Machine learning (ML) has achieved unprecedented empirical success in diverse applications. It now has been applied to solve scientific problems, which has become an emerging field, Scientific Machine Learning (SciML). Many ML techniques, h...

아이작 뉴턴의 계산과학에 관한 업적을 소개한다.

SNU-LeeAbstract.pdf

조선시대 영의정을 지낸 최석정(1646-1715)은 그의 저서 구수략에 여러 크기의 직교라틴방진을 남겼는데 이는 combinatorial mathematics의 효시로 알려진 Leonhard Euler(1707?1783) 의 직교라틴방진보다도 적어도 61년이 앞서는 기록이다. 놀랍게도 최석정이...

볼록다면체에서 permanent 함수의 최소값은 얼마인가? 그 때의 최소행렬은 어떤 형태인가? 그리고 이중확률구조를 갖는 행렬들에 대하여 제약조건이 주어지면 볼록다면체의 면 위에서 permanent 함수의 최소값들은 어떻게 결정하는가? 등에 관하여 연구된 내용...

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...

Non-vanishing modulo a prime of special values of various $L$-functions are of great importance in studying structures of relevant arithmetic objects such as class groups of number fields and Selmer groups of elliptic curves. While there hav...

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...

Metastability란 random process가 여러 개의 안정된 상태를 가질 때 반드시 나타나는 현상으로, 수리물리학이나 화학의 여러 모형들은 물론 딥러닝의 알고리즘 등 다양한 곳에서 공통적으로 나타나는 현상이다. 본 강연에서는 이 Metastability를 수학적으로...

A W-algebra is introduced as a symmetry algebra in 2-dimensional conformal field theory. Mathematical realization of a W-algebra was introduced by the theory of vertex algebras. Especially, W-algebras related to Lie superalgebras have been s...

If a problem has an approximate solution, we try to get some information of the linearized kernel of the problem at the approximate solution to find a real solution. In this talk, I would like to introduce a different approach which is purel...

We discuss on why we study partial differential equations.

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...

We discuss how the closed connected 1-dimensional manifold, namely the circle, can help understanding 3-manifolds. We describe so-called the universal circle proposed by a lengendary mathematician, William Thurston, and discuss certain gene...

The notion of essential dimension was introduced by Buhler and Reichstein in the late 90s. Roughly speaking, the essential dimension of an algebraic object is the minimal number of algebraically independent parameters one needs to define the...