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.

A hyperplane arrangement is an arrangement of a finite set of hyperplanes in some vector space. Hyperplane arrangements generalize other famous combinatorial objects such as graphs and matroids. In this talk, we introduce a characteristic po...

Black holes are perhaps the most celebrated predictions of general relativity. Miraculously, these complicated spacetimes arise as explicit (i.e., exact expression can be written down!) solutions to the vacuum Einstein equation. Looking thes...

사회에 대한 연구는 모형 중심의 연구와 자료 중심의 연구로 나눠볼 수 있다. 최근 빅데이터를 비롯한 자료 형태의 혁신은 연구의 중심을 모형 중심에서 자료 중심으로 옮기는 듯 하다. 그러나 "변수"를 중심으로 혁신적 자료를 활용한다면 여전히 모형이 과학...

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...

완전동형암호는 암호화된 상태에서 모든 계산을 지원하는 이상적인 암호로서 암호학계의 성배(holy grail)로 불리며 1978년 이후 오랫동안 미해결 문제로 알려져 있었다. 2009년 Gentry에 의해 처음 만들어진 후 많은 연구를 거쳐 실용화를 앞두고 있으며 2011...

The disk embedding problem is of fundamental importance in the study of 4-dimensional topology. I will discuss its significance and difficulty, including how disk embedding makes dimension four intrinsically different from other dimensions. ...

Computation facilitates to understand phenomena and processes from science and engineering; we no longer need to depend only on theory and experiment. Computational Science and Engineering (CSE) is a rapidly developing multidisciplinary area...

In many applications such as X-ray Crystallography, imaging, communication and others, one must construct a function/signal from only the magnitude of the measurements. These measurements can be, for example, the Fourier transform of the den...

I will talk in general about theory and applications of partial differential equations. A recent progress in the regularity theory for nonlinear problems will be also discussed, including uniform estimates of solutions in various function sp...

Many mathematical and computational analyses have been performed for deterministic partial differential equations (PDEs) that have perfectly known input data. However, in reality, many physical and engineering problems involve some level of ...

인터넷 혁명을 거치면서 인간이 생산 및 소비하는 정보의 양이 비약적으로 증가하고 있다. 다루는 정보와 신호의 차원이 커짐에 따라 정보를 획득, 압축, 저장 그리고 복원하는 일련의 과정에 대한 새로운 패러다임이 요구되어 왔으며, 특히 큰 차원의 신호에...

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초록 첨부: Void.pdf

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...

We consider different growth rates associated with the geometry (distance, volume, heat kernel) on a cover of a compact Riemannian manifold. We present general inequalities. We discuss the rigidity results and questions in the case of negati...

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...

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...

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...

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 ...