In this talk I will talk about existence and regularity for solutions to the compressible viscous Navier-Stokes equations on nonsmooth domains, especially with corners. The solution is constructed by the decomposition of the corner singulari...
If density of flow is globally a constant, then the flow is said incompressible. Otherwise, the flow is said compressible. Flow motion of compressible inviscid flow is governed by Euler system. The Euler system is a nonlinear PDE system desc...
From 1980’s, the study of Kleinian groups has been carried out in the framework of the paradigm of “Thurston’s problems”. Now they are all solved, and we can tackle deeper problems; for instance to determine the topological types of the defo...
In this talk, numerical methods to solve second-order elliptic partial dierential equations will be presented. First, some of the existing methods, such as the standard Galerkin method, mixed nite element methods etc., will be briey discusse...
Heavy-tailed large deviations and deep learning's generalization mystery
Abstract: While the typical behaviors of stochastic systems are often deceptively oblivious to the tail distributions of the underlying uncertainties, the ways rare events arise are vastly different depending on whether the underlying tail ...
Green’s function for initial-boundary value problem
In this talk, we will present an approach to construct the Green’s function for an initial boundary value problem with precise pointwise structure in the space-time domain. This approach is given in terms of transform variable and physical v...
Category수학강연회소속National Univ. of Singapore강연자Shih-Hsien Yu
It has been more than thirty years since white noise analysis was launched systematically. It is now a good time to have an overview of the theory and to reflect on its advantages in order to anticipate further developments of this theory. O...
Categorical representation theory, Categorification and Khovanov-Lauda-Rouquier algebras
Representation theory is to study the actions of groups or algebras on vector spaces. Recently, its categorical version, categorical representation theory, attracts researchers in representation theory. In this theory we replace "vector spac...
In the early 90's, physicists Bershadsky-Cecotti-Ooguri-Vafa conjectured that the analytic torsion was the counterpart in complex geometry of the counting problem of elliptic curves in Calabi-Yau threefolds. It seems that this conjecture is ...
A function from a group G to integers Z is called a quasi-morphism if there is a constant C such that for all g and h in G, |f(gh)-f(g)-f(h)| < C. Surprisingly, this idea has been useful. I will overview the theory of quasi-morphisms includi...
Chern-Simons invariant and eta invariant for Schottky hyperbolic manifolds
In this talk, I will explain a relationship of the Chern-Simons invariant and the eta invariant for Schottky hyperbolic manifolds. The relating formula involves a defect term given by the Bergman tau function over the conformal boundary Riem...
We rely on intuition every day, and we use mathematics every day. Intuition is fast, powerful and omniapplicable, but sometimes wrong. Mathematics is efficient, powerful and correct, when applicable. Whenever there is an uncertainty, a proof...
