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About the School

Abstracts

Keisuke Takasao
Associate Professor @ Kyoto University, Japan.
Professor Takasao received his PhD in 2013 from the Hokkaido University in Japan, under the supervision of Professor Yoshihiro Tonegawa. He continued his research as a postdoctoral researcher @ Hokkaido University until March 2014, and was then appointed as Assistant Professor @ Kanagawa University. Takaso was a postdoctoral researcher of Professor Yoshikazu Giga from 2015 until 2017 @ Tokyo University. Since October 2017, he is appointed as Associate Professor on a tenure-track @ Kyoto University.
Phase field method for volume preserving mean curvature flow

In 1993, Ilmanen proved a global existence of the weak soluton to the mean curvature flow in the sense of the Brakke flow by using the phase field method. On the other hand, if we try to apply Ilmanen's proof to the volume preserving mean curvature flow, difficultes arise in the \(L^2\)-estmates of the non-local term. In this talk, we show a global existence of the weak solution in the sense of \(L^2\)-flow, in the \(2\) or \(3\)-dimensional torus. We consider the Allen-Cahn equa+on with non-local term studied by Golovaty, and show the \(L^2\)-estmates of the non-local term and the monotonicity formula. As a recent result, we also prove a global existence of the weak solution to the mean curvature flow with forcing term in the suitable Sobolev space, by developing the method.

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Feng-Yu Wang
Cheung Kong Chair Professor @ Beijing Normal University, China.
Professor Wang received his PhD in 1993 @ the Beijing Normal University in China, where he also accepted the offer of employment to a tenure track position afterwards. Wang was promoted Professor @ the Beijing Normal University in 1995, where he also has the prestigious title of Changjiang Chair Professor since 2000. Since 2007, Professor Wang parallel to his appointed at BNU also Research Professor @ Swansea University in the UK and since 2016, Professor @ the Tiajin University.
Exponential Convergence in Entropy of McKean-Vlasov SDEs

By using log-Harnack and Talagrand inequalities, the exponential convergence in entropy is proved for non-degenerate or degenerate Mckean-Vlasov SDEs. As applications, this type exponential convergence is confirmed for non- degenerate/degenerate granular media type equations generalizing existing studies on the exponential convergence in a mean field entropy studied by J. A. Carrillo, R. J. McCann, C. Villani (2003) and A. Guillin, W. Liu, L. Wu, C. Zhang (2019).

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Benjamin Gess
Max Planck Institute for Mathematics in the Sciences, Leipzig Universität Bielefeld, Fakultät für Mathematik @ Germany.
Benjamin is a reseach group leader at the Max-Planck Institute for Mathematics in the Sciences. Their research centers around stochastic partial differential equations (SPDE), random dynamical systems, rough paths, stochastic scalar conservation laws and singular-degenerate quasilinear SPDE, with emphasis on stochastic porous media equations, stochastic fast diffusion equations and p-Laplace equations.
Large deviations for conservative, stochastic PDE and non-equilibrium fluctuations

Macroscopic fluctuation theory provides a general framework for far from equilibrium thermodynamics, based on a fundamental formula for large fluctuaWons around (local) equilibria. This fundamental postulate can be informally justified from the framework of fluctuating hydrodynamics, linking far from equilibrium behavior to zero-noise large deviaWons in conservative, stochastic PDE. In this talk, we will give rigorous justification to this relation in the special case of the zero range process. More precisely, we show that the rate funcWon describing its large fluctuations is identical to the rate function appearing in zero noise large deviations to conservative stochastic PDE, by means of proving the Gamma-convergence of rate functions to approximating stochastic PDE. The proof of Gamma-convergence is based on the well-posedness of the skeleton equation -- a degenerate parabolic-hyperbolic PDE with irregular coefficients, the proof of which extends DiPerna-Lions' renormalization techniques to nonlinear PDE.

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