Organizing Committee
- Huijun Fan (SMS PKU)
symplectic geometry and mathematical physics, geometric analysis - Sergey Gorchinskiy (MI RAS)
algebra and geometry: algebraic geometry, K-theory - Hailiang Li (SMS CNU)
fluid mechanics, partial differential equations, analysis - Jinsong Liu (AMSS)
algebraic geometry: singularity theory - Yi Liu (BICMR)
Topology of 3-manifolds, hyperbolic geometry - Denis Osipov (MI RAS)
algebraic geometry, number theory, integrable system - Ye Tian (UCAS, AMSS)
Number Theory, Arithmetic Geometry, Iwasawa Theory - Alexey Tuzhilin (MSU)
geometry: Riemannian and metric geometry - Yue Yang (CE PKU)
computation mathematics and mechanics - Ping Zhang (AMSS)
P. D. E.: fluid equation and semi-classical analysis - Alexander Zheglov (MSU)
geometry: algebraic geometry, integrable system
PROGRAM
11:00 (GMT+3)
| Vladimir Temlyakov Steklov Institute of Mathematics, Russia, University of South Carolina, USA |
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Bio: Vladimir Temlyakov works in Steklov Mathematical Institute of RAS, Moscow State University, University of South Carolina. He is a top expert in function theory: approximations of functions in one variable and multivariable cases (approximations by polynomials, n-widths, optimal cubature formulas). Integral operators (estimates of singular numbers, approximation numbers, bilinear approximation of kernels of these operators). |
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Discretization and recovery.
Recently, there was a big progress in studying sampling discretization of integral norms of functions from finite dimensional subspaces and from collections of such subspaces (universal discretization). It was established that sampling discretization results are useful in a number of applications. In particular, they turn out to be useful in sampling recovery. We will discuss some of those results.
The goal of this talk is to survey the corresponding results, and connect together ideas, methods, and results from different areas of research related to problems of discretization and recovery in the case of finite-dimensional subspaces.
12:00 (GMT+3)
| Huijiang Zhao Wuhan University |
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Bio: Huijiang Zhao, professor of School of Mathematics and Statistics of Wuhan University. He got his bachelor degree from Central China Normal University in 1988, and PhD. from the Chinese Academy of Sciences in 1997. He is interested in mathematical theories of nonlinear partial differential equations, especially the global well-posedness of kinetic equations and the corresponding hydrodynamic limits. |
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Hilbert expansion for some nonrelativistic kinetic equation.
The Vlasov-Maxwell-Landau (VML) system and the Vlasov-Maxwell-Boltzmann (VMB) system are fundamental models in dilute collisional plasmas. In this talk, we are concerned with the hydrodynamic limits of both the VML and the non-cutoff VMB systems in the entire space. Our primary objective is to rigorously prove that, within the framework of Hilbert expansion, the unique classical solution of the VML or non-cutoff VMB system converges globally over time to the smooth global solution of the Euler-Maxwell system as the Knudsen number approaches zero.
The core of our analysis hinges on deriving novel interplay energy estimates for the solutions of these two systems, concerning both a local Maxwellian and a global Maxwellian, respectively. Our findings address a problem in the hydrodynamic limit for Landau-type equations and non-cutoff Boltzmann-type equations with a magnetic field. Furthermore, the approach developed can be seamlessly extended to assess the validity of the Hilbert expansion for other types of kinetic equations.
The meeting will be held in the form of a webinar on the Voov platform.
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