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Parcours 2024-2025

Advanced mathematics master 2nd year, 2024 - 2025

Courses are organized in thematic programs, and there will be five such programs in 2024-2025. 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.

Slides of the presentation meeting, March 2024.

Partial Differential Equations and Applications

Basic courses

  • Evolutionary PDEs (Dragoş Iftimie)
  • 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)
  • Systems of Reaction-diffusion equations: global existence and stochastic modelling  (Julien Vovelle)
  • On the non linear Schrödinger equation (Nikolay Tzvetkov)
  • Semiclassical dynamics (Laurent Laflèche)

Probability and statistics

Some courses are joint with the M2 program ``Maths in action'' .

Details of the program.

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 (Aurélien Garivier, Clément Marteau)

Advanced courses

  • 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)
  • Scaling limits of interacting particle systems (Oriane Blondel, Christophe Poquet)
  • 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)

Basic courses

  • Local fields (Laurent Berger)
  • Algebraic curves and elliptic curves (François Brunault)
  • Modular forms (Sandra Rozensztajn)

Advanced courses

  • p-adic modular forms (Benjamin Schraen)
  • Bruhat-Tits tree of SL(2) and non-Archimedean geometry (Bertrand Rémy)
  • Elliptic curves in computational number theory (Benjamin Wesolowski)

Higher Algebra and Formalised Mathematics

Basic courses

  • Algebraic rewriting and Categorification (Stéphane Gaussent and Philippe Malbos)
  • Foundations of formalised mathematics and higher-dimensional rewriting (Georg Struth)
  • Introduction to LEAN (Sophie Morel, Filippo A. E. Nuccio, Xavier-François Roblot)

Advanced courses

  • Rewriting theory of higher algebras (Stéphane Gaussent, Philippe Malbos)
  • Calculus of Inductive Constructions and Coq (Damien Pous)
  • Advanced project on LEAN (Sophie Morel, Filippo A. E. Nuccio and Xavier-François Roblot)

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)


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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