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Curriculum

The academic year starts in September with 2 weeks of Preliminary Courses that are not followed by exams and are intended as a quick review of tools that students should mostly already know from previous studies.

During the M2 year, students must pass the exams of 7 courses freely chosen among the Fundamental and Specialized courses in the list below, the only constraint being that at least 2 courses should be Fundamental. It is also possible to validate up to 2 courses picked in other masters of the Paris area, upon prior approval from the program directors. See the map of those masters.

See here for special rules applying to students that intend to validate a minor in physics.

In addition, students must write a memoir on a research or reading project under the supervision of a research director either in PSL or in another institution. This project may also take the form of an internship in a company.

Each student will be followed by a scientific tutor who will orientate for the choice of the courses and help to find a suitable director for the research internship.

Examples of choices of courses
  1. Profile in Analysis
    • Introduction to non linear elliptic PDEs
    • Introduction to evolution PDEs
    • Introduction to dynamical systems
    • Variational problems and optimal transport
    • Continuous optimisation
    • Introduction to control theory
    • One course among
      • Dynamics of semi-linear wave equation
      • Variational and geodesic methods for image analysis
      • Numerical methods for deterministic and stochastic problems
  2. Profile in Probability
    • Limit theorems and large deviations
    • Stochastic Calculus
    • Markov Chains and Mixing times
    • Integrable probability and the KPZ universality class
    • Random geometric models
    • Introduction to statistical mechanics and interacting particle systems
    • Random walks and random media
  3. Profile at the interface Analysis-Probability
    • Stochastic Calculus
    • Introduction to evolution PDEs
    • Introduction to non linear elliptic PDEs
    • Pathwise (rough) stochastic analysis
    • 3 courses among
      • Entropy methods, functional inequalities and applications
      • Stochastic control
      • Numerical methods for deterministic and stochastic problems
      • Mean field games (pre-requisite: stochastic control)
      • Variational problems and optimal transport

Preliminary Courses

Fundamental Courses

Analysis

Probability

At the interface of analysis and probability

Dynamical Systems and Geometry