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 - 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 - 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


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 degree $n$ 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

Michael Harris (Université Paris-Diderot, Columbia University)

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.

Le jeudi 11 février 2016


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

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 !