Speaker: Immanuel Ben-Porat ，University of Basel

Inviter: 夏旭

Title: Singular flows with time evolving weights

Language: Chinese

Time & Venue: 2025.08.01 16:00-17:00 思源楼525

Abstract: The derivation of kinetic equations as mean field limits from microscopic dynamics is a longstanding problem in kinetic theory which goes back to the work of Dobrushin in the late 70s. Recently, this derivation has been resolved for first order systems with Riesz type singularities in the work of Serfaty-Duerinckx and Bresch-Jabin-Wang via the renormalized modulated energy method. The aim of this talk would be to review these developments and explain how this approach can be incorporated within the framework of systems of trajectories which include weights evolving in time according to some appropriate ODE. At the macroscopic PDE level this corresponds to a nonlocal transport equation with a nonlocal source terms. Joint work with Jose Carrillo and Pierre-Emmanuel Jabin.