# Mathematics Colloquium

#### Synchronization in the Kuramoto Mean Field Game and an Application to Jet Lag Recovery

**Speaker:**
Rene Carmona, Princeton

**Location:**
Warren Weaver Hall 1302

**Date:**
Monday, November 21, 2022, 3:45 p.m.

**Synopsis:**

We study the classical Kuramoto model as an infinite horizon mean field game. The system is shown to exhibit both incoherence and synchronization:

1) Incoherence when the interaction parameter is below a sharp critical value follows the stability of the uniform distribution.

2) Above the critical value, the game bifurcates and develops self-organizing time homogeneous Nash equilibria. As interactions strengthen, these stationary solutions become fully synchronized. Results are proved by a patchwork of techniques from nonlinear partial differential equations and stochastic optimal control. If time permits, the inclusion of a forcing term and an application to jet lag recovery will be discussed.

The talk will draw from an older paper with C. Graves and a recent work with M. Soner and Q. Cormier.