Program Description

The analysis group is affiliated with the CRM Mathematical Analysis Laboratory which organizes many scientific events. Current research interests of the members of this group may be roughly classified under the following headings:

  • Analysis on Manifolds: spectral geometry (eigenvalues and eigenfunctions of Laplacians), quantum chaos.
  • Classical Analysis
  • Complex Analysis: complex approximation, discrete two-generator groups, complex dynamics, several complex variables, analytic multifunctions.
  • Ergodic Theory: spectral theory of measure preserving transformations, Baire category results in ergodic theory, generalizations of the pointwise ergodic theorems to sequences of generalized projections.
  • Functional Analysis: Banach algebras, resolvents and controllability of operators, generalized spectral theorem and sequences of self-adjoint operators and their weak limits, matrix analysis and inequalities, spectral theory and mathematical physics.
  • Harmonic Analysis: trigonometric series, automorphic forms, singular integrals, Fourier transforms, multiplier operators, Littlewood-Paley theory, harmonic functions on Rn, Hardy spaces, square functions, connections to probability theory and to ergodic theory.
  • Partial Differential Equations: connections to functional, geometric and harmonic analysis.
  • Potential Theory: duality in potential theory, harmonic approximation, boundary behaviour, potential theory on trees.

Program Members

Academic program

This program is designed to introduce students to research in the broad area of analysis, ranging from classical analysis to modern analysis, with applications in such fields as geometry, mathematical physics, number theory, and statistics.


It is very important for students interested in the analysis program to follow one of the following sequences of introductory graduate level analysis courses. These courses provide the necessary preparation for the more advanced courses offered by the program.

Measure Theory (Concordia MAST 669)
Functional Analysis I (Concordia MAST 662)
Advanced Real Analysis I (McGill MATH-564)
Advanced Real Analysis II (McGill MATH-565)
Advanced Complex Analysis (McGill MATH-566)
Mesure et intégration (Université de Montréal MAT 6111)
Analyse fonctionnelle (Université de Montréal MAT 6112)
Topologie générale (Université de Montréal MAT 6310)
Analyse complexe: sujets spéciaux (Université de Montréal MAT 6182K)
Analyse fonctionnelle I (Laval MAT-7100)
Théorie de la mesure et intégration (Laval MAT-6000)
Équations aux derivées partielles (Laval MAT-7220)

2017-18 Course Listings


Functional Analysis

Prof. Alexander Shnirelman

MAST 662 / 837C

Institution: Concordia University

Advanced Real Analysis 1

Review of theory of measure and integration; product measures, Fubini's theorem; Lp spaces; basic principles of Banach spaces; Riesz representation theorem for C(X); Hilbert spaces; part of the material of MATH 565 may be covered as well.

Prof. Vojkan Jaksic

MATH 564

Institution: McGill University

Topics in Analysis: Fall semester

Prof. John Toth

MATH 595

Institution: McGill University

Mesure et intégration

Contenu du cours: ensembles mesurables,  mesure de Lebesgue; principes de Littlewood, théorèmes de Lusin et de Egorov; intégrale de Lebesgue, théorème de Fubini, espaces L1 et L2; mesures absolument continues, théorème de Radon-Nikodym; éléments de la théorie ergodique; mesure et dimension de Hausdorff, ensembles fractales.

Prof. Dimitris Koukoulopoulos

MAT 6111

Institution: Université de Montréal

Analyse fonctionnelle I

  • Espaces métriques
  • Topologiques, d'Hilbert, de Banach
  • Théorèmes de Hahn-Banach, de Banach-Steinhaus et du graphe fermé
  • Topologies faibles
  • Espaces réflexifs
  • Décomposition spectrale des opérateurs auto-adjoints compacts.

Prof. Marlène Frigon

MAT 6112

Institution: Université de Montréal


Topics in Analysis: Fourier Analysis

Prof. Galia Dafni

MAST 661/4 E (Master's level) or MAST 837/4 E (PhD level)

Institution: Concordia University

Topics in Analysis: Winter semester

Prof. Vojkan Jaksic

MATH 595

Institution: McGill University

Équations aux dérivées partielles - Université de Montréal

Équation des ondes, problème de Sturm-Liouville, distributions et transformation de Fourier, équation de Laplace, espaces de Sobolev, valeurs et fonctions propres du laplacien, éléments de la théorie spectrale, équation de la chaleur.


Prof. Iosif Polterovich

MAT 6110

Institution: Université de Montréal