Invited Speakers

◎ KIAS Plenary Lecture (10.24.(토) 15:40~16:20)

김강태   Kim, Kang-Tae


• 포스텍 수학과 교수

Title: Functions holomorphic along a pencil of holomorphic discs at a point

Generalization of Forelli's theorem (Forelli, Math. Scand. 1977) has been an active research subject in recent years. It was originally believed to be impossible to generalize by many experts for more than 25 years. Then, new activities were initiated by E. Chirka around 2005 (Proc. Steklov Inst. Math. 2006) in complex dimension 2. The main theme of this presentation is to introduce the most general version of generalization in all dimensions up to date, as far as it is concerned with the complex analyticity of functions holomorphic along a topological foliation by (as well as along a pencil of) Riemann surfaces at a point [K.T. Kim et al. Math. Ann. 2013; Ye-Won Cho and K.-T. Kim, Preprint (2020)]. We shall also present some interesting history behind this research.

◎ KIAS Public Lecture (10.23.(금) 17:00~18:00)

 정은옥   Jung, Eunok

• 건국대학교 이과대학 수학과 교수


Title: 수리모델링으로 분석한 코로나19 사회적 거리두기

인류와 함께 살고 있는 바이러스! 우리는 4차 산업혁명 시대에 살고 있지만, 신종감염병인 코로나바이러스감염증(COVID-19/코로나19)으로 전 세계가 공포와 패닉으로 사회적 거리두기 삶을 살고 있다. 2월 18일 대구에서 종교집단 집단감염을 시작으로 코로나19 확진자가 급증하였다. 정부 방역 정책에도 사회적 거리두기가 도입되고, 온 국민이 강화된 사회적 거리두기를 시행하였다. 본 강연에서는 수학으로 사회적 거리두기 방역 정책을 구현하여(수리모델링), 정부의 방역 정책에 따라 국민들의 행동 변화가 어떻게 바뀌었는지를 분석해보고자 한다. 이제는 정책결정자들이 수학자를 찾는 시대가 온 것 같다. 이제 수학은 선제적이고 효과적인 감염병 방역 정책에 과학적 근거를 제시하는 가장 핵심적인 학문이자 도구가 되었다. 본 강연을 통해 감염병 수리모델링이 단지 유행 예측에만 있는 것이 아니고, 선제적이고 과학적인 방역 정책을 위한 효과적인 중재 전략을 제안하는 뉴 노멀 시대의 학문임을 강조하고 싶다.  


  ◎ Special Invited Lecture (10.24.(토) 16:30~17:00)

[2019년 한국과학상 수상기념] 오용근   Oh, Yong-Geun


• IBS 기하학 수리물리 연구단 연구단장

• 포스텍 수학과 교수

Title: Gromov-Witten-Floer theory and symplectic topology

이 강연에서는 사교위상수학과 그로모프-위튼-플로어 이론의 태동과
그 상관관계를 역사적인 관점에서 되돌아 보고 최근의 강연자와 공동 연구자들(Fukaya, Ohta, Ono)의 이에 대한 결과들을 조명하고자 한다.
특히 그로모프-위튼-플로어 이론의 스펙트럴 불변량의 구성과 확장을 통한 사교위상수학에의 적용에 대하여 논의하려고 한다.

◎ Invited Lectures (10.24.(토) 13:10~13:40) 

[대수학 Algebra]-Ⅰ  백상훈   Baek, Sanghoon

• 카이스트 자연과학대학 수리과학과 교수

• 2020년도 대한수학회 논문상 수상자   
  The winner of 2020 Excellent Research Award    

Title: Noether’s problem and cohomological invariants

Consider a free action of a finite group G on a vector space V. In 1913, Emmy Noether asked whether the quotient variety V/G is rational. This problem has a positive answer for any abelian group over the field of complex numbers. However, it turned out to have a negative answer in general, due to Swan and Saltman. Since then Noether’s original problem has been generalized to an algebraic group and studied intensively, but it still remains open for a connected algebraic group over the field of complex numbers. A natural way of attacking Noether’s problem is to provide a nontrivial unramified cohomology group. In this talk, we shall discuss the notion of cohomological invariants for G-torsors, introduced by Serre, and then using this notion we shall determine the group of degree 3 unramified cohomology for an arbitrary reductive group G.


[대수학 Algebra]-Ⅱ   선해상   Sun, Hae-Sang

• 울산과학기술원 자연과학부 수리과학과 교수

• 2020년도 대한수학회 논문상 수상자       
  The winner of 2020 Excellent Research Award    

Title: Distribution of critical values of Dirichlet $L$-functions

Main topic of the talk is the distribution of critical values of Dirichlet $L$-functions. I will first review previous results on mod $p$ reduction of the values. A main result of the talk is the Zariski denseness of the complex $L$-values. One consequence of the result is the algebraic independence of the Kubota-Leopoldt $p$-adic $L$-functions. This can be regarded as a $p$-adic version of algebraic independence of Dirichlet $L$-functions, which is deduced from the joint universality of the $L$-functions.


[해석학 Analysis]  이지훈   Lee, Jihoon

• 중앙대학교 자연과학대학 수학과 교수

Title: Mathematical Analysis of the Incompressible Fluids with Rotation or Stratification

In this talk, we consider the equations governing the motion of rotating fluids and stratified fluids. In a spatial 3D fluid rotating at a constant rotation rate $\Omega$ about $x_3$ axis, motions in a plane normal to the axis of rotation are inhibited by the constraint of rotation. Similarly, if a fluid in a gravitational field is stably stratified, fluid motions parallel to the direction of gravity are inhibited due to the force of gravity.
We review the previous works of the equations of incompressible fluids with rotation or stratification. We also consider 3D MHD equations with rotation and 3D fractional diffusion Navier-Stokes equations with rotation. Also we consider the 3D Boussinesq equations with stratifications. This talk is based on the joint works with Jaewook Ahn(Dongguk University) and Junha Kim(Chung-Ang University).


[기하학 Geometry]  최경수  Choi, Kyeongsu

• 고등과학원 수학부 교수

Title: Mean curvature flow with generic initial data

Mean curvature flow is an evolution of hypersurfaces satisfying a geometric heat equation. The flow develops singularities, and thus its topology would be changed. Hence, one can study topological theory. including knot theory, via singularity analysis in parabolic PDEs.

To this end, we need to investigate singularities, but there exist infinitely many singularity models. However, there are only a few linearly stable singularities, and therefore one can conjecture that generic mean curvature flows can avoid linearly unstable singularities.

In this talk, we discuss generic mean curvature flows and its application to topology. If time permits we talk about how to avoid linearly unstable multiplicity one singularities.


[위상수학 Topology]  수영   Choi, Suyoung

아주대학교 자연과학대학 수학과 교수     

Title: real toric manifold, and its cohomology

The set $X^\mathbb{R}$ of real points of an algebraic variety $X$ is called a real algebraic variety. In particular, $X^\mathbb{R}$ is called a real toric manifold if $X$ is a toric manifold, that is, a nonsingular complete toric variety.

From the viewpoint of topologists, the topology of $X^\mathbb{R}$ is more complicated than the topology of $X$. Thus, the study of topology of the real varieties in specific cases is a good challenge to topologists. For instance, if $X$ is a toric manifold, then $X$ is simply connected whereas $X^\mathbb{R}$ is never simply connected. Indeed, although the cohomology formula of a projective toric manifold $X$ has been well-established since the late 1970s, only partial results of cohomology of $X^\mathbb{R}$ have been obtained.

In this talk, I introduce recent studies of real toric manifolds including the cohomology formula of real toric manifolds, and propose some interesting problems. If time permits, we also discuss the topological generalization, known as real toric spaces, of real toric manifolds.


[확률·통계학 Probability and Statistics]  황강욱   Hwang, Ganguk


• 카이스트 자연과학대학 수리과학과 교수


Title: Gaussian Process Regression and Machine Learning

Gaussian Process Regression (GPR) is a nonparametric Bayesian machine learning approach that places a flexible prior distribution over the space of functions and returns a predictive distribution through a combination of the prior and the data. Due to its analytical tractability and practical advantages, GPR is widely used as a powerful tool in inference, learning, and prediction.
In this talk, we examine the basics of GPR and focus on how to utilize GPR with the help of domain knowledge.


[응용수학(AI, Data Science 포함)-Applied Mathematics(including AI, Data Science)]  류경석   Ryu, Ernest K.


• 서울대학교 자연과학대학 수리과학부 교수

Title: Scaled Relative Graph: Nonexpansive operators via 2D Euclidean Geometry

Many iterative methods in applied mathematics can be thought of as fixed-point iterations, and such algorithms are usually analyzed analytically, with inequalities. In this talk, we present a geometric approach to analyzing contractive and nonexpansive fixed point iterations with a new tool called the scaled relative graph (SRG). The SRG provides a rigorous correspondence between nonlinear operators and subsets of the 2D plane. Under this framework, a geometric argument in the 2D plane becomes a rigorous proof of contractiveness of the corresponding operator.


[수학교육 Mathematical Education]  이상구   Lee, Sang-Gu


• 성균관대학교 자연과학대학 수학과 교수


Title: From the research of matrix to mathematics education for AI

본 발표에서는 발표자가 30여 년간 수학자로, 또 대학수학 교육자로 지내오면서, 연구와 교육에서 경험한 내용을 공유한다.

이번 초정강연 발표자는 1990년부터 2000년까지 선형보존자(linear preserver problem) 연구 및 조합적행렬론(combinatorial matrix theory) 등의 행렬 구조를 연구하였고, 2000년부터 2010년까지는 이런 연구 결과들을 대학원생과 대학생들에게 교육하여 대학과 연구소 및 기업에 취업 시키면서, 자연스럽게 대학교육에도 관심을 가지게 되었다. 이런 과정에서 사회가 필요로 하는 문제들에 수학적인 답을 제시하는 수학적 모델링, 3D 프린팅, 수학 발달사, 한국의 근대수학자, Math & Art, 모바일 수학 및 Math & Coding 으로 관심 연구분야가 넓어졌다. 특히 최근 10년간(2010년부터 2020년까지)은 행렬 연구와 이용 및 교육에 보태어 수학대중화와 관련된 대학수학교육 연구에 집중하였다. 최근 빅데이터와 인공지능이 핫 이슈가 되면서는 대학생을 대상으로 하는 <인공지능을 위한 기초수학>과 일반인과 고등학생 대상의 K-MOOC  <인공지능을 위한 기초수학 입문> 강의를 한 경험과 고등학교 <인공지능 수학> 교육과정 개발의 연구책임을 수행하였다.  

본 발표 내용은 위의 경험의 일부와 자연스럽게 수학교수의 연구가 대학수학교육으로 이어지는 과정을 공유한다. 학계와 사회 및 학생들의 니즈에 답하는 과정(수학적 모델링 강좌, 특허, 한국 근대수학사, Math & Coding, 모바일 수학)의 경험이 준 보람을 공유하는 시간이 되기를 기대한다.


[이산수학 Discrete Mathematics]  김장수   Kim, Jang Soo


• 성균관대학교 자연과학대학 수학과 교수


Title: Jacobi--Trudi formulas for flagged refined dual stable Grothendieck polynomials

Recently Galashin, Grinberg, and Liu introduced the refined dual stable Grothendieck polynomials, which are symmetric functions in $x=(x_1,x_2,\dots)$ with additional parameters $t=(t_1,t_2,\dots)$. The refined dual stable Grothendieck polynomials are defined as a generating function for reverse plane partitions of a given shape. They interpolate between Schur functions and dual stable Grothendieck polynomials introduced by Lam and Pylyavskyy in 2007. Flagged refined dual stable Grothendieck polynomials are a more refined version of refined dual stable Grothendieck polynomials, where lower and upper bounds are given for the entries of each row or column. In this talk we show Jacobi--Trudi-type formulas for flagged refined dual stable Grothendieck polynomials using plethystic substitution. This resolves a conjecture of Grinberg and generalizes a result by Iwao and Amanov--Yeliussizov.



[암호학 Cryptography]  이훈희   Lee, Hun Hee


• 서울대학교 자연과학대학 수리과학부 교수


Title: Introduction to quantum computing and its application to machine learning

We will make a gentle introduction to quantum computing and its recent developments towards applications on machine learning.