Topic: On the long time behavior of equilibria in a Kuramoto Mean Field Game

Lecturer: Marco Cirant, University of Padova, Italy

Time: November 6, 2024, 15:00-17:00, UTC+8

ZOOM Meeting: 656 484 6175

Biography:

Marco Cirant is currently an associate professor in the University of Padova. He received his Ph.D. degree in the University of Padova in 2014. He is now a postdoc in the University of Milan, Italy. Prof. Cirant’s research interest is in qualitative analysis of semilinear elliptic equation, nonlinear elliptic equations and parabolic equations. In particular, he has made a series of progress in Mean-Field Games Model, the theory of maximum regularity of solutions to Hamilton Jacobi equations, etc. He has published multiple high-quality papers in renowned journals in mathematics including JEMS, Math Ann., JMPA, ARMA.

Abstract:

In a recent work, R. Carmona, Q. Cormier and M. Soner revised the classical Kuramoto model, originally motivated by systems of chemical and biological oscillators, within the large population differential game framework of MFG. These MFG model exhibits several stationary equilibria, and the question of their ability to capture long time limits of dynamic equilibria is largely open. I will discuss in the talk how to show that (up to translations) there are two possible stationary equilibria only - the incoherent and the synchronised one - provided that the interaction parameter is large enough. Finally, I will present some local stability properties of the synchronised equilibrium.

Rewritten by: Mei Mengqi

Edited by: Li Tiantian

Source: School of Mathematics and Statistics