초록: In this lecture, we study various dissipative effect in a phase space from either entropy dissipation or boundary. We see how this effect leads mathematical studies on long time behavior and scale-uniform estimate of kinetic PDEs in g...

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

Volume conjecture를 설명하고 현재까지의 연구결과 그리고 앞으로의 연구계획을 소개한다.

In late 1970's John McKay discovered the astonishing identity 196884=196883+1, which lead Conway and Norton to formulate the famous Monstrous Moonshine conjectures about the Monster group, the largest sporadic finite simple group. The simple...

In this presentation, we introduce how matrices appeared in the history of mathematics and how they are used in today's fields. Also, we consider the necessary mathematics concepts to define the matrix functions. and the existence and conver...

The thirteen books "Elements" were written or collected by Euclid of Alexandria about 300 BCE. Many think that "Elements" is the most important example of deductive mathematics. In fact, the Common Notions and the Postulates of Elements are...

학부생을 위한 강연: 브라질과 프랑스는 왜 축구를 잘 할까? - 경제와 수학과 축구와 법률

In this talk, I am trying to introduce “what is high dimensional chaos” and also my research works in this area.

Generative adversarial networks (GAN) are a widely used class of deep generative models, but their minimax training dynamics are not understood very well. In this work, we show that GANs with a 2-layer infinite-width generator and a 2-layer...

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There are basically two approaches for solving linear systems: one is to exactly solve the linear sytem such as Gaussian-elimination. The other approximates the solution in the Krylov spaces; Conjugate-gradient and General minimum residual m...

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...

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 will talk about the Fourier restriction theorems for non-degenerate and degenerate curves in Euclidean space Rd. This problem was first studied by E. M. Stein and C. Fefferman for the circle and sphere, and it still remains an unsolved pr...

Despite of the fact that 4-dimensional manifolds together with 3-dimensional manifolds are the most fundamental and important objects in geometry and topology and topologists had great achievements in 1960's, there has been little known on 4...

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....

In this talk, I will explain a relationship of the Chern-Simons invariant and the eta invariant for Schottky hyperbolic manifolds. The relating formula involves a defect term given by the Bergman tau function over the conformal boundary Riem...