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Parcours 2022 - 2023

Advanced mathematics master 2nd year, 2022-2023

Courses are organized in thematic programs, and there will be five such programs in 2022-2023. Courses will start in mid September. However, the programs will also offer refresher courses, that will start during the week of August 29th. The following five programs will be offered.

Partial differential equations and applications

Basic courses (3x24h)

- Evolutionary PDEs, Dragos Iftimie
- Discontinuous finite-element methods and applications, Daniel Le Roux
- Calculus of variations and elliptic partial differential equations and systems, Petru Mironescu

Advanced courses (4x18h)

- Optimal transport: introduction, applications and derivation, Aymeric Baradat
- Compressible Viscous Flows with Low or Intermediate Regularity, Didier Bresch
- Many-body quantum mechanics and mean-field limits, Nicolas Rougerie
- Numerical methods for yield stress fluids, Paul Vigneaux

Geometry and dynamics

Basic courses (3x24h)

- Complex algebraic geometry, Sophie Morel
- Differentiable dynamical systems, Jean-Claude Sikorav
- Introduction to Lie groups and symmetric spaces, Bruno Sévennec

Advanced courses (3x24h)

- Introduction to symplectic dynamics, Marco Mazzucchelli
- Holomorphic foliations, Stéphane Druel
- Dynamics of complex differential equations, Aurélien Alvarez and Ghani Zeghib

Algebraic, topological, and homotopical aspects of computer algebra and formalisation

Basic courses (3x24h)

- Computational Algebraic Topology, Kenji Iohara and Olga Kravchenko
- Categorical representation theory, Stéphane Gaussent and Alistair Savage
- Introduction to homotopy type theory, Philippe Malbos and Samuel Mimram

Advanced courses (3x24h)

- Computational Topology and Persistent Homology, Kenji Iohara and Philippe Malbos
- Operadic and diagrammatic linear rewriting, Stéphane Gaussent and Yoann Dabrowski
- Formalisation for the working mathematician, Filippo Nuccio

Probability and statistics

Basic courses (3 out of 4x24h)

- Statistical Physics, Christophe Garban
- Stochastic Calculus, Grégory Miermont
- Concentration of measure, Guillaume Aubrun, Aurélien Garivier and Rémi Gribonval
- Stochastic Modelling and Statistical Learning, Aurélien Garivier and Clément Marteau

Advanced courses (4 out of 6x18h)

- Scaling Limits of Interacting Particle Systems, Oriane Blondel and Christophe Poquet
- Large random matrices and applications, Alice Guionnet
- An Approach of Disordered Systems, via PDEs, Jean-Christophe Mourrat
- Neural Networks, Aurélien Garivier
- Optimal Transport and Machine Learning, Filippo Santambrogio, Ivan Gentil, Yohann de Castro, Ievgen Reedko, Julie Digne and Nicolas Bonnel
- Inverse problems and parcimony, Yohann de Castro and Rémi Gribonval

p-adic Geometry and Representations

Basic courses (3x24h)

- Local fields, Laurent Berger
- Modular and automorphic forms, Olivier Taïbi
- Introduction to rigid analytic geometry, Sophie Morel

Advanced courses (3x24h)

- Galois representations, deformations, and families of Galois representations, Sandra Rozensztajn
- Rigid geometry of algebraic curves, Amaury Thuillier
- Reductive groups over local fields, Bertrand Rémy


Responsable du MA2 :

Laurent Berger,
ENS, site Monod, bâtiment GN1 (l’arche), 4e étage

Gestionnaires de scolarité

École normale supérieure

Sylvie Griot
Site Monod, bâtiment LE (accolé au GN1, côté nord de l’allée d’Italie)
bureau 536, allée Allan C. Wilson

Université Claude Bernard

Delphine Jouve


ENS de Lyon
15 parvis René Descartes - BP 7000
69342 Lyon Cedex 07 - FRANCE
Tél. : Site René Descartes (siège) : +33 (0) 4 37 37 60 00
Site Jacques Monod : +33 (0) 4 72 72 80 00

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