We will review a number of topological themes in number theory, starting with homology and ending with a discussion arithmetic homotopy.

초록 첨부: Void.pdf

In this talk, I will briefly introduce some properties of the incompressible Navier-Stokes equations. Then, I will review some classical results obtained by harmonic analysis tools.

Non-vanishing modulo a prime of special values of various $L$-functions are of great importance in studying structures of relevant arithmetic objects such as class groups of number fields and Selmer groups of elliptic curves. While there hav...

It is a fascinating and challenging problem to count number fields with bounded discriminant. It has so many applications in number theory. We give two examples. First, we compute the average of the smallest primes belonging to a conjugacy ...

수학의 기하학, 위상학 그리고 알고리즘의 건축디자인의 적용 사례 및 이론적 배경

I will give a very personal overview of the evolution of mainstream applied mathematics from the early 60's onwards. This era started pre computer with mostly analytic techniques, followed by linear stability analysis for finite difference a...

Since Fourier introduced the Fourier series to solve the heat equation, the Fourier or polynomial approximation has served as a useful tool in solving various problems arising in industrial applications. If the function to approximate with t...

Creating information and knowledge from large and complex data sets is one the fundamental intellectual challenges currently being faced by the mathematical sciences. One approach to this problem comes from the mathematical subdiscipline cal...

Lagrangian Floer theory in symplectic manifold associate a category (A infinity category) to a symplectic manifold. More than 20 years ago a relation of a relation between Lagrangian Floer theory and Gauge theory was studied by Floer himself...

In his survey paper in the Bulletin of the AMS from 2002, R. J. Gardner discussed the Brunn-Minkowski inequality, stating that it deserves to be better known and painted a beautiful picture of its relationship with other inequalities in anal...

I will talk on Cannes's Embedding Conjecture, which is considered as one of the most important open problems in the field of operator algebras. It asserts that every finite von Neumann algebra is approximable by matrix algebras in suitable s...

Partial differential equations with applications to biology

Given a one-parameter family of algebraic varieties, its point-wise limit is usually too small whereas its algebraic limit is usually too big. I will introduce a notion of meaningful geometric limit and explain how it can be effectively comp...

If a problem has an approximate solution, we try to get some information of the linearized kernel of the problem at the approximate solution to find a real solution. In this talk, I would like to introduce a different approach which is purel...

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...

On some nonlinear elliptic problems

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...