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Parcours 2023 - 2024

Advanced mathematics master 2nd year, 2023-2024

Courses are organized in thematic programs, and there will be five such programs in 2023-2024. Courses will start in mid September. However, the programs will also offer refresher courses, that will start during the last week of August. The following five programs will be offered.

Poster for the program.

Partial differential equations and applications

Basic courses (3x24h)

• PDE modeling in the natural sciences: an asymptotic viewpoint (Vincent Calvez)
• Evolutionary PDEs (Emmanuel Grenier)
• Calculus of variations and elliptic partial differential equations and systems (Petru Mironescu)

Advanced courses

• Optimal transport: introduction, applications and derivation (Aymeric Baradat)
• Compressible viscous flows with low or intermediate regularity (Didier Bresch)
• On the non linear Schrödinger equation (Nikolay Tzvetkov)
• Kinetic equations with collisions (Cédric Villani)

Statistics and probability

Basic courses (3x24h)

• Stochastic calculus (Marielle Simon)
• Concentration of measure in probability and high-dimensional statistical learning (Guillaume Aubrun, Aurélien Garivier, Rémi Gribonval)
• Stochastic modelization and statistical learning (Aurélien Garivier, Clément Marteau)

Advanced courses

• An approach of disordered systems via PDEs (Jean-Christophe Mourrat)
• Graphs and ecological networks (Clément Marteau, Thibault Espinasse)
• Neural Networks (Aurélien Garivier)
• Optimal transport and learning (Filippo Santambrogio, Ievgen Reedko, Nicolas Bonneel)
• Inverse problems and parcimony (Yohann de Castro, Rémi Gribonval)

Transcendence: between number theory, differential equations and model theory

Basic courses (3x24h)

• Introduction to transcendental number theory (Boris Adamczewski)
• Linear differential equations (Julien Roques)
• Introduction to model theory, ω-stability and o-minimality (Frank Wagner)

Advanced courses

• Diophantine approximation and transcendence theory (Anthony Poëls)
• An introduction to G-functions (Eric Delaygue)
• Model theory of differential fields of characteristic zero (Rémi Jaoui)

Groups and dynamics

Basic courses (3x24h)

• Representation theory (Sophie Morel, Bruno Sévennec)
• Geometric group theory (Adrien Le Boudec)
• Introduction to dynamical systems and ergodic theory (Jean-Claude Sikorav)

Advanced courses

• Amenability and orbit equivalence (Damien Gaboriau, Todor Tsankov)
• Groups arising from dynamical systems (Nicolás Matte Bon)
• Dynamics of complex differential equations (Aurélien Alvarez, Ghani Zeghib)
• Geodesic flows (Marco Mazzucchelli)

Mathematical physics

Basic courses (3x24h)

• Fiber Bundles in Differential Geometry and Gauge Theories (Eveline Legendre)
• Symplectic Geometry and Lie Groupoids (Leonid Ryvkin)
• Quantum Mechanics and Quantum Information Theory (Guillaume Aubrun)

Advanced courses

• Topological phases of matter (Johannes Kellendonk)
• Quantum Field Theory and Renormalization (Alessandra Frabetti)
• Seiberg-Witten Invariants (Klaus Niederkrüger)
• Poisson Sigma Models (Thomas Strobl)


Responsable du MA2 :

Nicolas Rougerie
ENS, site Monod, bâtiment GN1 (l’arche), 4e étage

Gestionnaires de scolarité

École normale supérieure

Sophie Bonche
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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