최영주   YoungJu Choie

• 포항공과대학교 수학과 교수
    

Title: Eisenstein series and automorphic forms

The modern theory of automorphic forms influences many areas, such as sphere packing problem, class field theory, Fermat last theorem, quadratic forms, elliptic curves, etc. Theory of Eisenstein series is one of the fundamental tools for the study of automorphic forms and essential part of the Langlands program.

On the other hand, Schubert Eisenstein series are defined by restricting the summation of a degenerate Eisenstein series to a particular Schubert variety. We try to explain the Poisson summation conjecture of Braverman - Kazhdan, later refined by Lafforge, Ngo and Sakellaridis, for a particular family of varieties related to Schubert varieties.

 김상현   Sang-hyun Kim

• 고등과학원 수학부 교수
    

Title: 공간의 풍경 The landscape of a mathematical universe

누구나 한 번쯤은 밤하늘의 쏟아질 듯한 별을 보며 우주의 장대함에 경외감을 가져보았을 만하다. 거대한 시공간에 놓인 우리 존재의 신비는, 시인과 철학자와 종교인뿐 아니라 수학자에게 역시 오래된 사색의 원천이 되었다. 공간이란 무엇일까. 아무런 물체도, 측정도 없는 마음속의 우주에 대하여, 인간은 얼마나 깊이 이해하고 있을까? 우리는 이천여 년 전의 유클리드에서 현대의 푸앵카레, 써스턴 등으로 이어진 이 수학적 전통에 대하여 알아보고, 여기에서 얻어진 마음속의 그림, 바로 공간의 풍경을 음미해 보고자 한다. 

[2021년 대한수학회 학술상 수상기념] 곽시종   Sijong Kwak

• 카이스트 수리과학과 교수
    

Title: Higher secant varieties of minimal degree and del Pezzo secant varieties

There are two basic objects in projective algebraic geometry: one is a variety of minimal degree and the other is a del Pezzo variety. In this talk, I'd like to introduce higher secant varieties of minimal degree and del Pezzo higher secant varieties to nonexpert with modest backgrounds. I also keep in mind to imagine
the Matryoshka structures in the category of secant varieties to classify and characterize such varieties. Many interesting examples explaining main results are provided. This is a joint work with Junho Choe in KIAS.

[2021년 한국과학상 수상기념] 김인강   In Kang Kim

• 고등과학원 수학부 교수
    

Title: Signature and Toledo invariant for flat unitary bundles over surfaces with
        boundary

This talk deals with the representations of the fundamental groups of compact surfaces with boundary into classical simple Lie groups of Hermitian type. We relate work on the signature of the associated local systems, due to Meyer and Atiyah, to Burger-Iozzi-Wienhard's Toledo invariant. To measure the difference, we extend Atiyah-Patodi-Singer's rho invariant, initially defined on U(p), to discontinuous class functions, first on U(p,q), and then on other classical groups via embeddings into U(p,q). As an application, we obtain a Milnor-Wood type inequality which slightly differs from, and sometimes improves upon Burger-Iozzi-Wienhard’s version.

[IMU Group 5 승급기념 강연] 김민형   Minhyong Kim

• 에든버러 국제수리과학연구소 소장
    

Title: 세계 수학 공동체의 존엄성

한국을 포함한 수학 선진국들이 세계 수학 공동체의 건설적인 발전에 기여할 수 있는 방법들에 대해서 같이 생각해 보고자 한다. 

[대수학 Algebra]-Ⅰ   김현규   Hyun Kyu Kim
* 4.29.(금) 10:40-11:15

• 이화여자대학교 수학과 교수
    

Title: Cluster variety approach to various moduli spaces

Cluster varieties, which appeared in 2000's, are schemes covered with special toric charts whose coordinate change formulas follow a certain combinatorial pattern. I will explain basic definitions, some problems and recent progress, and applications to various moduli spaces of geometric structures on a Riemann surface, such as ordinary and higher Teichmüller spaces, as well as the phase space of 3d gravity.

[대수학 Algebra]-Ⅱ   오정석   Jeongseok Oh
* 4.29.(금) 11:25-12:00   

• Imperial college, research associate
    

Title: Complex Kuranishi spaces

We develop a theory of complex Kuranishi structures on projective schemes. These are sufficiently rigid to be equivalent to weak perfect obstruction theories, but sufficiently flexible to admit global complex Kuranishi charts.
We apply the theory to projective moduli spaces M of stable sheaves on Calabi-Yau 4-folds. Borisov-Joyce produced a real virtual homology cycle on M using real derived differential geometry. In the prequel to this work we constructed an algebraic virtual cycle on M.
We prove the cycles coincide in homology after inverting 2 in the coefficients. In particular, when Borisov-Joyce’s real virtual dimension is odd, their virtual cycle is torsion.

[해석학 Analysis]-Ⅰ   곽철광   Chulkwang Kwak
* 4.29.(금) 10:40-11:15

• 2021년도 대한수학회 상산젊은수학자상 수상자
• 이화여자대학교 수학과 교수

Title: Study on water wave models

In this talk, we are going to discuss studies on water wave models, particularly involved in the class of dispersive equations. More precisely, I am going to briefly introduce some models arising from shallow water waves, and discuss well-posedness and stability theories for those models. Also, we are going to discuss recent progress on those theories.

[해석학 Analysis]-Ⅱ   박배준   Bae Jun Park
* 4.29.(금) 11:25-12:00   

• 성균관대학교 수학과 교수
    

Title: Recent progress on multilinear rough singular integrals 

In this talk, we will study multilinear rough singular integrals. We first review classical boundedness results for rough singular integral operators and then present recent progress on multilinear extensions of the operators. We will also discuss some open problems.
This talk is based on joint work with Grafakos, He, and Honzik. 

[기하학 Geometry]  최범준   Beomjun Choi
* 4.29.(금) 11:25-12:00   

• 2021년도 대한수학회 상산젊은수학자상 수상자
• 포항공과대학교 수학과 교수
    

Title: Ricci limit flows and weak solutions

In this talk, we first introduce different notions of weak solutions to Ricci flows which are defined through singularities. Our recent result shows every noncollapsed limit of Ricci flows, as provided by Bamler's precompactness theorem, as well as every singular Ricci flow from Kleiner-Lott, is a weak solution in the sense of Haslhofer-Naber. The key step to establish these results is a new hitting estimate for Brownian motion.

[위상수학 Topology]  박정환   JungHwan Park
* 4.29.(금) 10:40-11:15

• 2021년도 대한수학회 상산젊은수학자상 수상자
• 카이스트 수리과학과 교수
    

Title: Definite fillings of lens spaces

We consider the problem of determining the smallest (as measured by the second Betti number) smooth negative-definite filling of a lens space. We classify those lens spaces for which the associated negative-definite canonical plumbing is minimal. We establish that such a plumbing is minimal if and only if the associated string of weights does not contain any sequence from a certain finite list. We also show that whenever the plumbing is minimal any other negative-definite filling for the given lens space has, up to stabilizations, the same intersection form. We discuss consequences regarding smooth embeddings of lens spaces in definite 4-manifolds.

[확률·통계학 Probability and Statistics]  남경식   Kyeongsik Nam
* 4.29.(금) 10:40-11:15

• 카이스트 수리과학과 교수
    

Title: Spectral large deviations for sparse random matrices

Universality for the eigenvalues of Wigner random matrices has been actively studied in the random matrix community. A natural generalized version of Wigner matrices is called sparse random matrices, where each entry is multiplied by the independent Bernoulli random variable with mean p. When the sparsity is given by p = 1/n, it is known that universality phenomenon breaks down. However, its precise spectral property has not been understood yet. In this talk, I will talk about the spectral behavior of such sparse random matrices. 

[응용수학(AI, Data Science 포함)-Applied Mathematics(including AI, Data Science)]  김진수   Jinsu Kim
* 4.29.(금) 11:25-12:00   

• 포항공과대학교 수학과 교수
    

Title: Reaction networks for a graphical description of biochemical systems

Chemical reaction networks depict a biological system with a graph where 1. nodes (complexes) are created by a combination of variables (constituent species) and 2. directed edges (reactions) such as A+B -> C represent the chemical interactions. If the abundances of the network system are small, then the randomness inherent in the molecular interactions is important to the system dynamics, and the abundances are modeled stochastically as a jump by jump fashion continuous-time Markov chain. Otherwise, if the abundances are big, then intrinsic noise in the system can be averaged out so that the system is modeled with an ordinary differential equation. In this talk, we will introduce fundamental modeling aspects of reaction networks. We will also discuss one of the most important problems in reaction network theory: how the dynamical properties of a given biochemical system can be derived from the structural properties of the underlying reaction network.

[수학교육 Mathematical Education]  고상숙   Sang Sook Choi-Koh
* 4.29.(금) 10:40-11:15

• 단국대학교 사범대학 수학교육과 교수
    

Title: Looking for the ways that learners with math anxiety could survive

Affective domains that showed low achievements in international assessments such as PISA (Program for International Student Assessment) were included in 'Mathematics Attitudes and Practices' among the core competencies of the 2015 revised math curriculum. Along with the importance of this affective domain, a number of studies have been conducted to find the factors of learning difficulties in math anxiety (cf., Jong-hee Lee, Su-jin Kim, 2010; Hye-sook Han, Gye-hyun Choi, 2013). Since cognition and emotion are integrated in the brain, emotional responses to anxious experiences interfere with learning (Kim Doo-Jeong, 2010). Hopko et al. (1998) found that people with math anxiety have an incomplete control mechanism in which working memory resources are preoccupied with answers that are not related to the task.

Therefore, the subjects were divided into a group with high math anxiety (HMA) and a group with low math anxiety (LMA), and after applying a treatment program related to the functional area, EEG was measured to compare them. The result showed that the students of HMA had more improvements than the counterpart.

[이산수학 Discrete Mathematics]  Hong Liu
* 4.29.(금) 10:40-11:15   

• CI, IBS ECOPRO
    

Title: Exponential decay of intersection volume and  applications

When two balls in a metric space have small intersection? We give some natural conditions to guarantee an exponential decay on the volume of such intersections. Our proof is conceptually simple, making use of concentration of measure on a “slice”. We will discuss a couple of applications of this volume estimate in coding theory.
This is joint work with Jaehoon Kim and Tuan Tran.

[암호학 Cryptography]  김영식   Young-Sik Kim
* 4.29.(금) 11:25-12:00   

• 조선대학교 정보통신공학부 교수
    

Title: RNS-CKKS Homomorphic Encryption

Approximate homomorphic encryption with the residue number system (RNS), called RNS-variant Cheon-Kim-Kim-Song (RNS-CKKS) scheme, is a fully homomorphic encryption scheme that supports arithmetic operations for real or complex number data encrypted. In this paper, we improve the message precision in the bootstrapping operation of the RNS-CKKS scheme. Firstly, we propose a fast algorithm of obtaining the optimal minimax approximate polynomial of modular reduction function and the scaled sine/cosine function over the union of the approximation regions, called an improved multi-interval Remez algorithm. Next, we propose the composite function method using the inverse sine function to reduce the difference between the scaling factor used in the bootstrapping and the default scaling factor.