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DTSTART;TZID=America/New_York:20230322T123000
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DTSTAMP:20260406T210936
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UID:10001278-1679488200-1679491800@cmsa.fas.harvard.edu
SUMMARY:Synchronization in a Kuramoto Mean Field Game
DESCRIPTION:Speaker: Mete Soner (Princeton University) \nTitle: Synchronization in a Kuramoto Mean Field Game \nAbstract:  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 not synchronized 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 incoherence to self-organization.  This approach has found interesting applications including circadian rhythms and jet-lag recovery.  This is joint work with Rene Carmona of Princeton and Quentin Cormier of INRIA\, Paris.
URL:https://cmsa.fas.harvard.edu/event/collquium-32223/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-03.22.2023.png
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DTSTART;TZID=America/New_York:20230322T153000
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CREATED:20230807T172858Z
LAST-MODIFIED:20240215T105007Z
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SUMMARY:Some rigorous results on the Lévy spin glass model
DESCRIPTION:Probability Seminar \nSpeaker: Wei-Kuo Chen (Minnesota)\n\nTitle: Some rigorous results on the Lévy spin glass model \nAbstract: The Lévy spin glass model\, proposed by Cizeau-Bouchaud\, is a mean-field model defined on a fully connected graph\, where the spin interactions are formulated through a power-law distribution. This model is well-motivated from the study of the experimental metallic spin glasses. It is also expected to bridge between some mean-field and diluted models. In this talk\, we will discuss some recent progress on the Lévy model including its high temperature behavior and the existence and variational expression for the limiting free energy. Based on a joint work with Heejune Kim and Arnab Sen.
URL:https://cmsa.fas.harvard.edu/event/probability-32223/
LOCATION:Virtual
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-03.22.23.png
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