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Parcours 2019 - 2020

Master of Advanced Mathematics, 2nd year (MA2)

Programs of Courses for 2019-2020


There are four programs. Three of them are complete ie consist in three Basic Courses in September-December, and three Advanced Courses in January-March. The program "Geometry" comprises only two Basic Courses and two Advanced Courses, and must be supplemented by courses from other programs (for example the course of Olivier Druet).

With the agreement of the head of the MA2, it is possible to mix courses from different programs, provided some scientific consistency is maintained.


Geometry, h-principle and Effective Methods

    • Basic Courses: h-principle, Vincent Borrelli and Jean-Claude Sikorav / Riemannian geometry (towards isometric immersions), Abdelghani Zeghib and Bruno Sévennec

    • Advanced Courses: Effective Geometry, Francis Lazarus and Boris Thibert / Besse and Zoll manifolds, Marco Mazzucchelli.


Partial Differential Equations: Analysis and Use

    • Basic Courses: Variational methods and elliptic PDEs, Olivier Druet / Evolution equationsFrancesco Fanelli / Approximation by PDEs, Julien Vovelle

    • Advanced Courses: Scaling limits and kinetic theory, Sergio Simonella / Mathematical methods for the Navier-Stokes equations, Lorenzo Brandolese / Analysis of PDE models for biology, Vincent Calvez.



    • Basic Courses: Stochastic Calculus, Grégory Miermont / Statistical Physics, Christophe Garban / Random Walks on Graphs, Fabio Toninelli

    • Advanced Courses: High-dimensional phenomena, Guillaume Aubrun / Random GraphDieter Mitsche / Integrable probability, Jérémie Bouttier.


Representation Theory, from Schubert Calculus to Rewriting

    • Basic Courses: Schubert Calculus, Riccardo Biagioli and Philippe Nadeau / Representation Theory of GLn(C), Stéphane Gaussent and Nicolas Ressayre / Algebraic Structure of Rewriting, Philippe Malbos and Fabio Zanasi.

    • Advanced Courses: Coxeter Systems, Riccardo Biagioli and Olivier Mathieu / Diagrammatic Categories and Representations, Stéphane Gaussent and Kenji Iohara / Operadic and categorical rewriting, Yoann Dabrowski and Philippe Malbos.


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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