PROGRAM

Weizhu Bao National University of Singapore

Bio: Weizhu BAO is a Professor at the Department of Mathematics, National University of Singapore (NUS). He got his PhD from Tsinghua University in 1995 and afterwards he had postdoc and faculty positions at Tsinghua University, Imperial College, Georgia Institute of Technology and the University of Wisconsin at Madison. His research interests include numerical methods for partial differential equations, scientific computing/numerical analysis, analysis and computation for problems from physics, chemistry, biology and engineering sciences. He has made significant contributions in modeling and simulation of Bose-Einstein condensation, solid-state dewetting and geometric PDEs; and in multiscale methods and analysis for highly oscillatory PDEs. He had been on the Editorial Board of SIAM Journal on Scientific Computing during 2009—2014 and is currently on the Editorial Board of SIAM Journal of Numerical Analysis. He was awarded the Feng Kang Prize in Scientific Computing by the Chinese Computational Mathematics Society in 2013. Weizhu Bao was an invited speaker at the ICM 2014 in Seoul. He is a Fellow of the American Mathematical Society, the Society of Industrial and Applied Mathematics and the Singapore National Academy of Science.

Energy-stable parametric finite element methods (PFEM) for geometric PDEs and applications.

In this talk, I begin with a review of different geometric flows (PDEs) including mean curvature (curve shortening) flow, surface diffusion flow, Willmore flow, etc., which arise from materials science, interface dynamics in multi-phase flows, biology membrane, computer graphics, geometry, etc. Different mathematical formulations and numerical methods for mean curvature flow are then discussed. In particular, an energy-stable semi-implicit parametric finite element method (PFEM) is presented in detail. Then the PFEM is extended to surface diffusion flow and anisotropic surface diffusion flow, and a structure-preserving implicit PFEM is proposed. Finally, sharp interface models and their PFEM approximations are presented for solid-state dewetting. This talk is based on joint works with Harald Garcke, Wei Jiang, Yifei Li, Robert Nuernberg, Yan Wang and Quan Zhao.

Sergei Kuksin Steklov Mathematical Institute of RAS

Bio: Sergey Kuksin is a Leading Scientific Researcher at Steklov Mathematical Institute of RAS, a Senior Researcher at the Mathematics Institute of Jussieu–Paris Rive Gauche and a Professor at Heriot-Watt University. He became Doctor of Sciences from Lomonosov Moscow State University in 1981. Kuksin’s research deals with KAM theory in PDE. He was an invited speaker of ICM 1998 in Berlin. In 2016, he received Lyapunov Award from the Russian Academy of Sciences.

Kolmogorov's theory of turbulence, the Landau criticism and their rigorous 1d versions.

Kolmogorov's theory of turbulence contains two celebrated heuristic laws, related to the second and third moments of increments of the fluid's velocity field u(t,x+r)-u(t,x) for "small but not too small r". Kolmogorov claimed that the moments as functions of r have the form (universal pre-factor) x (certain exponent of |r|). Landau's criticism was that the pre-factor indeed may be universal for the third moment, but not for the second. In my talk, I will explain that the two heuristic laws allow rigorous versions, related to a fictitious one-dimensional fluid, described by the Burgers equation. There - indeed - the pre-factor in the law for the third moment is explicit and universal, but that for the second moment cannot be such. I will explain the difference between the two moments which leads to this effect.

 The meeting will be held in the form of a webinar on the Zoom platform.

Pre-registration for the event is not required.

Link to the conference:

https://us06web.zoom.us/j/83770735283?pwd=NTZxNTJkMjNLWWRWK3pXdzRXRW5iQT09

Meeting ID : 837 7073 5283

Passcode：987654