Applied Mathematics Colloquium with Mete Soner: Synchronization in a Kuramoto Mean Field Game

Join the Illinois Tech Department of Applied Mathematics on Monday November 14, at 1:50 p.m., in IT 6D6-1 for a Colloquium by Professor Mete Soner of Princeton University entitled “Synchronization in a Kuramoto Mean Field Game.”

Speaker: Mete Soner, Princeton University

Title: Synchronization in a Kuramoto Mean Field Game

Abstract:

Originally motivated by systems of chemical and biological oscillators, the classical Kuramoto model has found an amazing range of applications from neuroscience to Josephson junctions in superconductors, and has become a key mathematical model to describe self organization in complex systems. These autonomous oscillators are coupled through a nonlinear interaction term which plays a central role in the long term behavior of the system. While the system is unsynchronized when this term is not sufficiently strong, fascinatingly, they exhibit an abrupt transition to a full synchronization above a critical value of the interaction parameter. We explore this system in the mean field formalism. We treat the system of oscillators as an infinite particle system, but instead of positing the dynamics of the particles, we let the individual particles determine endogenously their behaviors by minimizing a cost functional and eventually, settling in a Nash equilibrium. The mean field game also exhibits a bifurcation from unsynhcronization to self-organization. This approach has found interesting applications including circadian rhythms and jet-lag recovery. This is joint work with Rene Carmona and Quentin Cormier of Princeton University.

Speaker Bio:
Mete Soner is a professor, and acting department chair, of Operations Research and Financial Engineering at Princeton University; Prof Soner is also affiliated with the Bendheim Center of Finance and with the program in Applied & Computation Mathematics. He has previously served as professor of mathematics and the Chair of the department at ETH Z├╝rich (the Swiss Federal Institute of Technology in Zurich) and has taught at Carnegie Mellon, and Sabanci and Koc Universities in Istanbul.

His research is on decisions under uncertainty, working on related problems in stochastic optimal control, Markov decision processes, nonlinear partial differential equations, probability theory, mathematical finance and financial economics. He has recently been interested in modern computational approaches to high dimensional stochastic optimal control and mean-field (or McKean-Vlasov) stochastic optimal control.

The speaker has co-authored a book, with Wendell Fleming, on viscosity solutions and stochastic control; Controlled Markov Processes and Viscosity Solutions, and authored or co-authored several articles on nonlinear partial differential equations, viscosity solutions, stochastic optimal control and mathematical finance.

Professor Soner is Editor-in-Chief of SIAM Journal of Financial Mathematics (SIFIN), a Co-Editor of Mathematics and Financial Economics (MAFE) and an associate editor for Finance and Stochastics, Interfaces and Free Boundaries, Mathematics of Operations Research.

During 2011-2016, Professor Soner was the Executive Secretary of the Bachelier Finance Society. He received an Alexander von Humbolt Foundation Research Award in 2014 and was elected as a SIAM Fellow in 2015.