. But how many of them remain the the cone C? One of the motivations for studying such questions is that lattice walks are ubiquitous in various mathematical fields, where they encode important classes of objects: in discrete mathematics (permutations, trees, words...), in statistical physics (polymers...), in probability theory (urns, branching processes, systems of queues), among other fields. The systematic study of these counting problems started about 20 years ago. Beforehand, only sporadic cases had been solved, with the exception of walks with small steps confined to a Weyl chamber, for which a general reflection principle had been developed. Since then, several approaches have been combined to understand how the choice of the steps and of the cone influence the nature of the counting sequence a(n), or of the the associated series A(t)=\sum a(n) tn. For instance, if C is the first quadrant of the plane and S only consists of "small" steps, it is now understood when A(t) is rational, algebraic, or when it satisfies a linear, or a non-linear, differential equation. Even in this simple case, the classification involves tools coming from an attractive variety of fields: algebra on formal power series, complex analysis, computer algebra, differential Galois theory, to cite just a few. And much remains to be done, for other cones and sets of steps. This talk will survey these recent developments, and conclude a series of talks by the author, in the framework of the Aisenstadt chair. Date / Heure: Vendredi, 5 octobre 2018 - 16:00 Lieu: CRM, Université de Montréal, Pavillon André-Aisenstadt, salle 6254 ## Colloque des sciences mathématiques du Québec - Hans-Otto Walther (Universität Giessen) le vendredi 28 septembre 2018 A delay differential equation with a solution whose shortened segments are dense Simple-looking autonomous delay differential equations x'(t)=f(x(t-r)) with a real function f and single time lag r>0 can generate complicated (chaotic) solution behaviour, depending on the shape of f. The same could be shown for equations with a variable, state-dependent delay r=d(xt), even for the linear case f(\xi)=-\alpha\,\xi with \alpha>0. Here the argument xt of the delay functional d is the history of the solution x between t-r and t defined as the function xt:[-r,0] to\mathbb{R}) given by xt(s)=x(t+s). So the delay alone may be responsible for complicated solution behaviour. In both cases the complicated behaviour which could be established occurs in a thin dust-like invariant subset of the infinite-dimensional Banach space or manifold of functions [-r,0]\to\mathbb{R} on which the delay equation defines a nice semiflow. The lecture presents a result which grew out of an attempt to obtain complicated motion on a larger set with non-empty interior, as certain numerical experiments seem to suggest. For some r>1 we construct a delay functional d:Y\to(0,r), Y an infinite-dimensional subset of the space C1([-r,0],\mathbb{R}), so that the equation x'(t)=-\alpha\,x(t-d(x_t)) has a solution whose short segments x_t|[-1,0], t\ge0, are dense in the space C1([-1,0],\mathbb{R}). This implies a new kind of complicated behaviour of the flowline [0,\infty)\ni t\mapsto xt\in C1r. Reference: H. O. Walther, A delay differential equation with a solution whose shortened segments are dense. J. Dynamics Dif. Eqs., to appear. Date / Time: Le vendredi 28 septembre 2018 - 16:00 Venue: McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104 ## Colloque des sciences mathématiques du Québec - Ezra Miller (Duke University) le vendredi 21 septembre 2018 Algebraic structures for topological summaries of data This talk introduces an algebraic framework to encode, compute, and analyze topological summaries of data. The main motivating problem, from evolutionary biology, involves statistics on a dataset comprising images of fruit fly wing veins, which amount to embedded planar graphs with varying combinatorics. Additional motivation comes from statistics more generally, the goal being to summarize unknown probability distributions from samples. The algebraic structures for topological summaries take their cue from graded polynomial rings and their modules, but the theory is complicated by the passage from integer exponent vectors to real exponent vectors. The key to making the structures practical for data science applications is a finiteness condition that encodes topological tameness -- which occurs in all modules arising from data -- robustly, in equivalent combinatorial and homological algebraic ways. Out of the tameness condition surprisingly falls much of ordinary commutative algebra, including syzygy theorems and primary decomposition. Date / Heure: Vendredi, le 21 septembre 2018 - 16:00 Lieu: UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, room PK-5115 ## Colloque des sciences mathématiques du Québec - Sylvia Serfaty (Courant Institute, NYU) le vendredi 14 septembre 2018 Systems of points with Coulomb interactions Large ensembles of points with Coulomb interactions arise in various settings of condensed matter physics, classical and quantum mechanics, statistical mechanics, random matrices and even approximation theory, and they give rise to a variety of questions pertaining to analysis, Partial Differential Equations and probability. We will first review these motivations, then present the "mean-field" derivation of effective models and equations describing the system at the macroscopic scale. We then explain how to analyze the next order behavior, giving information on the configurations at the microscopic level and connecting with crystallization questions, and finish with the description of the effect of temperature. Date / Heure: Vendredi, 14 septembre 2018 - 16:00 Lieu: CRM, Université de Montréal, Pavillon André-Aisenstadt, salle 6254 ## Colloque des sciences mathématiques du Québec - Kasia Rejzner (University of York) le vendredi 7 septembre 2018 Mathematical challenges in constructing quantum field theory models This talk is an overview of algebraic quantum field theory (AQFT) and its perturbative generalization: pAQFT. Both are axiomatic systems meant to provide foundations for quantum field theory (the theory underlying particle physics). I will explain what is the current status of constructing physically relevant models in both approaches and present future perspectives. The most recent results include applications of pAQFT in Yang-Mills theories and effective quantum gravity, as well as some progress in understanding how to go beyond the perturbation theory. Date / Heure: Vendredi, 7 septembre 2018 - 16:00 Lieu: CRM, Université de Montréal, Pavillon André-Aisenstadt, salle 6254 ## Atelier au Festival Eurêka animé par les étudiants de l’ISM le dimanche 10 juin 2018 Le carréousel du géomètre Sur le thème du mouvement, l'ISM vous convie à une séance d'activités dirigées pour tout âge. Un bric-à-brac de curiosités mathématiques viendra chambouler vos présupposés en matière de roulement. Roues carrées, bouches d'égoût savamment réalisées et perceuses de trous carrés ne seront que quelques-unes des curiosités avec lesquelles vous pourrez expérimenter. Une activité de programmation permettra de généraliser les constructions présentées et de tester les limites de nos hypothèses de modélisation! Rendez-vous au Festival Eurêka au Vieux-Port de Montréal Le dimanche, 10 juin 2018 16h00 à 18h00 Conçu et animé par: Alexis Langlois-Rémillard, Olivier Binette et Pierre-Alexandre Mailhot ## École d'été McGill / ISM en statistique de la santé le lundi 28 mai 2018 L’école d’été se déroulera à l’Université McGill à Montréal du 28 mai au 1er juin 2018. L’école précèdera le Congrès annuel de la Société statistique du Canada qui aura lieu également à l’Université MCgill. Le congrès sera suivi d’un programme d’un mois au Centre de recherches mathématiques sur « L’inférence causale en présence de dépendance et de structure de réseau: stratégies de modélisation et de sélection de modèles ». ## Colloque panquébécois des étudiants et étudiantes de l’ISM le vendredi 25 mai 2018 Le département de mathématiques de l’Université de Sherbrooke vous invite à prendre part à la 21e édition du colloque panquébécois des étudiants et étudiantes de l’ISM qui se déroulera du 25 au 27 mai 2018. Cette année, c’est trois chercheurs et une chercheuse qui présenteront une partie de leur recherche dans le cadre des conférences plénières. Louigi Addario-Berry de l’Université McGill, Karim Oualkacha de l’Université du Québec à Montréal, Hugo Chapdelaine de l’Université Laval ainsi que Vasilisa Schramchenko de l’Université de Sherbrooke se partageront l’auditorium au cours de la fin de semaine. Nous vous invitons également à venir partager vos recherches dans le cadre d’une présentation étudiante de 20 minutes. Belle ville, beau campus, bonne bouffe et bonne compagnie sont à l’horaire pour cette fin de semaine ! Vous pouvez trouver le formulaire d’inscription, les détails concernant l’évènement ainsi que les informations pour nous joindre sur notre site internet : https://www.ism21colloque.com. ## Les 24 heures de science: Les mathématiques de la magie! le samedi 12 mai 2018 Vous avez toujours rêvé de concevoir vos propres tours de magie? Vous souhaitez savoir ce que les mathématiques peuvent vous apporter? L'Institut des sciences mathématiques vous invite à voir des tours de magie utilisant cartes, noeuds et mathématiques, mais surtout pas votre intuition... elle pourrait être trompeuse! Samedi 12 mai, 11h à 14h UQAM, Pavillon Président-Kennedy 201, ave du Président-Kennedy local PK-1630, Montréal ## Colloque des sciences mathématiques du Québec - Emmanuel Hebey (Université de Cergy-Pontoise) le vendredi 4 mai 2018 Klein-Gordon-Maxwell-Proca systems in the Riemannian setting We intend to give a general talk about Klein-Gordon-Maxwell-Proca systems which we aim to be accessible to a broad audience. We will insist on the Proca contribution and then discuss the kind of results one can prove in the electro-magneto static case of the equations. Date / Heure: Vendredi, le 4 mai 2018 - 16h00 Lieu: UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, salle PK-5115 ## Colloque des sciences mathématiques du Québec - Eva Bayer (Ecole Polytechnique Fédérale de Lausane) le vendredi 13 avril 2018 Local-global principles in number theory One of the classical tools of number theory is the so-called local-global principle, or Hasse principle, going back to Hasse's work in the 1920's. His first results concern quadratic forms, and norms of number fields. Over the years, many positive and negative results were proved, and there is nowa huge number of results in this topic. This talk will present some old and new results, in particular in the continuation of Hasse's cyclic norm theorem. These have been obtained jointly with Parimala and Tingyu Lee. Date / Heure: Vendredi, le 13 avril 2018 - 16:00 Lieu: UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, salle PK-5115 ## Colloque des sciences mathématiques du Québec - Glenn Stevens (Boston University) le jeudi 1 mars 2018 p-Adic Variation in the Theory of Automorphic Forms This will be an expository lecture intended to illustrate through examples the theme of p-adic variation in the classical theory of modular forms. Classically, modular forms are complex analytic objects, but because their fourier coefficients are typically integral, it is possible to do elementary arithmetic with them. Early examples arose already in the work of Ramanujan. Today one knows that modular forms encode deep arithmetic information about elliptic curves and galois representations. The main goal of the lecture will be to motivate a beautiful theorem of Robert Coleman and Barry Mazur, who constructed the so-called Eigenvariety, which leads to a geometric approach to varying modular forms, their associated galois representations, as well as their L-functions, in p-adic analytic families. We will briefly discuss important applications to Number Theory and Iwasawa Theory. Date / Heure: Jeudi, 1er mars 2018 - 15h30 Lieu: Université Laval, salle 3840, Pavillon Alexandre-Vachon ## Colloque des sciences mathématiques du Québec - Sabin Cautis (University of British Columbia) le vendredi 23 février 2018 Cluster theory of the coherent Satake category The affine Grassmannian, though a somewhat esoteric looking object at first sight, is a fundamental algebro-geometric construction lying at the heart of a series of ideas connecting number theory (and the Langlands program) to geometric representation theory, low dimensional topology and mathematical physics. Historically it is popular to study the category of constructible perverse sheaves on the affine Grassmannian. This leads to the *constructible* Satake category and the celebrated (geometric) Satake equivalence. More recently it has become apparent that it makes sense to also study the category of perverse *coherent* sheaves (the coherent Satake category). Motivated by certain ideas in mathematical physics this category is conjecturally governed by a cluster algebra structure. We will illustrate the geometry of the affine Grassmannian in an elementary way, discuss what we mean by a cluster algebra structure and then describe a solution to this conjecture in the case of general linear groups. Date / Heure: Vendredi, le 23 février 2018 - 16:00 Lieu: UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, room PK-5115 ## Colloque des sciences mathématiques du Québec - Alexander Turbiner (UNAM) le vendredi 16 février 2018 Quantum n-body problem: generalized Euler coordinates (from J-L Lagrange to Figure Eight by Moore and Ter-Martirosyan, then and today) The potential of the n-body problem, both classical and quantum, depends only on the relative (mutual) distances between bodies. By generalized Euler coordinates we mean relative distances and angles. Their advantage over Jacobi coordinates is emphasized. The NEW IDEA is to study trajectories in both classical, and eigenstates in quantum systems which depends on relative distances ALONE. We show how this study is equivalent to the study of (i) the motion of a particle (quantum or classical) in curved space of dimension n(n-1)/2 or the study of (ii) the Euler-Arnold (quantum or classical) - sl(n(n-1)/2, R) algebra top. The curved space of (i) has a number of remarkable properties. In the 3-body case the de-Quantization of quantum Hamiltonian leads to a classical Hamiltonian which solves a ~250-years old problem posed by Lagrange on 3-body planar motion. Date : le vendredi 16 février 2018 Heure : 16 h Lieu : UdeM, Pavillon André-Aisenstadt, salle 6254 ## Colloque des sciences mathématiques du Québec - Xiao-Li Meng (Harvard University) le vendredi 16 février 2018 The Law of Large Populations: The return of the long-ignored N and how it can affect our 2020 vision For over a century now, we statisticians have successfully convinced ourselves and almost everyone else, that in statistical inference the size of the population N can be ignored, especially when it is large. Instead, we focused on the size of the sample, n, the key driving force for both the Law of Large Numbers and the Central Limit Theorem. We were thus taught that the statistical error (standard error) goes down with n typically at the rate of 1/√n. However, all these rely on the presumption that our data have perfect quality, in the sense of being equivalent to a probabilistic sample. A largely overlooked statistical identity, a potential counterpart to the Euler identity in mathematics, reveals a Law of Large Populations (LLP), a law that we should be all afraid of. That is, once we lose control over data quality, the systematic error (bias) in the usual estimators, relative to the benchmarking standard error from simple random sampling, goes up with N at the rate of √N. The coefficient in front of √N can be viewed as a data defect index, which is the simple Pearson correlation between the reporting/recording indicator and the value reported/recorded. Because of the multiplier√N, a seemingly tiny correlation, say, 0.005, can have detrimental effect on the quality of inference. Without understanding of this LLP, “big data” can do more harm than good because of the drastically inflated precision assessment hence a gross overconfidence, setting us up to be caught by surprise when the reality unfolds, as we all experienced during the 2016 US presidential election. Data from Cooperative Congressional Election Study (CCES, conducted by Stephen Ansolabehere, Douglas River and others, and analyzed by Shiro Kuriwaki), are used to estimate the data defect index for the 2016 US election, with the aim to gain a clearer vision for the 2020 election and beyond. Date: Le vendredi 16 février 2018 Heure: 15h30 Lieu: Université McGill , OTTO MAASS 217 ## Colloque des sciences mathématiques du Québec - Egor Shelukhin (Université de Montréal) le vendredi 9 février 2018 Persistence modules in symplectic topology I n order to resolve Vladimir Arnol'd's famous conjecture from the 1960's, giving lower bounds on the number of fixed points of Hamiltonian diffeomorphisms of a symplectic manifold, Andreas Floer has associated in the late 1980's a homology theory to the Hamiltonian action functional on the loop space of the manifold. It was known for a long time that this homology theory can be filtered by the values of the action functional, yielding information about metric invariants in symplectic topology (Hofer's metric, for example). We discuss a recent marriage between the filtered version of Floer theory and persistent homology, a new field of mathematics that has its origins in data analysis, providing examples of new ensuing results. Date / Heure: Vendredi, le 9 février 2018 - 16:00 Lieu: UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, room PK-5115 ## SUMM 2018 le vendredi 12 janvier 2018 Les Séminaires Universitaires en Mathématiques à Montréal (SUMM) est un évènement organisé annuellement par des étudiant-es de premier cycle en mathématiques et ayant lieu dans l’une des quatre universités montréalaises. L’association des Séminaires Universitaires en Mathématiques à Montréal (SUMM) a pour but d’organiser pour les étudiants au baccalauréat un colloque annuel de mathématiques. Au cours de la conférence d’une durée d’une fin de semaine, le SUMM invite les étudiants de premier cycle à partager des notions ou problèmes mathématiques qui leur sont d’un intérêt particulier. De plus, le séminaire présente les exposés de quatre professeurs invités. L’objectif principal de la conférence, organisée par des étudiants de l’Université Concordia, de l’Université McGill, de l’Université de Montréal et de l’Université du Québec à Montréal et à laquelle les étudiants de Montréal et du reste du Canada sont invités, est de faciliter le partage d’intérêts et d’idées et de mettre en relation les étudiants des différentes universités afin de créer un milieu universitaire de premier cycle qui soit dynamique et stimulant. Pour sa neuvième édition, se déroulant le 12, 13 et 14 janvier 2018 à l’université Concordia, toutes les personnes intéressées à participer à l’événement sont encouragés à s’inscrire sur notre site dès la mise en ligne des inscriptions. ## Colloque des sciences mathématiques du Québec - Semyon Dyatlov (University of California, Berkeley) le vendredi 12 janvier 2018 What is quantum chaos? Where do eigenfunctions of the Laplacian concentrate as eigenvalues go to infinity? Do they equidistribute or do they concentrate in an uneven way? It turns out that the answer depends on the nature of the geodesic flow. I will discuss various results in the case when the flow is chaotic: the Quantum Ergodicity theorem of Shnirelman, Colin de Verdière, and Zelditch, the Quantum Unique Ergodicity conjecture of Rudnick-Sarnak, the progress on it by Lindenstrauss and Soundararajan, and the entropy bounds of Anantharaman-Nonnenmacher. I will conclude with a recent lower bound on the mass of eigenfunctions obtained with Jin. It relies on a new tool called "fractal uncertainty principle" developed in the works with Bourgain and Zahl. Date : le vendredi 12 janvier 2018 Heure : 16 h Lieu : UdeM, Pavillon André-Aisenstadt, salle 6254 ## Colloque des sciences mathématiques du Québec - Anthony Bonato (Ryerson University) le jeudi 14 décembre 2017 The new world of infinite random geometric graphs The infinite random or Rado graph R has been of interest to graph theorists, probabilists, and logicians for the last half-century. The graph R has many peculiar properties, such as its categoricity: R is the unique countable graph satisfying certain adjacency properties. Erdös and Rényi proved in 1963 that a countably infinite binomial random graph is isomorphic to R. Random graph processes giving unique limits are, however, rare. Recent joint work with Jeannette Janssen proved the existence of a family of random geometric graphs with unique limits. These graphs arise in the normed space$\ell^n_\infty$, which consists of$\mathbb{R}^n$equipped with the$L_\infty$-norm. Balister, Bollobás, Gunderson, Leader, and Walters used tools from functional analysis to show that these unique limit graphs are deeply tied to the$L_\infty$-norm. Precisely, a random geometric graph on any normed, finite-dimensional space not isometric$\ell^n_\infty$gives non-isomorphic limits with probability 1. With Janssen and Anthony Quas, we have discovered unique limits in infinite dimensional settings including sequences spaces and spaces of continuous functions. We survey these newly discovered infinite random geometric graphs and their properties. Date: Le jeudi 14 décembre 2017 Time: 15:30 Lieu: Université Laval, Pavillon Vachon, room 2830 ## Colloque des sciences mathématiques du Québec - James Maynard (Oxford) le vendredi 8 décembre 2017 Primes with missing digits Many famous open questions about primes can be interpreted as questions about the digits of primes in a given base. We will talk about recent work showing there are infinitely many primes with no 7 in their decimal expansion. (And similarly with 7 replaced by any other digit.) This shows the existence of primes in a 'thin' set of numbers (sets which contain at most X1-c elements less than X) which is typically very difficult. Date / Heure: Vendredi, le 8 décembre 2017 - 16:00 Lieu: UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, room PK-5115 ## Colloque des sciences mathématiques du Québec - David R. Bellhouse (Western) le vendredi 24 novembre 2017 150 years (and more) of data analysis in Canada As Canada celebrates its 150th anniversary, it may be good to reflect on the past and future of data analysis and statistics in this country. In this talk, I will review the Victorian Statistics Movement and its effect in Canada, data analysis by a Montréal physician in the 1850s, a controversy over data analysis in the 1850s and 60s centred in Montréal, John A. MacDonald’s use of statistics, the Canadian insurance industry and the use of statistics, the beginning of mathematical statistics in Canada, the Fisherian revolution, the influence of Fisher, Neyman and Pearson, the computer revolution, and the emergence of data science. Date: Vendredi, le 24 novembre 2017 Heure: 15h30 Lieu: Université McGill, Pavillon Leacock, salle LEA 232 ## Colloque des sciences mathématiques du Québec - Stanislav Smirnov (University of Geneva and Skolkovo Institute of Science and Technology) le vendredi 24 novembre 2017 Complex analysis and 2D statistical physics Over the last decades, there was much progress in understanding 2D lattice models of critical phenomena. It started with several theories, developed by physicists. Most notably, Conformal Field Theory led to spectacular predictions for 2D lattice models: e.g., critical percolation cluster a.s. has Hausdorff dimension 91/48, while the number of self-avoiding length N walks on the hexagonal lattice grows like (\sqrt{2+\sqrt{2}})N N11/32. While the algebraic framework of CFT is rather solid, rigorous arguments relating it to lattice models were lacking. More recently, mathematical approaches were developed, allowing not only for rigorous proofs of many such results, but also for new physical intuition. We will discuss some of the applications of complex analysis to the study of 2D lattice models. Date : le vendredi 24 novembre 2017 Heure : 16 h Lieu : UdeM, Pavillon André-Aisenstadt, salle 6254 ## Colloque des sciences mathématiques du Québec - Jun-Cheng Wei (UBC) le vendredi 17 novembre 2017 Recent progress on De Giorgi Conjecture Classifying solutions to nonlinear partial differential equations are fundamental research in PDEs. In this talk, I will report recent progress made in classifying some elementary PDEs, starting with the De Giorgi Conjecture (1978). I will discuss the classification of global minimizers and finite Morse index solutions, relation with minimal surfaces and Toda integrable systems, as well as recent exciting developments in fractional De Giorgi Conjecture. Date / Heure: Vendredi, le 17 novembre 2017 - 16:00 Lieu: UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, room PK-5115 ## Colloque des sciences mathématiques du Québec - Justin Solomon (MIT) le vendredi 27 octobre 2017 Beneath the Surface: Geometry Processing at the Intrinsic/Extrinsic Interface Algorithms for analyzing 3D surfaces find application in diverse fields from computer animation to medical imaging, manufacturing, and robotics. Reflecting a bias dating back to the early development of differential geometry, a disproportionate fraction of these algorithms focuses on discovering intrinsic shape properties, or those measurable along a surface without considering the surrounding space. This talk will summarize techniques to overcome this bias by developing a geometry processing pipeline that treats intrinsic and extrinsic geometry democratically. We describe theoretically-justified, stable algorithms that can characterize extrinsic shape from surface representations. In particular, we will show two strategies for computational extrinsic geometry. In our first approach, we will show how the discrete Laplace-Beltrami operator of a triangulated surface accompanied with the same operator for its offset determines the surface embedding up to rigid motion. In the second, we will treat a surface as the boundary of a volume rather than as a thin shell, using the Steklov (Dirichlet-to-Neumann) eigenproblem as the basis for developing volumetric spectral shape analysis algorithms without discretizing the interior. Date : le vendredi 27 octobre 2017 Heure : 16 h Lieu : UdeM, Pavillon André-Aisenstadt, salle 6254 ## Colloque des sciences mathématiques du Québec - Avi Soffer (Rutgers University) le vendredi 13 octobre 2017 Supercritical Wave Equations I will review the problem of Global existence for dispersive equations, in particular, supercritical equations. These equations who play a fundamental role in science, have been , and remain a major challenge in the field of Partial Differential Equations. They come in various forms, derived from Geometry, General Relativity, Fluid Dynamics, Field Theory. I present a new approach to classify the asymptotic behavior of wave equations, supercritical and others, and construct global solutions with large initial data. I will then describe current extensions to Nonlinear Schroedinger Equations. Date : le vendredi 13 octobre 2017 Heure : 16 h Lieu : UdeM, Pavillon André-Aisenstadt, salle 6254 ## Colloque des sciences mathématiques du Québec - John H. Conway (Princeton University) le vendredi 29 septembre 2017 The first field The “first field” is obtained by making the entries in its addition and multiplication tables be the smallest possibilities. It is really an interesting field that contains the integers, but with new addition and multiplication tables. For example, 2 x 2 = 3, 5 x 7 = 13, ... It extends to the infinite ordinals and the first infinite ordinal is the cube root of 2! Date : le vendredi 29 septembre 2017 Heure : 16 h Lieu : UdeM, Pavillon André-Aisenstadt, salle 1140 ## Colloque des sciences mathématiques du Québec (Conférence du lauréat du Prix Carl Herz) - Siyuan Lu (McGill) le vendredi 15 septembre 2017 Isometric embedding and quasi-local type inequality In this talk, we will first review the classic Weyl's embedding problem and its application in quasi-local mass. We will then discuss some recent progress on Weyl's embedding problem in general Riemannian manifold. Assuming isometric embedding into Schwarzschild manifold, we will further establish a quasi-local type inequality. This talk is based on works joint with Pengfei Guan and Pengzi Miao. Date / Heure: Vendredi, le 15 septembre 2017 - 16:00 Lieu: UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, room PK-5115 ## Congrès canadien des étudiant.e.s en mathématiques le mercredi 19 juillet 2017 Le CCÉM est un congrès académique visant les étudiantes et étudiants de premier cycle qui étudient en mathématiques ou dans un domaine connexe. Cette année, le congrès se déroulera à Montréal, du 19 au 23 juillet 2017 grâce à la collaboration de l'Université de Montréal, l'Université Concordia, l'Université du Québec à Montréal et l'Université McGill. ## Camp mathématique à Montréal le lundi 26 juin 2017 Le Camp de math de Concordia offre une expérience enrichissante aux étudiants qui ont manifesté un intérêt ou une aptitude pour les mathématiques. Dirigé par un instructeur bilingue, expérimenté dans les activités de sensibilisation et les concours mathématiques internationaux, et animé par des étudiants des cycles supérieurs en mathématiques ou en didactique des mathématiques des universités montréalaises, le camp permettra à des élèves de 10 à 15 ans de relever des défis mathématiques tout en s’amusant. Les élèves participeront à des séances de résolution de problèmes et vivront des expériences mathématiques à travers des jeux, des projets, de l’expérimentation et d'autres activités amusantes. Le camp mettra également en valeur les mathématiques dans la vie quotidienne, que ce soit dans les domaines pratiques ou dans les arts. Enfin, il s’agit d’une occasion pour les enfants intéressés par les mathématiques de rencontrer d'autres enfants qui partagent le même intérêt et de développer ainsi de nouvelles amitiés. Le coût du camp est de 225$ par semaine (M-F: 9 h à 16 h) avec un supplément de 35 par semaine pour le service de garde (M-F: 8 h-9 h et 16 h-17 h). Le camp se déroule au Département de mathématiques et de statistique de l'Université Concordia, au 9e étage du pavillon de la bibliothèque (LB) du campus SGW: http://www.concordia.ca/maps/sgw-campus.html Une activité du Cercle mathématique de Montréal, le camp est rendu possible par l'Université Concordia en collaboration avec l'Institut des sciences mathématiques (ISM) et le soutien de la Société mathématique du Canada (CMS) et du progamme Promoscience du CRSNG. Les activités mathématiques sont choisies parmi: - la résolution de problèmes de niveau approprié; - les défis: à titre d’exemple des problèmes ouverts et des activités de découverte; - des activités exploratoires avec des thèmes mathématiques tels que les nombres polygonaux, - les mathématiques dans les peintures, la logique Escher et les tessellations; ou une promenade mathématique autour du département. - des mathématiques récréatives avec des activités style grand public et les puzzles; des histoires ou des films sur les mathématiques et les mathématiciens. Nous viserons à trouver au moins une activité quotidienne où les élèves pourront dépenser de l'énergie physique. Vous pouvez adressez toute question à montrealmathclub@gmail.com. Merci d’indiquer Camp juin comme l’objet du message. Pour inscrire votre enfant, merci de compléter le formulaire. ## Les mathématiques de la magie! le samedi 13 mai 2017 Vous avez toujours rêvé de concevoir vos propres tours de magie? Vous souhaitez savoir ce que les mathématiques peuvent vous apporter? L'Institut des sciences mathématiques vous invite à voir des tours de magie utilisant cartes, noeuds et mathématiques, mais surtout pas votre intuition... elle pourrait être trompeuse! Samedi 13 mai, 10h à 14h UQAM, Pavillon Président-Kennedy 201, ave du Président-Kennedy local PK-R650, Montréal ## Colloque panquébécois des étudiants de l'ISM le vendredi 12 mai 2017 Ce colloque annuel a pour but de réunir, pour une fin de semaine, les étudiantes et les étudiants du Québec inscrits aux cycles supérieurs en sciences mathématiques. Cette année, le colloque se tiendra à Trois-Rivières du 12 au 14 mai 2017 et tous sont invités à venir y présenter leurs travaux de recherche ou un sujet qui les passionne. ## Colloque des sciences mathématiques du Québec - Gerard Freixas (Jussieu) le vendredi 5 mai 2017 From the geometry of numbers to Arakelov geometry Arakelov geometry is a modern formalism that extends in various directions the geometry of numbers founded by Minkowski in the nineteenth century. The objects of study are arithmetic varieties, namely complex varieties that can be defined by polynomial equations with integer coefficients. The theory exploits the interplay between algebraic geometry and number theory and complex analysis and differential geometry. Recently, the formalism found beautiful and important applications to the so-called Kudla programme and the Colmez conjecture. In the talk, I will first introduce elementary facts in Minkowski's geometry of numbers. This will provide a motivation for the sequel, where I will give my own view of Arakelov geometry, by focusing on toy (but non-trivial) examples of one of the central theorems in the theory, the arithmetic Riemann-Roch theorem mainly due to Bismut, Gillet and Soulé, and generalizations. I hope there will be ingredients to satisfy different tastes, for instance modular forms (arithmetic aspect), analytic torsion (analytic aspect) and Selberg zeta functions (arithmetic, analytic and dynamic aspects). Date / Heure: Vendredi, le 5 mai 2017 - 16:00 Lieu: UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, room PK-5115 ## Colloque des sciences mathématiques du Québec - Aaron Naber (Northwestern) le vendredi 21 avril 2017 Introduction to the Energy Identity for Yang-Mills In this talk we give an introduction to the analysis of the Yang-Mills equation in higher dimensions. In particular, when studying sequences of solutions we will study the manner in which blow up can occur, and how this blow up may be understood through the classical notions of the defect measure and bubbles. The energy identity is an explicit conjectural relationship, known to be true in dimension four, relating the energy density of the defect measure at a point to the bubbles which occur at that point, and we will give a brief overview of the recent proof of this result for general stationary Yang Mills in higher dimensions. The work is joint with Daniele Valtorta. Date / Heure: Vendredi 21 avril 2017 - 16:00 Lieu: UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, salle PK-5115 ## Colloque des sciences mathématiques du Québec - Xihong Lin (Harvard University) le vendredi 21 avril 2017 Date / Heure : Le vendredi 21 avril 2017 - 15:30 Lieu : McGill University, Burnside Hall, 805 Sherbrooke Ouest, salle 1205 ## Colloque des sciences mathématiques du Québec - Gabor Szekelyhidi (Notre-Dame) le vendredi 7 avril 2017 Kahler-Einstein metrics Kahler-Einstein metrics are of fundamental importance in Kahler geometry, with connections to algebraic geometry, geometric analysis, string theory amongst other fields. Their study has received a great deal of attention recently, culminating in the solution of the Yau-Tian-Donaldson conjecture, characterizing which complex manifolds admit Kahler-Einstein metrics. I will give an overview of the field, including some recent developments. Date / Heure: Vendredi, le 7 avril 2017 - 16:00 Lieu: UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, salle PK-5115 ## Colloque des sciences mathématiques du Québec - Jason Fine (UNC at Chapel Hill) le jeudi 6 avril 2017 Instrumental variable regression with survival outcomes Instrumental variable (IV) methods are popular in non-experimental studies to estimate the causal effects of medical interventions or exposures. These approaches allow for the consistent estimation of such effects even if important confounding factors are unobserved. Despite the increasing use of these methods, there have been few extensions of IV methods to censored data regression problems. We discuss challenges in applying IV structural equational modelling techniques to the proportional hazards model and suggest alternative modelling frameworks. We demonstrate the utility of the accelerated lifetime and additive hazards models for IV analyses with censored data. Assuming linear structural equation models for either the event time or the hazard function, we proposed closed-form, two-stage estimators for the causal effect in the structural models for the failure time outcomes. The asymptotic properties of the estimators are derived and the resulting inferences are shown to perform well in simulation studies and in an application to a data set on the effectiveness of a novel chemotherapeutic agent for colon cancer. Date / Heure: Le jeudi 6 avril 2017 - 15:30 Venue: Université Laval, Pavillon Vachon, salle 3840 ## Colloque des sciences mathématiques du Québec - Tatiana Toro (University of Washington) le vendredi 31 mars 2017 PDEs on non-smooth domains Abstract: In these lecture we will discuss the relationship between the boundary regularity of the solutions to elliptic second order divergence form partial differential equations and the geometry of the boundary of the domain where they are defined. While in the smooth setting tools from classical PDEs are used to address this question, in the non-smooth setting techniques from harmonic analysis and geometric measure theory are needed to tackle the problem. The goal is to present an overview of the recent developments in this very active area of research. Date / Heure : Le vendredi 31 mars 2017 - 16:00 Lieu : UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, salle PK-5115 ## Colloque des sciences mathématiques du Québec - Sayan Mukherjee (Duke University) le vendredi 17 mars 2017 Inference in Dynamical Systems We consider the asymptotic consistency of maximum likelihood parameter estimation for dynamical systems observed with noise. Under suitable conditions on the dynamical systems and the observations, we show that maximum likelihood parameter estimation is consistent. Furthermore, we show how some well-studied properties of dynamical systems imply the general statistical properties related to maximum likelihood estimation. Finally, we exhibit classical families of dynamical systems for which maximum likelihood estimation is consistent. Examples include shifts of finite type with Gibbs measures and Axiom A attractors with SRB measures. We also relate Bayesian inference to the thermodynamic formalism in tracking dynamical systems. Date / Heure : Le vendredi 17 mars 2017 - 15:30 Lieu : McGill University, Burnside Hall, 805 Sherbrooke Ouest, salle 1205 ## Colloque des sciences mathématiques du Québec - Louigi Addario-Berry (Université McGill) le vendredi 10 mars 2017 Probabilistic aspects of minimum spanning trees One of the most dynamic areas of probability theory is the study of the behaviour of discrete optimization problems on random inputs. My talk will focus on the probabilistic analysis of one of the first and foundational combinatorial optimization problems: the minimum spanning tree problem. The structure of a random minimum spanning tree (MST) of a graph G turns out to be intimately linked to the behaviour of critical and near-critical percolation on G. I will describe this connection, and present some results on the structure, scaling limits, and volume growth of random MSTs. It turns out that, on high-dimensional graphs, random minimum spanning trees are expected to be three-dimensional when viewed intrinsically, and six-dimensional when viewed as embedded objects. Based on joint works with Nicolas Broutin, Christina Goldschmidt, Simon Griffiths, Ross Kang, Gregory Miermont, Bruce Reed, Sanchayan Sen. Date / Heure : Le vendredi 10 mars 2017 - 16:00 Lieu : CRM, Université de Montréal, Pavillon André-Aisenstadt, 2920 Chemin de la Tour, salle 6254 ## Colloque des sciences mathématiques du Québec - Frithjof Lutscher (Université d'Ottawa) le vendredi 24 février 2017 Spreading phenomena in integrodifference equations with overcompensatory growth function The globally observed phenomenon of the spread of invasive biological species with all its sometimes detrimental effects on native ecosystems has spurred intense mathematical research and modelling efforts into corresponding phenomena of spreading speeds and travelling waves. The standard modelling framework for such processes is based on reaction- diffusion equations, but several aspects of an invasion can only be appropriately described by a discrete-time analogues, called integrodifference equations. The theory of spreading speeds and travelling waves in such integrodifference equations is well established for the "mono-stable" case, i.e. when the non-spatial dynamics show a globally stable positive steady state. When the positive state of the non-spatial dynamics is not stable, as is the case with the famous discrete logistic equation, it is unclear how the corresponding spatial spread profile evolves and at what speed. Previous simulations seemed to reveal a travelling profile in the form of a two-cycle, with or without spatial oscillations. The existence of a travelling wave solution has been proven, but its shape and stability remain unclear. In this talk, I will show simulations that suggest that there are several travelling profiles at different speeds. I will establish corresponding generalizations of the concept of a spreading speed and prove the existence of such speeds and travelling waves in the second- iterate operator. I conjecture that rather than a travelling two-cycle for the next-generation operator, one observes a pair of stacked fronts for the second-iterate operator. I will relate the observations to the phenomenon of dynamic stabilization. Date / Heure : Le vendredi 24 février 2017 - 16:00 Lieu : CRM, Université de Montréal, Pavillon André-Aisenstadt, 2920 Chemin de la Tour, salle 6254 ## Colloque des sciences mathématiques du Québec - Mark Powell (UQAM) le vendredi 10 février 2017 Knot concordance I will introduce the knot concordance group, give a survey of our current understanding of it and discuss some relationships with the topology of 4-manifolds. Date / Heure : Le vendredi 10 février 2017 - 16:00 Lieu : UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, salle PK-5115 ## Colloque des sciences mathématiques du Québec - Christopher Skinner (Princeton University) le vendredi 20 janvier 2017 The Birch-Swinnerton Dyer Conjecture and counting elliptic curves of ranks 0 and 1 This colloquium talk will begin with an introduction to the Birch--Swinnerton-Dyer conjecture for elliptic curves -- just curves defined by the equations y2=x3+Ax+B -- and then describe recent advances that allow us to prove that lots of elliptic curves have rank zero or one. Date / Heure : Le vendredi 20 janvier 2017 - 16:00 Lieu : UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, salle PK-5115 ## SUMM 2017 le vendredi 13 janvier 2017 Les Séminaires Universitaires en Mathématiques à Montréal (SUMM) sont un évènement organisé annuellement par des étudiants de premier cycle en mathématiques et ayant lieu dans l’une des quatre universités montréalaises. L’édition 2017 des SUMM se déroulera le 13, 14 et 15 janvier à l’Université McGill. ## Colloque des sciences mathématiques du Québec - Gui-Qiang G. Chen (University of Oxford) le vendredi 2 décembre 2016 Partial differential equations of mixed elliptic-hyperbolic type in mechanics and geometry As is well-known, two of the basic types of linear partial differential equations (PDEs) are hyperbolic PDEs and elliptic PDEs, following the classification for linear PDEs first proposed by Jacques Hadamard in the 1920s; and linear theories of PDEs of these two types have been well established, respectively. On the other hand, many nonlinear PDEs arising in mechanics, geometry, and other areas naturally are of mixed elliptic-hyperbolic type. The solution of some longstanding fundamental problems in these areas greatly requires a deep understanding of such nonlinear PDEs of mixed type. Important examples include shock reflection-diffraction problems in fluid mechanics (the Euler equations) and isometric embedding problems in differential geometry (the Gauss-Codazzi-Ricci equations), among many others. In this talk we will present natural connections of nonlinear PDEs of mixed elliptic-hyperbolic type with these longstanding problems and will then discuss some recent developments in the analysis of these nonlinear PDEs through the examples with emphasis on developing and identifying mathematical approaches, ideas, and techniques for dealing with the mixed-type problems. Further trends, perspectives, and open problems in this direction will also be addressed. Date / Heure : Le vendredi 2 décembre 2016 - 16:00 Lieu : UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, salle PK-5115 ## Colloque des sciences mathématiques du Québec - Richard Samworth (University of Cambridge) le jeudi 1 décembre 2016 High-dimensional changepoint estimation via sparse projection Changepoints are a very common feature of Big Data that arrive in the form of a data stream. We study high-dimensional time series in which, at certain time points, the mean structure changes in a sparse subset of the coordinates. The challenge is to borrow strength across the coordinates in order to detect smaller changes than could be observed in any individual component series. We propose a two-stage procedure called 'inspect' for estimation of the changepoints: first, we argue that a good projection direction can be obtained as the leading left singular vector of the matrix that solves a convex optimisation problem derived from the CUSUM transformation of the time series. We then apply an existing univariate changepoint detection algorithm to the projected series. Our theory provides strong guarantees on both the number of estimated changepoints and the rates of convergence of their locations, and our numerical studies validate its highly competitive empirical performance for a wide range of data generating mechanisms. Date / Heure : Le jeudi 1 décembre 2016 - 15:30 Lieu/Venue : Salle 1205, Pavillon Burnside , 805 Sherbrooke ouest ## Colloque des sciences mathématiques du Québec - Maksym Radziwill (McGill University) le vendredi 25 novembre 2016 Around the Möbius function The Moebius function plays a central role in number theory; both the prime number theorem and the Riemann Hypothesis are naturally formulated in terms of the amount of cancellations one gets when summing the Moebius function. In recent joint work with K. Matomaki the speaker showed that the sum of the Moebius function exhibits cancellations in "almost all intervals" of increasing length. This goes beyond what was previously known conditionally on the Riemann Hypothesis. The result holds in fact in greater generality. Exploiting this generality one can show that between a fixed number of consecutive squares there is always an integer composed of only "small" prime factors. This is related to the running time of Lenstra's factoring algorithm. I will also discuss some further developments : the work of Tao on correlations between consecutive values of Chowla, and his application of this result to the resolution of the Erdos discrepancy problem. Date / Heure : Le vendredi 25 novembre 2016 - 16:00 Lieu : UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, salle PK-5115 ## Colloque des sciences mathématiques du Québec - Philippe G. LeFloch (Université Paris 6) le vendredi 4 novembre 2016 The nonlinear stability of Minkowski space for self-gravitating massive fields I will review results on the global evolution of self-gravitating massive matter in the context of Einstein's theory as well as the f(R)-theory of gravity. In collaboration with Yue Ma (Xian), I have investigated the global existence problem for the Einstein equations coupled with a Klein-Gordon equation describing the evolution of a massive scalar field. Our main theorem establishes the global nonlinear stability of Minkowski spacetime upon small perturbations of the metric and the matter field. Recall that the fully geometric proof by Christodoulou and Klainerman in 1993, as well as the proof in wave gauge by Lindblad and Rodnianski in 2010, both apply to vacuum spacetimes and massless fields only. Our new technique of proof, which we refer to as the Hyperboloidal Foliation Method, does not use Minkowski's scaling field and is based on a foliation of the spacetime by asymptotically hyperboloidal spacelike hypersurfaces, on sharp estimates for wave and Klein-Gordon equations, and on an analysis of the quasi-null hyperboloidal structure (as we call it) of the Einstein equations in wave gauge. Date / Heure : Le vendredi 4 novembre 2016 - 16:00 Lieu : UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, salle PK-5115 ## Colloque des sciences mathématiques du Québec - Jerry Lawless (University of Waterloo) le vendredi 28 octobre 2016 Efficient tests of covariate effects in two-phase failure time studies Two-phase studies are frequently used when observations on certain variables are expensive or difficult to obtain. One such situation is when a cohort exists for which certain variables have been measured (phase 1 data); then, a sub-sample of individuals is selected, and additional data are collected on them (phase 2). Efficiency for tests and estimators can be increased by basing the selection of phase 2 individuals on data collected at phase 1. For example, in large cohorts, expensive genomic measurements are often collected at phase 2, with oversampling of persons with “extreme” phenotypic responses. A second example is case-cohort or nested case-control studies involving times to rare events, where phase 2 oversamples persons who have experienced the event by a certain time. In this talk I will describe two-phase studies on failure times, present efficient methods for testing covariate effects. Some extensions to more complex outcomes and areas needing further development will be discussed. Date: Le vendredi 28 octobre 2016 Heure: 15h30 à 16h30 Lieu: Salle 1205, Burnside Hall, 805 Sherbrooke ouest ## Colloque des sciences mathématiques du Québec - Ivan Corwin (Columbia University) le vendredi 21 octobre 2016 Integrable probability and the KPZ universality class I will explain how certain integrable structures give rise to meaningful probabilistic systems and methods to analyze them. Asymptotics reveal universal phenomena, such as the Kardar-Parisi-Zhang universality class. No prior knowledge will be assumed. Date / Heure : Le vendredi 21 octobre 2016 - 16h00 Lieu : CRM, Pavillon André-Aisenstadt, 2920 chemin de la tour, salle 6254 ## Colloque des sciences mathématiques du Québec - Jean-Philippe Lessard (Université Laval) le vendredi 14 octobre 2016 Rigorously verified computing for infinite dimensional nonlinear dynamics: a functional analytic approach Studying and proving existence of solutions of nonlinear dynamical systems using standard analytic techniques is a challenging problem. In particular, this problem is even more challenging for partial differential equations, variational problems or functional delay equations which are naturally defined on infinite dimensional function spaces. The goal of this talk is to present rigorous numerical technique relying on functional analytic and topological tools to prove existence of steady states, time periodic solutions, traveling waves and connecting orbits for the above mentioned dynamical systems. We will spend some time identifying difficulties of the proposed approach as well as time to identify future directions of research. Date / Heure : Le vendredi 14 octobre 2016 - 16:00 Lieu : CRM, Pavillon André-Aisenstadt, 2920 chemin de la tour, salle 6254 ## Colloque des sciences mathématiques du Québec - Liam Watson (Université de Sherbrooke) le vendredi 30 septembre 2016 Notions of simplicity in low-dimensions Various auxiliary structures arise naturally in low-dimensions. I will discuss three of these: left-orders on the fundamental group, taut foliations on three-manifolds, and non-trivial Floer homological invariants. Perhaps surprisingly, for (closed, connected, orientable, irreducible) three-manifolds, it has been conjectured that the existence of any one of these structures implies the others. I will describe what is currently known about this conjectural relationship, as well as some of the machinery — particularly in Heegaard Floer theory — that has been developed in pursuit of the conjecture. Date / Heure : Le vendredi 30 septembre 2016 - 16:00 Lieu : UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, salle PK-5115 ## Colloque des sciences mathématiques du Québec - B. L. S. Prakasa Rao (CR Rao Advanced Institute) le vendredi 16 septembre 2016 Statistical Inference for fractional diffusion processes There are some time series which exhibit long-range dependence as noticed by Hurst in his investigations of river water levels along Nile river. Long-range dependence is connected with the concept of self-similarity in that increments of a self-similar process with stationary increments exhibit long-range dependence under some conditions. Fractional Brownian motion is an example of such a process. We discuss statistical inference for stochastic processes modeled by stochastic differential equations driven by a fractional Brownian motion. These processes are termed as fractional diffusion processes. Since fractional Brownian motion is not a semimartingale, it is not possible to extend the notion of a stochastic integral with respect to a fractional Brownian motion following the ideas of Ito integration. There are other methods of extending integration with respect to a fractional Brownian motion. Suppose a complete path of a fractional diffusion process is observed over a finite time interval. We will present some results on inference problems for such processes. Date: Le vendredi 16 septembre 2016 Heure : 16 h Lieu : Université Concordia, Library Building, 1400 de Maisonneuve O., salle LB-921.04 ## Colloque des sciences mathématiques du Québec - Nick Trefethen (University of Oxford) le vendredi 16 septembre 2016 Cubature, approximation, and isotropy in the hypercube The hypercube is the standard domain for computation in higher dimensions. We describe two respects in which the anisotropy of this domain has practical consequences. The first is a matter well known to experts (and to Chebfun users): the importance of axis-alignment in low-rank compression of multivariate functions. Rotating a function by a few degrees in two or more dimensions may change its numerical rank completely. The second is new. The standard notion of degree of a multivariate polynomial, total degree, is isotropic – invariant under rotation. The hypercube, however, is highly anisotropic. We present a theorem showing that as a consequence, the convergence rate of multivariate polynomial approximations in a hypercube is determined not by the total degree but by the Euclidean degree, defined in terms of not the 1-norm but the 2-norm of the exponent vector k of a monomial x1k1... xsks. The consequences, which relate to established ideas of cubature and approximation going back to James Clark Maxwell, are exponentially pronounced as the dimension of the hypercube increases. The talk will include numerical demonstrations. Date : Le vendredi 16 septembre 2016 Heure : 16 h Lieu : UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, salle PK-5115 ## Théorie spectrale et applications: École d'été à l'Université Laval le lundi 4 juillet 2016 L'objectif de l'École d'été du CRM 2016 à Québec est de préparer les étudiants pour la recherche reliée à la théorie spectrale. L'école offrira un aperçu d'un choix de sujets sur la théorie spectrale interprétée au sens large. Elle traitera de sujets en mathématiques pures et appliquées qui seront chacun présentés par des experts réputés lors de mini-cours de 5 heures. Ces cours seront complétés par des laboratoires informatiques supervisés et des sessions de travaux pratiques. À la fin de l'école, les conférenciers invités donneront des conférences spéciales. Cette riche thématique mêle diverses sous-disciplines des mathématiques, particulièrement avantageuses pour les étudiants. Le sujet est aussi très à propos, tandis que la théorie spectrale enregistre des progrès majeurs dans ses sous-disciplines mathématiques et ses applications à la technologie et la science en général. L'école est destinée aux étudiants avancés de premier cycle et aux étudiants débutants de cycle supérieur. Comme tel, les pré-requis sont minimes et la documentation sera fournie quelques semaines avant l'événement. ## Mathfest à l'Université Concordia le dimanche 12 juin 2016 Tout le monde est le bienvenue au premier Mathfest annuel pour une matinée de jeux et de découvertes mathématiques. Où: Pavillon John Molson, Université Concordia, salle MB 3.430, 1450 rue Guy Quand: le 12 juin de 10h00 à 12h00 GRATUIT L'événement est organisé par le Département de mathématiques et de statistique de l'Université Concordial et par l'ISM. ## Colloque des sciences mathématiques du Québec - Gérard Ben Arous (Courant Institute of Mathematical Sciences) le vendredi 20 mai 2016 Complexité des fonctions d'un grand nombre de variables: de la physique statistique aux algorithmes de "deep learning" Date / Heure : Le vendredi 20 mai 2016 - 16:00 Lieu : CRM, UdeM, Pav. André-Aisenstadt, 2920, ch. de la Tour, salle 6214 ## Colloque panquébécois des étudiants 2016 le vendredi 13 mai 2016 Ce colloque annuel a pour but de réunir, pour une fin de semaine, les étudiantes et étudiants du Québec inscrits aux cycles supérieurs en sciences mathématiques. Cette année, le colloque se tiendra à l'Université du Québec à Montréal du 13 au 15 mai 2016 et tous sont invités à venir y présenter leurs travaux de recherche ou un sujet qui les passionne. Les présentations étudiantes, d'une durée de 20 minutes, sont l'occasion idéale de prendre connaissance du travail de vos pairs. Elles seront regroupées en sessions thématiques qui couvriront un large éventail de sujets allant de la combinatoire aux mathématiques financières en passant par la physique mathématique. Les présentations en français et en anglais sont les bienvenues. Les séances seront ponctuées de conférences plénières données par des chercheurs renommés. Puisque l'ISM célèbre son 25e anniversaire cette année, toutes les conférences plénières seront présentées par d'anciens étudiants de l'ISM. La journée du vendredi se terminera par une activité sociale qui permettra à tous de faire connaissance. Pour vous inscrire, cliquez ici. Au plaisir de vous y voir ce printemps ! ## Colloque des sciences mathématiques du Québec - Ovidiu Savin (Columbia University) le vendredi 15 avril 2016 Elliptic PDEs in two dimensions I will give a short survey of the several approaches to the regularity theory of elliptic equations in two dimensions. In particular I will focus on some old ideas of Bernstein and their application to the infinity Laplace equation and to the Bellman equation in two dimensions. Date / Heure : Le vendredi 15 avril 2016 - 16:00 Lieu : UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, salle PK-5115 ## Colloque des sciences mathématiques du Québec - Andrew L. Rukhin (NIST, Information Technology Laboratory) le jeudi 14 avril 2016 Statistical Estimation Problems in Meta-Analysis The principal statistical estimation problem in meta-analysis is to obtain a reliable confidence interval for the treatment effect. Several possible approaches and settings are described. In particular a Bayesian model with non-informative priors and the default data-dependent priors is discussed along with relevant optimization issues. Date: Le jeudi 14 avril 2016 Heure: 16 h 30 Lieu: Université de Sherbrooke, 2500, boul. de l'Université, salle D3-2041 ## Colloque des sciences mathématiques du Québec - Philippe Rigollet (MIT) le jeudi 14 avril 2016 The statistical price for computational efficiency With the explosion of the size of data, computation has become an integral part of statistics. Ad hoc remedies such as employing convex relaxations, or manipulating sufficient statistics, have been successful to derive efficient procedures with provably optimal statistical guarantees. Unfortunately, computational efficiency sometimes comes at an inevitable statistical cost. Therefore, one needs to redefine optimality among computationally efficient procedures. Using tools from information theory and computational complexity, we quantify this cost in the context of two models: (i) the multi-armed bandit problem, and (ii) sparse principal component analysis [Based on joint work with Q. Berthet, S. Chassang, V. Perchet and E. Snowberg] Date / Heure : Le jeudi 14 avril 2016 - 15:30 Lieu : Université Laval, Pavillon Adrien-Pouliot, salle 2840 ## Colloque des sciences mathématiques du Québec - Nathanael Berestycki (University of Cambridge) le vendredi 8 avril 2016 The dimer model: universality and conformal invariance The dimer model on a finite bipartite planar graph is a uniformly chosen set of edges which cover every vertex exactly once. It is a classical model of statistical mechanics, going back to work of Kasteleyn and Temperley/Fisher in the 1960s who computed its partition function. After giving an overview, I will discuss some recent joint work with Benoit Laslier and Gourab Ray, where we prove in a variety of situations that when the mesh size tends to 0 the fluctuations are described by a universal and conformally invariant limit known as the Gaussian free field. A key novelty in our approach is that the exact solvability of the model plays only a minor role. Instead, we rely on a connection to imaginary geometry, where Schramm-Loewner Evolution curves are viewed as flow lines of an underlying Gaussian free field. Date / Heure : Le vendredi 8 avril 2016 - 16:00 Lieu : CRM, UdeM, Pav. André-Aisenstadt, 2920, ch. de la Tour, salle 6214 ## Colloque des sciences mathématiques du Québec - Malabika Pramanik (UBC) le vendredi 1 avril 2016 Needles, Bushes, Hairbrushes and Polynomials Pretend that your car is a unit line segment. How do you perform a three point turn using an infinitesimally small area on the road? It turns out that this seemingly impossible driving stunt is related to the fundamental theorem of calculus, as well as all the objects in the title of this talk! We will explore these connections and see how they have been useful in many problems in mathematics. Date / Heure : Le vendredi 1 avril 2016 - 16:00 Lieu : UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, salle PK-5115 ## Quebec Mathematical Sciences Colloquium - Gunther Uhlmann (University of Washington) le vendredi 18 mars 2016 Harry Potter's Cloak via Transformation Optics Can we make objects invisible? This has been a subject of human fascination for millennia in Greek mythology, movies, science fiction, etc., including the legend of Perseus versus Medusa and the more recent Star Trek and Harry Potter. In the last decade or so, there have been several scientific proposals to achieve invisibility. We will introduce some of these in a non-technical fashion, concentrating on the so-called "transformation optics" that has received the most attention in the scientific literature. Date / Heure : Le vendredi 18 mars 2016 - 16:00 Lieu : CRM, UdeM, Pav. André-Aisenstadt, 2920, ch. de la Tour, salle 6214 ## Colloque des sciences mathématiques du Québec - Vern Paulsen (University of Waterloo) le jeudi 17 mars 2016 Quantum Chromatic Numbers and the conjectures of Connes and Tsirelson It is possible to characterize the chromatic number of a graph in terms of a game. It is the fewest number of colours for which a winning strategy exists using classical random variables to a certain graph colouring game. If one allows the players to use quantum experiments to generate their random outcomes, then for many graphs this game can be won with far fewer colours. This leads to the definition of the quantum chromatic number of a graph. However, there are several mathematical models for the set of probability densities generated by quantum experiments and whether or not these models agree depends on deep conjectures of Connes and Tsirelson. Thus, there are potentially several "different" quantum chromatic numbers and computing them for various graphs gives us a combinatorial means to test these conjectures. In this talk I will present these ideas and some of the results in this area. I will only assume that the audience is familiar with the basics of Hilbert space theory and assume no background in quantum theory. Date /Heure : Le jeudi 17 mars 2016 - 15:30 Lieu : Université Laval, Pavillon Alexandre Vachon, salle VCH-2830 ## Colloque des sciences mathématiques du Québec - Gennady Samorodnitsky (Cornell University) le jeudi 10 mars 2016 Ridges and valleys in the high excursion sets of Gaussian random fields It is well known that normal random variables do not like taking large values. Therefore, a continuous Gaussian random field on a compact set does not like exceeding a large level. If it does exceed a large level at some point, it tends to go back below the level a short distance away from that point. One, therefore, does not expect the excursion set above a high for such a field to possess any interesting structure. Nonetheless, if we want to know how likely are two points in such an excursion set to be connected by a path ("a ridge") in the excursion set, how do we figure that out? If we know that a ridge in the excursion set exists (e.g. the field is above a high level on the surface of a sphere), how likely is there to be also a valley (e.g. the field going to below a fraction of the level somewhere inside that sphere)? We use the large deviation approach. Some surprising results (and pictures) are obtained. Date / Heure : Le jeudi 10 mars 2016 - 15:30 Lieu : McGill University, Burnside Hall, salle à venir ## Colloque des sciences mathématiques du Québec - Dmitry Khavison (University of South Florida) le vendredi 26 février 2016 The fundamental theorem of algebra, complex analysis and ... astrophysics The fundamental theorem of algebra, complex analysis and ... astrophysicsThe Fundamental Theorem of Algebra first rigorously proved by Gauss states that each complex polynomial of degreen$has precisely$n$complex roots. In recent years various extensions of this celebrated result have been considered. We shall discuss the extension of the FTA to harmonic polynomials of degree$n$. In particular, the theorem of D. Khavinson and G. Swiatek that shows that the harmonic polynomial \bar{z}-p(z), deg \, p=n>1 has at most 3n-2 zeros as was conjectured in the early 90's by T. Sheil-Small and A. Wilmshurst. L. Geyer was able to show that the result is sharp for all n. G. Neumann and D. Khavinson proved that the maximal number of zeros of rational harmonic functions \bar{z}-r(z), deg \,r =n>1 is 5n-5. It turned out that this result confirmed several consecutive conjectures made by astrophysicists S. Mao, A. Petters, H. Witt and, in its final form, the conjecture of S. H. Rhie that were dealing with the estimate of the maximal number of images of a star if the light from it is deflected by n co-planar masses. The first non-trivial case of one mass was already investigated by A. Einstein around 1912. We shall also discuss the problem of gravitational lensing of a point source of light, e.g., a star, by an elliptic galaxy, more precisely the problem of the maximal number of images that one can observe. Under some more or less "natural" assumptions on the mass distribution within the galaxy one can prove (A.Eremenko and W. Bergweiler - 2010, also, K - E. Lundberg - 2010) that the number of visible images can never be more than four in some cases and six in the other. Interestingly, the former situation can actually occur and has been observed by astronomers. Still there are much more open questions than there are answers. Date /Heure : Le vendredi 26 février 2016 - 16:00 Lieu : CRM, UdeM, Pav. André-Aisenstadt, 2920, ch. de la Tour, salle 6214 ## Colloque des sciences mathématiques du Québec - Dorin Bucur (Université de Savoie) le vendredi 12 février 2016 Date / Heure : Le vendredi 12 février 2016 - 16:00 Lieu : CRM, UdeM, Pav. André-Aisenstadt, 2920, ch. de la Tour, salle 6214 ## Séance de dédicaces : Mathematics without Apologies, Michael Harris le jeudi 11 février 2016 AUTEUR: Michael Harris (Université Paris-Diderot, Columbia University) MATHEMATICS WITHOUT APOLOGIES An unapologetic guided tour of the mathematical life ** Le livre sera en vente sur place au prix de$25 (comptant seulement) **

Que font les mathématiciens purs et pourquoi le font-ils? Regard au-delà des concepts conventionnels -- au nom de la vérité, de la beauté et des applications pratiques -- ce livre propose un panorama éclectique des vies et des valeurs, des espoirs et des peurs des mathématiciens au 21e siècle en rassemblant du matériel surprenant d'un assortiment diversifié de sources scientifique, journalistique et de la culture populaire.

DATE :
Le jeudi 11 février 2016

HEURE :
16h00

LIEU :
Concordia University, Library Building, 9th floor, Salle/Room LB 921-04
1400 De Maisonneuve West

## Colloque des sciences mathématiques du Québec - Tadashi Tokieda (Cambridge / Stanford)

le vendredi 5 février 2016

Chain reactions
To every action, there is an equal and opposite reaction. However, there turn out to exist in nature situations where the reaction seems to be neither equal in magnitude nor opposite in direction to the action.  We will see a series of table-top demos and experimental movies, apparently in more and more violation of Newton's 3rd law, and give a full analysis of what is happening, discovering in the end that this phenomenon are in a sense generic.  The keys are shock, singular material property, and supply of "critical geometry".

Date / Heure : Le vendredi 5 février 2016 - 16:00

Lieu : UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, salle PK-5115

## Colloque des sciences mathématiques du Québec - Jérôme Vetois (McGill University)

le vendredi 29 janvier 2016

Stability and instability for nonlinear elliptic PDE with slight variations to the data
We will consider the question of stability of solutions to nonlinear elliptic PDE when slightly varying the data. We will take as a model the Standing Wave Equation for critical nonlinear Schrödinger and Klein-Gordon Equations on a closed manifold, and we will look at variations to the potential functions in these equations. A number of results have been obtained on this question in the last two decades, and we now have an accurate picture of the stability and instability of solutions to these equations. I will give an overview of these results and explain why certain types of unstable solutions can exist for some potential functions or in some geometries, and not others.

Date / Heure : Le vendredi 29 janvier 2016 - 16:00

Lieu : CRM, UdeM, Pav. André-Aisenstadt, 2920, ch. de la Tour, salle 6214

## Colloque des sciences mathématiques du Québec - Andrea Lodi (École Polytechnique de Montréal)

le vendredi 22 janvier 2016

Big data & mixed-integer (non linear) programming
In this talk I review a couple of applications on Big Data that I personally like and I try to explain my point of view as a Mathematical Optimizer -- especially concerned with discrete (integer) decisions -- on the subject. I advocate a tight integration of Data Mining, Machine Learning and Mathematical Optimization (among others) to deal with the challenges of decision-making in Data Science. Those challenges are the core of the mission of the Canada Excellence Research Chair in "Data Science for Real-time Decision Making" that I hold.

Date / heure : Le vendredi 22 janvier 2016 - 16h00

Lieu: UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, salle PK-5115

## Conférence du lauréat du Prix Aisenstadt 2015 : Louis-Pierre Arguin (Université de Montréal & CUNY, Baruch College and Graduate Center)

le vendredi 15 janvier 2016

Maximum de variables aléatoires fortement corrélées
La théorie des probabilités a pour objectif principal de déterminer des lois dites "universelles". Les exemples les plus communs sont sans doute la Loi des Grands Nombres et le Théorème Central Limite, datant du 18e siècle, qui décrivent la convergence de la somme de variables aléatoires avec des hypothèses minimales sur leurs lois. Plusieurs problèmes actuels en probabilités cherchent à définir des lois universelles pour le maximum de variables aléatoire corrélées. Une classe particulièrement intéressante pour les mathématiques et la physique est celle des processus dont les corrélations décroissent logarithmiquement avec la distance. Dans cet exposé, nous survolerons les résultats récents sur le sujet et leurs connexions avec des problèmes divers tels que le maximum de la fonction zeta de Riemann sur l'axe critique ainsi que le celui des polynômes caractéristiques des matrices aléatoires.

** Présentation en français avec diapos en anglais. **

Le café sera servi à 15h30 et une réception suivra la conférence au Salon Maurice-L’Abbé (salle 6245).

Date et heure : Le vendredi 15 janvier 2016, 16:00 - 17:00

Lieu: Salle 6254, Centre de recherches mathématiques, Pavillon André-Aisenstadt, 2920, chemin de la Tour

## SUMM 2016

le vendredi 8 janvier 2016

Les Séminaires Universitaires en Mathématiques à Montréal (SUMM) sont un évènement organisé annuellement par des étudiants de premier cycle en mathématiques et ayant lieu dans l’une des quatre universités montréalaises.

L’édition 2016 des SUMM se déroulera le 8-9-10 janvier à l’Université du Québec à Montréal (UQÀM).

Comme à chaque année, quatre conférences plénières seront données par des enseignants des universités participantes. Au programme des SUMM 2016 :

– Dimiter Dryanov, Department of Mathematics and Statistics, Concordia University.

– Marlène Frigon, Département de Mathématiques et de Statistique, Université de Montréal.

– Christian Genest, Department of Mathematics and Statistics, McGill University.

– Franco Saliola, Département de Mathématiques, Université du Québec à Montréal.

Pour toute autre information, n’hésitez pas à communiquer avec le SUMM.

## Colloque des sciences mathématiques du Québec - Nicolai Meinshausen (ETH Zürich)

le jeudi 10 décembre 2015

Causal discovery with confidence using invariance principles
What is interesting about causal inference? One of the most compelling aspects is that any prediction under a causal model is valid in environments that are possibly very different to the environment used for inference. For example, variables can be actively changed and predictions will still be valid and useful. This invariance is very useful but still leaves open the difficult question of inference. We propose to turn this invariance principle around and exploit the invariance for inference. If we observe a system in different environments (or under different but possibly not well specified interventions) we can identify all models that are invariant. We know that any causal model has to be in this subset of invariant models. This allows causal inference with valid confidence intervals. We propose different estimators, depending on the nature of the interventions and depending on whether hidden variables and feedbacks are present. Some empirical examples demonstrate the power and possible pitfalls of this approach.

Date / Heure : Le jeudi 10 décembre 2015 - 15:30

Lieu : UdeM, Pav. Roger-Gaudry, salle S-116

## Réunion d'hiver de la SMC 2015

le vendredi 4 décembre 2015

La Société mathématique du Canada (SMC) invite la communauté mathématique à la Réunion d'hiver de la SMC 2015 qui se tiendra à Montréal, Québec, du 4 au 7 decembre. Toutes les activités auront lieu au Hyatt Regency Montréal (1255 Jeanne-Mance, Montreal, Quebec, Canada, H5B 1E5).

## Colloque des sciences mathématiques du Québec - Stéphane Jaffard (Université de Paris Est)

le vendredi 27 novembre 2015

Measuring irregularities in data : Can fractals help to classify Van Gogh paintings?
Benoît Mandelbrot defined fractal geometry as the geometry of irregular sets; he and his followers successfully used the mathematical concepts of fractional dimensions to quantify this irregularity and thus popularized new classification tools among scientists working in many disciplines. Recently, these ideas have proved very fruitful in multifractal analysis, which deals with the analysis of irregular functions. We will show how the seminal ideas introduced in fractal geometry have been diverted in order to supply new classification tools for signals and images, and we will present a selected choice of applications including: - Model classification in the context of fully developed turbulence and the diagnostic of heart-beat failure. - Modeling of internet flowl - Stylometry tools helping art historians to differentiate between the paintings of several masters.

Date / Heure : Le vendredi 27 novembre 2015 - 16:00

Lieu : CRM, UdeM, Pav. André-Aisenstadt, 2920, ch. de la Tour, salle 6214

## Colloque des sciences mathématiques du Québec - Richard Cook (University of Waterloo)

le jeudi 26 novembre 2015

Inference regarding within-family association in disease onset times under biased sampling schemes
In preliminary studies of the genetic basis for chronic conditions, interest routinely lies in the within-family dependence in disease status. When probands are selected from    disease registries and their respective families are recruited, a variety of ascertainment    bias-corrected methods of inference are available which are typically based on models for correlated binary data. This approach ignores the age that family members are at the time of assessment. We consider copula-based models for assessing the within-family dependence    in the disease onset time and disease progression, based on right-censored and current status observation of the non-probands. Inferences based on likelihood, composite likelihood and    estimating functions are each discussed and compared in terms of asymptotic and empirical relative efficiency. This is joint work with Yujie Zhong.

Date / Heure : Le jeudi 26 novembre 2015 - 15:30

Lieu : McGill, Pavillon Burnside, salle 306

## Colloque des sciences mathématiques du Québec - Lia Bronsard (Université McMaster)

le vendredi 20 novembre 2015

Sur l'étude des singularités dans des modèles mathématiques de cristaux liquides
L'analyse de modèles mathématiques pour les cristaux liquides pose beaucoup de défis, vu leurs proximités à l'étude des singularités dans les applications harmoniques. Dans ce colloque, je vais présenter des modèles mathématiques utilisés dans l'étude des cristaux liquides, la connexion avec les résultats classiques pour les applications harmoniques, ainsi que les nouvelles méthodes utilisées pour étudier les singularités dans le modèle de Landau-de Gennes. Ce modèle permet une plus grande variété de singularités que le modèle d'Oseen-Frank basé sur les applications harmoniques à valeur dans la sphère. (The talk will delivered in French with English slides.)

Date / Heure : Le vendredi 20 novembre 2015 - 16:00

Lieu : UQAM, Pavillon Sherbrooke, Salle SH-2420

## Colloque des sciences mathématiques du Québec - Alexander Fribergh (Université de Montréal)

le vendredi 13 novembre 2015

Random walks in random environments
The goal of this talk is to present some recent developments in the field of random walks in random environments. We chose to do this by presenting a specific model, known as biased random walk on Galton-Watson trees, which is intuitively easy to understand but gives rise to many interesting and challenging questions. We will then explain why this model is actually representative of a whole class of models which exhibit universal limiting behaviours.

Date / Heure : Le vendredi 13 novembre 2015 - 16:00

Lieu : CRM, UdeM, Pav. André-Aisenstadt, 2920, ch. de la Tour, salle 6214

## Colloque des sciences mathématiques du Québec - Piotr Przytycki (Université McGill)

le vendredi 6 novembre 2015

Walls in random groups
I will give an overview of Gromov's density model for random groups. These groups are hyperbolic and for large densities are exotic enough to have Kazhdan's property (T). I will focus on small densities and explain the techniques of Ollivier and Wise, and Mackay and myself to tame these groups by finding "walls" and hence an action on a CAT(0) cube complex.

Date : Vendredi, 6 novembre 2015

Heure : 16h00

Lieu : UQAM, Pavillon Sherbrooke, salle SH-2420

La conférence sera suivie d'une réception.

## Colloque des sciences mathématiques du Québec - Emmanuel Candès (Stanford University)

le vendredi 30 octobre 2015

A knockoff filter for controlling the false discovery rate
The big data era has created a new scientific paradigm: collect data first, ask questions later. Imagine that we observe a response variable together with a large number of potential explanatory variables, and would like to be able to discover which variables are truly associated with the response. At the same time, we need to know that the false discovery rate (FDR)---the expected fraction of false discoveries among all discoveries---is not too high, in order to assure the scientist that most of the discoveries are indeed true and replicable. We introduce the knockoff filter, a new variable selection procedure controlling the FDR in the statistical linear model whenever there are at least as many observations as variables. This method works by constructing fake variables, knockoffs, which can then be used as controls for the true variables; the method achieves exact FDR control in finite sample settings no matter the design or covariates, the number of variables in the model, and the amplitudes of the unknown regression coefficients, and does not require any knowledge of the noise level. This is joint work with Rina Foygel Barber.

Date / Heure : Le vendredi 30 octobre 2015 - 16:00

Lieu : CRM, UdeM, Pav. André-Aisenstadt, 2920, ch. de la Tour, salle 1360

## Colloque des sciences mathématiques du Québec - John Harnad (Concordia & CRM)

le vendredi 23 octobre 2015

Weighted Hurwitz Numbers: Classical and Quantum
The study of Hurwitz numbers, which enumerate branched coverings of the Riemann sphere, is classical, going back to the pioneering work of Hurwitz in the 1880’s. There is an equivalent combinatorial problem, related by monodromy that was developed by Frobenius in his pioneering work on character theory, consisting of enumeration of factorizations of elements of the symmetric group. In 2000, Okounkov and Pandharipande began their program relating Hurwitz numbers to other combinatorial/topological invariants associated to Riemann surfaces, such as as Gromov-Witten and Donaldson-Thomas invariants. This has since been further developed by others to include, e.g., Hodge invariants and relations to knot invariants. A key result of Okounkov and Pandharipande was to express the generating functions for special classes of Hurwitz numbers, e.g., including only simple branching, plus one, or two other branch points, as special types of Tau functions of integrable hierarchies such as Sato's KP hierarchy and Takasaki-Takebe’s 2D Toda lattice hierarchy, together with associated semi-infinite wedge product representations. The differential/algebraic equations satisfied by such generating functions provide a new perspective, implying deep interrelations between these various types of enumerative invariants. In more recent work, these ideas have been extended to include generating functions for a very wide class of branched coverings, with suitable combinatorial interpretations, including broad class of weighted enumerations that select amongst infinite parametric families of weights. These make use not only of the six standard bases for the ring of symmetric functions, such as Schur functions, and monomomial sum symmetric functions, but also their “quantum” deformations, involving the pair of deformation parameters (q,t) appearing the in theory of Macdonald polynomials. The general theory of weighted Hurwitz numbers, together with various applications and examples coming from Random Matrix theory and enumerative geometry will be explained in a simple, unified way, based on special elements of and bases for the center of the symmetric group algebra, and the characteristic map to the ring of symmetric polynomials. The simplest quantum case provides a relation between special weighted enumerations of branched coverings and the statistical nechanics of Bose-Eintein gases. Various other specializations, to such bases as: Hall-Littlewood, Jack, q-Whittaker, dual q-Whttaker as well as certain special classical weightings have further applications, in physics, geometry, group theory and combinatorics.

Date / Heure : Le vendredi 23 octobre 2015 - 16:00

Lieu : UQAM - Pavillon Sherbrooke, Salle SH-2420 (un étage en dessous de la salle habituelle)

Un vin d'honneur suivra la conférence.

## Colloque des sciences mathématiques du Québec - Emmanuel Giroux (ENS-Lyon & UMI-CRM)

le vendredi 16 octobre 2015

Holomorphic functions, convexity and transversality
Morse theory is a powerful tool to study the topology of real manifolds. After recalling its basic features, we will discuss the existence, on complex manifolds, of holomorphic functions giving similar information on the topology. More specifically, we will review the notions of pseudoconvexity and of Stein manifold so as to gradually explain the significance of a recent result, jointly obtained with John Pardon, which shows that any Stein domain can be presented as a Lefschetz fibration over the disk. The talk will be aimed at a general mathematical audience.

Date / Heure : Le vendredi 16 octobre 2015 - 16:00

Lieu : CRM, UdeM, Pav. André-Aisenstadt, 2920, ch. de la Tour, salle 6254

## Colloque des sciences mathématiques du Québec - Hugh Thomas (UQAM)

le vendredi 9 octobre 2015

Coxeter Groups and Quiver Representations
It has been understood since almost the beginning of the development of quiver representations, in the 1970s, that there are important connections between Coxeter groups and quiver representations. Nonetheless, further relations continue to appear. I will touch on the classical connections and some of the more recent ones, including the example of the parallel elaboration of the closely related concepts of exceptional sequences of representations and factorizations of Coxeter elements.

Date / Heure : Le vendredi 9 octobre 2015 - 16:00

Lieu : UQAM - Pavillon Sherbrooke, Salle SH-2420 (un étage en dessous de la salle habituelle)

Un vin d'honneur suivra la conférence.

## Colloque des sciences mathématiques du Québec - Dmitri Vassiliev (University College London)

le vendredi 25 septembre 2015

Analysis of first order systems of PDEs on manifolds without boundary
In layman's terms a typical problem in this subject area is formulated as follows. Suppose that our universe has finite size but does not have a boundary. An example of such a situation would be a universe in the shape of a 3-dimensional sphere embedded in 4-dimensional Euclidean space. And imagine now that there is only one particle living in this universe, say, a massless neutrino. Then one can address a number of mathematical questions. How does the neutrino field (solution of the massless Dirac equation) propagate as a function of time? What are the eigenvalues (stationary energy levels) of the particle? Are there nontrivial (i.e. without obvious symmetries) special cases when the eigenvalues can be evaluated explicitly? What is the difference between the neutrino (positive energy) and the antineutrino (negative energy)? What is the nature of spin? Why do neutrinos propagate with the speed of light? Why are neutrinos and photons (solutions of the Maxwell system) so different and, yet, so similar? The speaker will approach the study of first order systems of PDEs from the perspective of a spectral theorist using techniques of microlocal analysis and without involving geometry or physics. However, a fascinating feature of the subject is that this purely analytic approach inevitably leads to differential geometric constructions with a strong theoretical physics flavour. References [1] See items 98-101, 103 and 104 on my publications page http://www.homepages.ucl.ac.uk/~ucahdva/publicat/publicat.html [2] Futurama TV series, Mars University episode (1999): Fry: Hey, professor. What are you teaching this semester? Professor Hubert Farnsworth: Same thing I teach every semester. The Mathematics of Quantum Neutrino Fields. I made up the title so that no student would dare take it.

Date / Heure : Le vendredi 25 septembre 2015 - 16:00

Lieu : UQAM - Pavillon Sherbrooke, Salle SH-2420 (un étage en dessous de la salle habituelle)

Un vin d'honneur suivra la conférence.

## École d'été CRM-PIMS en probabilités

le lundi 15 juin 2015

l'Université McGill sera le hôte de l'école d'été CRM-PIMS en probabilités du 15 juin au 11 juillet 2015.

Deux cours seront donnés par Alice Guionnet et Remco van der Hofstad, ainsi que des mini-cours par Louigi Addario-Berry, Shankar Bhamidi et Jonathan Mattingly.

Pour plus de renseignements, veuillez voir le site: http://problab.ca/ssprob2015/index.php

## École d'été SMS: Théorie spectrale géométrique et computationnelle

le lundi 15 juin 2015

Le Séminaire de Mathématiques Supérieures 2015 présentera environ une douzaine de mini-cours sur la géométrie des valeurs propres, la géométrie des fonctions propres, la théorie spectrale sur les variétés avec singularités et la théorie spectrale computationnelle. Il y a eu récemment plusieurs développements remarquables dans ces domaines étroitement reliés. L'objectif de cette école d'été est de faire la lumière sur différentes facettes de la théorie spectrale moderne et d'offrir une occasion aux étudiants des cycles supérieurs et aux jeunes chercheurs d'obtenir une perspective de ce domaine des mathématiques en rapide évolution. Les conférences seront données par des experts réputés. Les mini-cours seront complétés par des sessions d'exercices, ainsi que par des conférences invitées par les participants juniors qui ont déjà fait d'importantes contributions au domaine. Un aspect particulièrement nouveau de l'école se trouve dans l'accent mis sur les interactions entre la géométrie spectrale et la théorie spectrale computationnelle. Nous ne supposerons pas que les étudiants sont familiers avec les méthodes computationnelles et par conséquent nous entendons offrir des tutoriels où les participants apprendront à développer et à mettre en oeuvre des algorithmes pour l'analyse numérique de problèmes aux valeurs propres.

## Colloque panquébécois des étudiants de l'ISM

le vendredi 15 mai 2015

La 18e édition du colloque panquébécois des étudiants de l'ISM aura lieu au HEC Montréal du 15 au 17 mai 2015. Vous pouvez y présenter vos travaux (date limite pour soumettre un exposé : 15 avril 2015) ou simplement assister aux présentations et profiter des activités de réseautage.  Les conférenciers invités sont : Nantel Bergeron (York University), Matt Davison (University of Western Ontario), Stephen Fienberg (Carnegie Mellon), et le gagnant du prix Carl-Herz 2015. Pour plus de renseignements et pour vous inscrire, veuillez voir le site web du colloque : http://www.crm.umontreal.ca/2015/ISM2015/index.php.

## À la lumière des mathématiques: 10ième édition des 24 heures de science

le vendredi 8 mai 2015

Cette année, les mathématiques fêtent l'année internationale de la lumière en accueillant John Dudley, son instigateur. Vous êtes invité(e) à une demi-journée d'activités où vous découvrirez le rôle de la lumière dans notre civilisation et comment les mathématiques permettent de l'étudier. Inscription gratuite. Renseignements.

## Colloque des sciences mathématiques du Québec - Stephen S. Kudla (University of Toronto)

le jeudi 9 avril 2015

Modular generating series and arithmetic geometry
I will survey the development of the theory of theta series and describe some recent advances/work in progress on arithmetic theta series. The construction and modularity of theta series as counting functions for lattice points for positive definite quadratic forms is a beautiful piece of classical mathematics with its origins in the mid 19th century. Siegel initiated the study of the analogue for indefinite quadratic forms. Millson and I introduced a geometric variant in which the theta series give rise to modular generating series for the cohomology classes of "special" algebraic cycles on locally symmetric varieties. These results motivate the definition of analogous generating series for the classes of such special cycles in the Chow groups and for the classes in the arithmetic Chow groups of their integral extensions. The modularity of such series is a difficult problem. I will discuss various cases in which recent progress has been made and some of the difficulties involved.

Date / Time : Le jeudi 9 avril 2015 - 16:00

Lieu : CRM, UdeM, Pav. André-Aisenstadt, 2920, ch. de la Tour, salle 6254

## Colloque des sciences mathématiques du Québec - Konstantin Mischaikow (Rutgers)

le jeudi 2 avril 2015

A combinatorial approach to dynamics applied to switching networks
Models of multiscale systems, such as those encountered in systems biology, are often characterized by heuristic nonlinearities and poorly defined parameters. Furthermore, it is typically not possible to obtain precise experimental data for these systems. Nevertheless, verification of the models requires the ability to obtain meaningful dynamical structures that can be compared quantitatively with the experimental data. With this in mind we present a purely combinatorial approach to modeling dynamics. We will discuss this approach in the context of switching networks.

Date / Heure : Le jeudi 2 avril 2015 - 16:30

Lieu : Université de Sherbrooke

## Colloque des sciences mathématiques du Québec - William Minicozzi (MIT)

le jeudi 2 avril 2015

Uniqueness of blowups and Lojasiewicz inequalities
The mean curvature flow (MCF) of any closed hypersurface becomes singular in finite time. Once one knows that singularities occur, one naturally wonders what the singularities are like. For minimal varieties the first answer, by Federer-Fleming in 1959, is that they weakly resemble cones. For MCF, by the combined work of Huisken, Ilmanen, and White, singularities weakly resemble shrinkers. Unfortunately, the simple proofs leave open the possibility that a minimal variety or a MCF looked at under a microscope will resemble one blowup, but under higher magnification, it might (as far as anyone knows) resemble a completely different blowup. Whether this ever happens is perhaps the most fundamental question about singularities. We will discuss the proof of this long standing open question for MCF at all generic singularities and for mean convex MCF at all singularities. This is joint work with Toby Colding.

Date / Heure : Le jeudi 2 avril 2015 - 16:00

Lieu : McGill University, Burnside Hall, 805 rue Sherbrooke 0., Montréal, salle 920

## Colloque des sciences mathématiques du Québec - Steven Boyer (UQAM)

le jeudi 26 mars 2015

Left-orderings of groups and the topology of 3-manifolds
Many decades of work culminating in Perelman's proof of Thurston's geometrisation conjecture showed that a closed, connected, orientable, prime 3-dimensional manifold W is essentially determined by its fundamental group π1(W). This group consists of classes of based loops in W and its multiplication corresponds to their concatenation. An important problem is to describe the topological and geometric properties of W in terms of π1(W). For instance, geometrisation implies that W admits a hyperbolic structure if and only if π1(W) is infinite, freely indecomposable, and contains no ZZ subgroups. In this talk I will describe recent work which has determined a surprisingly strong correlation between the existence of a left-order on π1(W) (a total order invariant under left multiplication) and the following two measures of largeness for W:

a) the existence of a co-oriented taut foliation on W - a special type of partition of W into surfaces which fit together locally like a deck of cards.

b) the condition that W not be an L-space - an analytically defined condition representing the non-triviality of its Heegaard-Floer homology.

I will introduce each of these notions, describe the results which connect them, and state a number of open problems and conjectures concerning their precise relationship.

Date / Heure : Le jeudi 26 mars 2015 - 16:00

Lieu : McGill University, Burnside Hall, 805 rue Sherbrooke 0., Montréal, salle 920

## Colloque des sciences mathématiques du Québec - Alexei Borodin (MIT)

le jeudi 19 mars 2015

Integrable probability
The goal of the talk is to survey the emerging field of integrable probability, whose goal is to identify and analyze exactly solvable probabilistic models. The models and results are often easy to describe, yet difficult to find, and they carry essential information about broad universality classes of stochastic processes.

Date / Heure : Le jeudi 19 mars 2015 - 16:00

Lieu : McGill University, Burnside Hall, 805 rue Sherbrooke 0., Montréal, salle 920

## Colloque des sciences mathématiques du Québec - Pierre Colmez (CNRS & Paris VI Jussieu)

le jeudi 12 mars 2015

The upper half-planes
The upper half-planes (complex and p-adic) are very elementary objects, but they have a surprisingly rich structure that I will explore in the talk.

Date / Heure : Le jeudi 12 mars 2015 - 16:00

Lieu : CRM, UdeM, Pav. André-Aisenstadt, 2920, ch. de la Tour, salle 1360

## Colloque des sciences mathématiques du Québec - Sophie Morel (Princeton University)

le jeudi 5 mars 2015

Periods
We will discuss periods, in particular the periods conjecture of Kontsevich and Zagier and the relationship between formal periods and Nori motives.

Date /Heure  : Le jeudi 5 mars 2015 - 16:00

Lieu : McGill University, Burnside Hall, 805 rue Sherbrooke 0., Montréal, salle 920

## Colloque des sciences mathématiques du Québec - Alistair Savage (Université d'Ottawa)

le jeudi 26 février 2015

Categorification in representation theory
This will be an expository talk concerning the idea of categorification and its role in representation theory. We will begin with some very simple yet beautiful observations about how various ideas from basic algebra (monoids, groups, rings, representations etc.) can be reformulated in the language of category theory. We will then explain how this viewpoint leads to new ideas such as the "categorification" of the above-mentioned algebraic objects. We will conclude with a brief synopsis of some current active areas of research involving the categorification of quantum groups. One of the goals of this idea is to produce four-dimensional topological quantum field theories. Very little background knowledge will be assumed.

Date / Heure  : Le jeudi 26 février 2015 - 16:00

Lieu  : McGill University, Burnside Hall, 805 rue Sherbrooke 0., Montréal, salle 920

## Colloque des sciences mathématiques du Québec - Francis Brown (IHES)

le jeudi 19 février 2015

Irrationality proofs, moduli spaces and dinner parties
After introducing an elementary criterion for a real number to be irrational, I will discuss Apery’s famous result proving the irrationality of zeta(3). Then I will give an overview of subsequent results in this field, and finally propose a simple geometric interpretation based on a classical dinner party game.

Date / Heure : Le jeudi 19 février 2015 - 16:00

Lieu : CRM, UdeM, Pav. André-Aisenstadt, 2920, ch. de la Tour, salle 6214

## Colloque des sciences mathématiques du Québec - Laure Saint-Raymond (École normale supérieure, Paris)

le jeudi 12 février 2015

Influence des côtes sur les courants marins
Comprendre les mécanismes qui régissent la circulation océanique est un défi pour les géophysiciens, mais aussi pour les mathématiciens qui doivent développer de nouveaux outils d'analyse pour ces modèles complexes (qui font intervenir en particulier de très nombreuses échelles de temps et d'espace). Un mécanisme particulièrement important pour la circulation à l'échelle planétaire est le phénomène de couche limite qui explique une partie des échanges énergétiques. On montrera ici au travers d'un modèle très simplifié qu'il permet d'expliquer notamment l'intensification des courants de bord Ouest. On évoquera ensuite les difficultés mathématiques liées à la prise en compte de la géométrie. Note : l'exposé sera en anglais avec des transparents en français.

Date / Heure : Le jeudi 12 février 2015 - 16:00

Lieu : McGill University, Burnside Hall, 805 rue Sherbrooke 0., Montréal, salle 920

## Colloque des sciences mathématiques du Québec - Octav Cornea (Université de Montréal)

le jeudi 5 février 2015

Cobordism and Lagrangian topology
This talk aims to discuss how two different basic organizing principles in topology come together in the study of Lagrangian submanifolds. The first principle is cobordism and it emerged in topology in the 1950’s, mainly starting with the work of Thom. It was introduced in Lagrangian topology by Arnold in the 1970’s. The second principle is to reconstruct a subspace of a given space from a family of "slices", each one obtained by intersecting the subspace with a member of a preferred class of special "test" subspaces. For instance, a subspace of 3d euclidean space can be described as the union of all its intersections with horizontal planes. The key issue from this point of view is, of course, how to assemble all the slices together. The perspective that is central for my talk originates in the work of Gromov and Floer in the 1980’s: if the ambient space is a symplectic manifold M, and if the subspace to be described is a Lagrangian submanifold, then, surprisingly,the "glue" that puts the slices together in an efficient algebraic fashion is a reflection of the combinatorial properties of J-holomorphic curves in M. This point of view has been pursued actively since then by many researchers such as Hofer, Fukaya, Seidel leading to a structure called the Fukaya category. Through recent work of Paul Biran and myself, cobordism and the Fukaya category turn out to be intimately related and at the end of the talk I intend to give an idea about this relation.

Date / Heure : Le jeudi 5 février 2015 - 16:00

Lieu : McGill University, Burnside Hall, 805 rue Sherbrooke 0., Montréal, salle 920

## Colloque des sciences mathématiques du Québec - Thomas Ransford (Université Laval)

le jeudi 29 janvier 2015

Spectres et pseudospectres
Les valeurs propres sont parmi les notions les plus utiles en mathématiques: elles permettent la diagonalisation des matrices, elles décrivent l'asymptotique et la stabilité, elles donnent de la personnalité à une matrice. Cependant, lorsque la matrice en question n'est pas normale, l'analyse par des valeurs propres ne donne qu'une information très partielle, et peut même nous induire en erreur. Cet exposé se veut une introduction à la théorie des pseudospectres, un raffinement de la théorie spectrale standard qui s'est avéré utile dans des applications concernant des matrices non normales. Je vais m'intéresser surtout à la question suivante: À quel point les pseudospectres d'une matrice déterminent-ils le comportement de la matrice?

Date / Heure : Le jeudi 29 janvier 2015 - 16:00

Lieu : McGill University, Burnside Hall, 805 rue Sherbrooke 0., Montréal, salle 920

## Colloque des sciences mathématiques du Québec - Hansjoerg Albrecher (HEC, Lausanne)

le jeudi 22 janvier 2015

On the usefulness of mathematics for insurance risk theory - and vice versa
This talk is on applications of various branches of mathematics in the field of risk theory, a branch of actuarial mathematics dealing with the analysis of the surplus process of a portfolio of insurance contracts over time. At the same time such practical problems frequently trigger mathematical research questions, in some cases leading to remarkable identities and connections. Next to the close interactions with probability and statistics, examples will include the branches of real and complex analysis, algebra, symbolic computation, number theory and discrete mathematics.

Date / Heure : Le jeudi 22 janvier 2015 - 16:00

Lieu : McGill University, Burnside Hall, 805, rue  Sherbrooke ouest, Montréal, salle 920

## Colloque des sciences mathématiques du Québec - Fang Yao (University of Toronto)

le jeudi 15 janvier 2015

Functional data analysis and related topics
Functional data analysis (FDA) has received substantial attention, with applications arising from various disciplines, such as engineering, public health, finance, etc. In general, the FDA approaches focus on nonparametric underlying models that assume the data are observed from realizations of stochastic processes satisfying some regularity conditions, e.g., smoothness constraints. The estimation and inference procedures usually do not depend on merely a finite number of parameters, which contrasts with parametric models, and exploit techniques, such as smoothing methods and dimension reduction, that allow data to speak for themselves. In this talk, I will give an overview of FDA methods and related topics developed in recent years.

Date / Heure : Le jeudi 15 janvier 2015 - 16:00

Lieu : CRM, UdeM, Pav. André-Aisenstadt, 2920, ch. de la Tour, salle 1360

## Colloque des sciences mathématiques du Québec - François Bergeron (UQAM)

le jeudi 4 décembre 2014

Algebraic combinatorics and finite reflection groups
The lecture will be delivered in French, with English slides, so that anyone may enjoy it. ----- La conférence sera présentée en français, avec des transparents en anglais, pour que tous puissent suivre. Les dernières années ont vu une explosion d’activités à la frontière entre la combinatoire algébrique, la théorie de la représentation et la géométrie algébrique, avec des liens captivants avec la théorie des nœuds et la physique mathématique. En gardant un large auditoire en tête, nous esquisserons en quoi cette interaction a été très fructueuse et a soulevé de nouvelles questions intrigantes dans les divers domaines concernés. Nous essaierons de donner la saveur des résultats obtenus, des techniques utilisées, du grand nombre de questions ouvertes, et du pourquoi de leur intérêt. Ce fascinant échange entre combinatoire et algèbre fait d’une part intervenir des généralisations au contexte des rectangles des « chemins de Dyck ». Il est bien connu, depuis Euler, que ces chemins sont comptés par les nombres de Catalan, dans le cas d’un carré. De plus, les fonctions de stationnement (parking functions) sont intimement reliées à ces chemins. D’autre part, du côté algébrique, apparaissent des Sn-module bigradué de polynômes harmoniques diagonaux du groupe symétrique Sn. Il a été conjecturé qu’une énumération adéquate des fonctions de stationnement, associées à certaines familles de chemins de Dyck, fournit une formule combinatoire explicite du caractère bigradué de ces modules. Cette conjecture, connue sous le nom de conjecture « shuffle », a récemment été grandement étendue pour couvrir tous les cas rectangulaires. Interviennent dans tout ceci, des opérateurs sur les polynômes de Macdonald, l’algèbre de Hall elliptique, les algèbres de Hecke affines doubles (DAHA), le schéma de Hilbert de points dans le plan, etc.

Date / Heure  : Le jeudi 4 décembre 2014 - 16:00

Lieu  : CRM, UdeM, Pav. André-Aisenstadt, 2920, ch. de la Tour, salle 6214

## Colloque des sciences mathématiques du Québec - Nilima Nigam (Simon Fraser University)

le jeudi 27 novembre 2014

On the well-posedness of the 2D stochastic Allen-Cahn equation
Non-linear parabolic PDE arise in many physical and biological settings; we often need to incorporate the effects of  additive white noise. The resultant stochastic partial differential equations are well-understood in 1D. In higher spatial dimensions, there is an interesting dichotomy: such models are popular in application, while mathematicians assume these models to be ill-posed. We investigate  the specific case of the two dimensional Allen-Cahn equation driven by additive white noise. Without noise, the Allen-Cahn equation is 'pattern-forming'. Does the presence of noise affect this behaviour?  The precise notion of a weak solution to this equation is unclear. Instead, we regularize the noise and introduce a family of approximations. We discuss the continuum limit of these approximations and show that it exhibits divergent behavior. Our results show that a series of published numerical studies are somewhat problematic: shrinking the mesh size in these simulations does not lead to the recovery of a physically meaningful limit. This is joint work with Marc Ryser and Paul Tupper.

Date / Heure : Le jeudi 27 novembre 2014 - 15:30

Lieu : Université Laval, Pavillon Alexandre Vachon, salle 2830

## Colloque des sciences mathématiques du Québec - Martin Wainright (University of California, Berkeley)

le jeudi 20 novembre 2014

High-dimensional phenomena in mathematical statistics and convex analysis
Statistical models in which the ambient dimension is of the same order or larger than the sample size arise frequently in different areas of science and engineering. Although high-dimensional models of this type date back to the work of Kolmogorov, they have been the subject of intensive study over the past decade, and have interesting connections to many branches of mathematics (including concentration of measure, random matrix theory, convex geometry, and information theory). In this talk, we provide a broad overview of the general area, including vignettes on phase transitions in high-dimensional graph recovery, and randomized approximations of convex programs.

Date / Heure : Le jeudi 20 novembre 2014 - 16:00

Lieu : CRM, UdeM, Pav. André-Aisenstadt, 2920, ch. de la Tour, salle 6214

## Colloque des sciences mathématiques du Québec - Kartik Prasanna (University of Michigan, Ann Arbor)

le jeudi 13 novembre 2014

Recent advances in the arithmetic of elliptic curves
In the past few years there have been several spectacular advances in understanding the arithmetic of elliptic curves including results about ranks on average and on the conjecture of Birch and Swinnerton-Dyer. I will give an introduction to the main problems of interest and survey some of these developments. This talk will be addressed to a general mathematical audience.

Date / Heure: Le jeudi 13 novembre 2014 - 16:00

Lieu : CRM, UdeM, Pav. André-Aisenstadt, 2920, ch. de la Tour, salle 6214

## Colloque des sciences mathématiques du Québec - Dani Wise (Université McGill)

le jeudi 6 novembre 2014

The cubical route to understanding groups
Cube complexes have come to play an increasingly central role within geometric group theory, as their connection to right-angled Artin groups provides a powerful combinatorial bridge between geometry and algebra. This talk will primarily aim to introduce nonpositively curved cube complexes, and then describe some of the developments that have recently culminated in the resolution of the virtual Haken conjecture for 3-manifolds, and simultaneously dramatically extended our understanding of many infinite groups.

Date / Heure : Le jeudi 6 novembre 2014 - 16:00

Lieu : CRM, UdeM, Pav. André-Aisenstadt, 2920, ch. de la Tour, salle 6214

## Colloque des sciences mathématiques du Québec - Georgia Benkart (University of Wisconsin-Madison)

le jeudi 30 octobre 2014

A pedestrian approach to group representations
Determining the number of walks of n steps from vertex A to vertex B on a graph often involves clever combinatorics or tedious treading. But if the graph is the representation graph of a group, representation theory can facilitate the counting and provide much insight. This talk will focus on connections between Schur-Weyl duality and walking on representation graphs. Examples of special interest are the simply-laced affine Dynkin diagrams, which are the representation graphs of the finite subgroups of the special unitary group SU(2) by the McKay  correspondence. The duality between the SU(2) subgroups and certain algebras enables us to count walks and solve other combinatorial problems, and to obtain connections with the Temperley-Lieb algebras of statistical mechanics, with partitions, with Stirling numbers, and much more.

Date / Heure : Le jeudi 30 octobre 2014 - 16:00

Lieu : CRM, Université de Montréal, Pav. André-Aisenstadt, 2920, ch. de la Tour, salle 6214

## Colloque des sciences mathématiques du Québec - Alex Kontorovich (Rutgers)

le jeudi 9 octobre 2014

Applications of additive combinatorics to homogeneous dynamics
We will discuss the role played by additive combinatorics in attacks on various problems in dynamics related to finer equidistribution questions beyond Duke's Theorem, particularly those posed by McMullen and Einsiedler-Lindenstrauss-Michel-Venkatesh. This work is joint with Jean Bourgain.

Date / Heure : Le jeudi 9 octobre 2014 - 16:00

Lieu : CRM, UdeM, Pav. André-Aisenstadt, 2920, ch. de la Tour, salle 1140

## Colloque des sciences mathématiques du Québec - Paul Bourgade (New York University)

le jeudi 2 octobre 2014

Universality in random matrix theory
Wigner stated the general hypothesis that the distribution of eigenvalue spacings of large complicated quantum systems is universal, in the sense that it depends only on the symmetry class of the physical system but not on other detailed structures. The simplest case for this hypothesis concerns large but finite dimensional matrices. I will explain some historical aspects random matrix theory, as well as recent techniques developed to prove eigenvalues and eigenvectors universality, for matrices with independent entries from all symmetry classes. The methods are both probabilist (random walks and coupling) and analytic (homogenization for parabolic PDEs).

Date / Heure : Le jeudi 2 octobre 2014 - 16:00

Venue : CRM, UdeM, Pav. André-Aisenstadt, 2920, ch. de la Tour, salle 6214

## La statistique au service de la collectivité: hommage à Louis-Paul Rivest pour ses 60 ans

le vendredi 29 août 2014

Un colloque en l’honneur de Louis-Paul Rivest aura lieu à l’Université Laval les 28 et 29 août pour marquer ses 60 ans et ses nombreuses contributions à la science.

Nous espérons que vous serez des nôtres. Inscrivez-vous à http://www.crm.umontreal.ca/2014/Rivest14/index.php

## SMS 2014 - Comptage d'objets arithmétiques : 23 juin - 4 juillet 2014

le lundi 23 juin 2014

Le comptage d'objets arithmétiques (formes quadratiques, corps de nombres, courbes elliptiques, courbes de genre donné,…) figure parmi les thèmes les plus fondamentaux de la théorie des nombres. Les travaux de Gauss sur la loi de composition des formes quadratiques binaires et sur les groupes de classe de corps quadratiques ont, depuis près de deux siècles, conféré à leur étude ses lettres de noblesse.

Or la dernière décennie a été le témoin de progrès spectaculaires dans ce domaine, grâce notamment au programme de Bhargava qui a réussi à y introduire de nouvelles structures algébriques d'une grande élégance, alliées à des outils analytiques puissants. On dispose ainsi désormais de bornes remarquables sur la taille des groupes de Selmer (et par conséquent, du rang) des courbes élliptiques ainsi même que des Jacobiennes des courbes hyperelliptiques de genre plus élevé, pour ne mentionner qu'une parmi les percées les plus saillantes à être issues de ce cercle d'idées.

L'école d'été de 2014 sera consacrée au programme de Bhargava, et aura pour objectif d'attirer les chercheurs en début de carrière vers cette branche en plein essor de la théorie des nombres.

Pour plus de renseignements voir le site web.

## Colloque panquébécois des étudiants de l'ISM

le vendredi 16 mai 2014

Ce colloque annuel est l'occasion de réunir les étudiants du Québec en mathématiques et en statistique le temps d'une fin de semaine. Cette année, le colloque aura lieu du 16 au 18 mai 2014. Tous sont invités à y présenter leur recherche courante ou un sujet qu'ils jugent digne d'intérêt.

Les présentations étudiantes, d'une durée de vingt minutes, sont toujours de bons prétextes pour découvrir différents sujets et échanger des idées avec d'autres étudiants. Nous encouragons fortement les participants à présenter en français. Les exposés en anglais seront tout de même les bienvenus. Les séances de conférences étudiantes seront ponctuées de conférences plénières de 50 minutes données par des professeurs renommés.

La journée du vendredi s'achèvera par une dégustation de vins et fromages permettant à tous de faire connaissance et de passer ainsi une fin de semaine des plus agréables.

L'édition 2014 du colloque panquébécois des étudiants de l'ISM aura lieu à l'Université Laval.

Nous espérons vous y voir ce printemps !