Regularity of solutions of Hamilton-Jacobi equation on a domain

The revolution of molecular biology in the early 1980s has revealed complex network of non-linear and stochastic biochemical interactions underlying biological systems. To understand this complex system, mathematical models have been widely ...

Given a group of isometries of a metric space, one can draw a random sequence of group elements, and look at its action on the space.  What are the asymptotic properties of such a random walk?  The answer depends on the geometry of the space...

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...

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현대 사회에서 수학의 역할과 수학자에 대한 수요는 갈수록 증가하고 있다. 미국의 어떤 조사에서는 수학자가 가장 선망 받는 직업으로 분류되고, 영국에서 수학이 경제에 미치는 영향을 분석한 Deloitte 보고서에 따르면 영국 직업의 10%가 수학 연구와 직접...

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The character of the finite-dimensional irreducible modules over a finite-dimensional simple Lie algebra is given by the celebrated Weyl character formula. However, such a formula does not hold in general for finite-dimensional irreducible m...

Empirical observations have shown that for an adequate description of many random phenomena non-Gaussian processes are needed. The paths of these Markov processes necessarily have jumps. Their generators are nonlocal operators which admit a ...

The goal of this lecture is to explain and motivate the connection between AubryMather theory (Dynamical Systems), and viscosity solutions of the Hamilton-Jacobi equation (PDE). This connection is the content of weak KAM Theory. The talk sho...

정년퇴임기념강연

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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...

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...

To explain Ramanujan's integer partition function congruences, Dyson's rank and Andrews-Garvan's crank have been introduced. The generating functions for these two partition statistics are typical examples of mock Jacobi forms and Jacobi for...

In this talk, I will talk about the definition Q-curvature and some of its properties. Then I will talk about the problem of prescribing Q-curvature, especially I will explain the ideas of studying the problem using flow approach.

I will introduce behavior of the derivatives of the Riemann zeta function.

I will explain the basic concepts of moduli and how moduli spaces can be constructed in algebraic geometry. Exploring the moduli spaces and issues arising from their construction lead to interesting interplay of geometry, algebra and computa...

Gromov introduced the analytic method of pseudoholomorphic curves into the study of symplectic topology in the mid 80's and then Floer broke the conformal symmetry of the equation by twisting the equation by Hamiltonian vector fields. We sur...