Parcours 2025 -2026
Advanced mathematics master 2nd year, 2025 - 2026
Courses are organized in thematic programs, and there will be four such programs in 2025-2026. 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 four programs will be offered.
Poster for the program.
Probability and statistics
Basic courses
- Stochastic calculus (Marielle Simon)
- Random walks (Thomas Budzinski)
- Concentration of measure in probability and high-dimensional statistical learning (Guillaume Aubrun, Aurélien Garivier, Rémi Gribonval)
- Stochastic modelization and statistical learning (Romain Azaïs, Aurélien Garivier, Clément Marteau)
Advanced courses
- Graphs and ecological networks (Clément Marteau, Thibault Espinasse)
- Stochastic Partial Differential Equations and application to turbulence theory (Igor Honoré, Laurent Chevillard)
- Neural Networks (Cédric Gerbelot, Aurélien Garivier, Rémi Gribonval, Julian Tachella)
- Optimal transport and learning (Aymeric Baradat, Nicolas Boneel, Titouan Vayer)
- Inverse problems and parcimony (Yohann de Castro, Rémi Gribonval)
- Spectral Theory of random operators (Raphaël Ducatez, Christophe Sabot)
- Phase transitions in spin systems (Christophe Garban)
- Scaling limits for stochastic processes: applications to biology (Hélène Leman and Céline Bonnet)
Partial differential equations and applications
Basic courses
- Evolutionary PDEs (Dragoş Iftimie, Nikolat Tzvetkov)
- Calculus of variations and elliptic equations (Filippo Santambrogio)
- A few models and methods for life sciences (Thomas Lepoutre
Advanced courses
- Optimal transport: introduction and overview (Cédric Villani)
- Random and stochastic reaction-diffusion equations (Julien Vovelle)
- Hyperbolic and parabolic partial differential equations: theory and approximation (Frédéric Lagoutière)
- Semiclassical dynamics (Laurent Laflèche)
Transcendence
Basic courses
- Introduction to transcendental number theory (Boris Adamczewski)
- Linear differential equations (Julien Roques)
- Introduction to model theory, omega-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)
Topics in Complex, Algebraic, Kähler and Symplectic geometries
Basic courses
- Introduction to Kähler geometry (Jean-Claude Sikorav)
- Introduction to Complex algebraic geometry (Antoine Etesse)
- Convexity in symplectic geometry (Klaus Niederkrüger)
- Reductive algebraic group over C (Jérôme Germoni)
Advanced courses
- GIT and Kempf-Ness theorem (Nicolas Ressayre)
- Symplectic capacities (Marco Mazzucchelli)
- Hermite-Einstein metrics and slope stability (Eveline Legendre)
contacts
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
04.72.72.85.53
Université Claude Bernard
Aline Ghedira et Ségolène Serre
scolarite.mathematiques@univ-lyon1.fr
Contact
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