Medium-field games (continued)

The lecture, a continuation of last year's, continues the presentation of a new theory called " mean-field games theory ", developed in collaboration with Mr. Jean-Michel Lasry. The aim of this theory is to introduce, justify, analyze and apply in different contexts a new class of mathematical models for studying the collective behavior of a very large number of interacting agents (or players in the sense of game theory), all of whom wish to " optimize " their decisions.

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This year, we have completed the detailed presentation of the mathematical framework required to (rigorously) justify the limit when the number of players N tends towards infinity. On the one hand, we indicated the methods for solving non-linear PDEs posed on the space of probability measures, and on the other, we explained how this mathematical framework allowed us to rigorously deduce the equations and systems of " mean-field games " from the systems of equations corresponding to N-player Nash equilibria.

Program

Lecture

09:00 - 10:00

Program

Medium-field games (continued) (1)

Medium-field games (continued) (2)

Non-ergodicity of the Euler equation for incompressible fluids and energy transfer to small scales

Medium-field games (continued) (3)

Medium-field games (continued) (4)

Medium-field games (continued) (5)

Medium-field games (continued) (6)

Price dynamics in a market with asymmetric information

Medium-field games (continued) (7)

Medium-field games (continued) (8)

(Quasi-)variational inequalities and retrograde EDS with constrained jumps

Medium-field games (continued) (9)

Medium-field games (continued) (10)

The compressed sensing and the Shannon-Nyquist theorem

Medium-field games (continued) (11)

Medium-field games (continued) (12)

A priori estimation and existence for elliptic problems with sub-quadratic non-linearity with respect to the gradient

Medium-field games (continued) (13)

Medium-field games (continued) (14)

Modeling the human lung with an infinite tree

Analytical and numerical resolution of mean field games : the case of

Medium-field games (continued) (15)

Medium-field games (continued) (16)

Medium-field games (continued) (17)

Medium-field games (continued) (18)

Self-organization of cell populations : why hyperbolic and kinetic models ?

Medium-field games (continued) (19)

Medium-field games (continued) (20)

Geodesic lines and image analysis

Numerical methods for medium-field games

Global existence and explosion of oscillating solutions of the nonlinear heat equation

Soliton collision for generalized non-integrable Korteweg-de Vries equations

Qualitative properties of Landau-de Gennes energy minimizers

Predicting the propagation path of brittle fracture cracks

Interfaces, surface energy and martensitic transformations

From the Saint-Venant system to the variable-density Navier-Stokes equations. Modeling, kinetic interpretation and numerical simulations

Stability Criteria in a Collisionless Plasma

Feedback control in quantum optics

A continuous theory for congested traffic : models, equilibrium, numerics and regularity

A result on controlling the displacement of a fluid zone

On the regularity problem for Navier-Stokes solutions and other reaction-diffusion systems

Convergence of a Large Time-Step Scheme for Mean Curvature Motion

Explosive solutions, state constraints and asymptotic behavior for viscous Hamilton-Jacobi equations

Some recent results on nonlinear elliptic and parabolic equations

See also