We introduce and study a new complexity function in combinatorics on words, which takes into account the smallest return time of a factor of an infinite word. We characterize the eventually periodic words and the Sturmian words by means of t...

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...

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...

Elliptic curves defined over the rationals satisfy two finiteness properties; its group of rational points is a finitely generated abelian group and it has only finitely many points with integral coordinates. Bhargava and his collaborators e...

정년퇴임기념강연

Stochastic Model, Integrals 그리고 PDE의 기본 개념과 최신 연구 동향을 소개한다.

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 ...

We will introduce the behavior of zeros of linear combinations of zeta functions. Those linear combinations are related to the Riemann zeta function, the Eisenstein series, Periods, etc.

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

상산수리과학관 20주년 기념강연

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...

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...

2000년 국제수학교육위원회( International Commission on Mathematical Instruction)는 수학교육연구에 탁월한 업적을 이룬 학자에게 수여하는 Freudenthal 메달과 Klein메달을 제정하여, 2003년 부터 홀수 해에 수상하고 있다. 이 강연에서는 2012년 서울에...

Normal form method is a classical ODE technique begun by H. Poincare. Via a suitable transformation one reduce a differential equation to a simpler form, where most of nonresonant terms are cancelled. In this talk, I begin to explain the not...

For an isolated singularity, the intersection with a small sphere forms a smooth manifold, called the link of a singularity. It admits a canonical contact structure, and this turns out to be a fine invariant of singularities and provides an...

A COMBINATORIAL FORMULA FOR INFORMATION FLOW IN A NETWORK

The main topic of the talk is a determinantal formula for high dimensional tree numbers of acyclic complexes via combinatorial Laplace operators . This result is a generalization of Temperley's tree number formula for graphs, motivated by a ...