In this talk we will take a look at analysis on quantum spaces using non-commutative Lp spaces. We will first review what a non-commutative Lpspace is, and then we will see few examples of quantum spaces where Lp analysis problems arise natu...

Stochastic heat equations (SHE) usually refer to heat equations perturbed by noise and can be a model for the density of diffusing particles under a random potential. When the irregularity of noise is dominating the diffusion, SHE exhibits ...

The general theory implies that the distribution of an irreducible Markov chain converges to its stationary distribution as time diverges to infinity. The speed of corresponding convergence is a significant issue in the study of mathematical...

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...

※ 강연 앞 부분이 잘렸습니다. (강연자료 다운: Mirror symmetry of pairings.pdf ) 초록: Mirror symmetry has served as a rich source of striking coincidences of various kinds. In this talk we will first review two kinds of mirror symmetry statem...

I will give a broad introduction to how to mechanize mathematics (or proof), which will be mainly about the proof assistant Coq. Mechanizing mathematics consists of (i) defining a set theory, (2) developing a tool that allows writing definit...

The 21st century is the age of life science. Two issues in the life sciences are that humans live long, healthy lives and maintain a steady state of the earth's ecosystems despite disturbances. In this talk, we will look at how mathematics i...

Emerging infectious diseases have long been recognized as a continuous, inevitable, unpredictable threat to the global public health. Hence, understanding the underlying dynamics why they spread and what causes epidemics gives key ideas of i...

헤지펀드에서 사용하고 있는 전략들을 간단히 소개하고 수학적 아이디어가 사용되는 예를 들어 퀀트의 필요한 능력을 소개한다. 수학과 헤지펀드의 관점에서 머신러닝(인공지능)의 사용 예를 설명한다.

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...

For a given compact Lie group G, classifying all manifolds equipped with G-actions is one of the most fundamental and important problems in differential geometry. In this talk, We will discuss the problem in the symplectic category and expl...

Several L-functions with the names Dirichlet, Dedekind, Elliptic, and so on usually have p-adic counterparts, so called p-adic L-functions, which share many similar properties such as an evaluation formula at s=1, class number formula, and e...

The theory of L-functions and zeta functions have been the key subject of mathematical research during the centuries since the Riemann zeta function was introduced and its important connection to the arithmetic of the integer was recognized....

For the irreducible representations of the Hecke algebras, the minimal elements in each conjugacy class play an important role. In this talk, we try to review the minimal length elements and characterize in a more efficient way to find the m...

We survey work on a class of nonlinear elliptic PDEs that was initiated by Moser. Methods from PDE, dynamical systems, and geometry set in the framework of the calculus of variations are used to construct a rich collection of solutions.

Introduction to Non-Positively Curved Groups

In this talk, we briefly introduce how a combinatorial object, Integer partition, is related with number theoretic subjects : q-series and modular forms. In particular, we will focus on (1) combinatorial proof for q-series identities (2) ari...

A knot is a smooth embedding of an oriented circle into the three-sphere, and two knots are concordant if they cobound a smoothly embedded annulus in the three-sphere times the interval. Concordance gives an equivalence relation, and the se...

We obtain a quantitative and robust proof that incompressible fluid models are strongly ill-posed in critical Sobolev spaces, in the sense that norm inflation and even nonexistence occur for critical initial data. We then show how to use th...

A classical theorem of Jacobs, de Leeuw and Glicksberg shows that a representation of a group on a reflexive Banach space may be decomposed into a returning subspace and a weakly mixing subspace. This may be realized as arising from the idem...