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Parcours 2020 - 2021

Advanced mathematics 2nd year 2020-2021

A detailed description of the courses offered in 2020-2021 can be found in this document. Courses will start in mid September. However, some of the programs will offer refresher courses, that will start during the week of August 31st. Courses are organized in thematic programs, and there will be the following three programs:

Partial Differential Equations and applications

Refresher courses:

Basic tools of functional analysis (Simon Masnou)
Stochastic tools (Grégory Miermont)
Starting with PDEs (Petru Mironescu)
Basic courses (3x24h): 
Evolution equations (Emmanuel Grenier)
Calculus of variations and elliptic equations (Filippo Santambrogio)
Approximation by PDEs (Julien Vovelle)
Advanced courses (4x18h):
Stochastic PDEs and their asymptotic behaviour (Alexandre Boritchev)
Kinetic theory (Laure Saint-Raymond)
Optimal transport theory and links with parabolic equations (Ivan Gentil)
Numerical approximation methods for fluid mechanics (Khaled Saleh)

Number theory and arithmetic geometry

Basic courses (3x24h): 
Modular and automorphic forms (Gabriel Dospinescu)
Modern algebraic geometry (Sophie Morel)
The fundamental group in arithmetic geometry (Philippe Gille) 
Advanced courses (3x24h):
The stack of vector bundles on a curve (Vincent Pilloni)
An introduction to Drinfeld modules (Tuan Ngo Dac and Federico Pellarin)
The Arthur-Selberg trace formula and the local Jacquet-Langlands correspondence (Olivier Taïbi)

Probability and statistics

Refresher courses:

Basic tools of functional analysis (Simon Masnou)
Stochastic tools (Grégory Miermont)
Starting with PDEs (Petru Mironescu)
Basic courses (3 out of 4x24h):
Concentration of measure in probability and high-dimensional statistical learning (Guillaume Aubrun, Aurélien Garivier, Rémi Gribonval)
Non-parametrics (Irène Gannaz, Clément Marteau, Franck Picard)
Stochastic calculus (Grégory Miermont)
Statistical physics (Christophe Garban)
Advanced courses (4 out of 6x18h):
Branching random walks (Xinxin Chen)
Determinantal processes (Adrien Kassel)
Random graphs (Dieter Mitsche)
Mathematical foundations of deep neural networks (Aurélien Garivier, Rémi Gribonval)
Inverse problems and high dimension (Yohann de Castro, Rémi Gribonval)
Advanced machine learning theory (Romain Azais, Antoine Chambaz, Laurent Jacob)

Other topics

There will be no thematic program in geometry. Such a program (groups and geometry) will be offered, for instance, in Grenoble, see the program here.


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

Prisca Blachier
Bâtiment Jean Braconnier (rez-de-chaussée)


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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