2019년 2학기 인천대학교 수학과 Colloquium

10월 28일 (월) 4시 30분, 장소 : 5호관 102호

[동문특강 + 콜로키움 강연] 인천대 수학과 07학번 동문인 오준석 박사

제목 : An introduction to Combinatorial and Additive Number Theory

초록 : Let G be a (multiplicatively written) finite group. In Combinatorial Number Theory, a sequence over G means a finite sequence of terms from G, where repetition is allowed and the order is disregarded. A product-one sequence is a sequence whose elements can be ordered such that their product (in G) equals the identity element of G. In this talk, we will discuss the product-one problems in finite groups and its applications to the study of non-unique factorization of monoids and domains.

11월 29일 (금) 4시, 장소 : 5호관 102호

연사 : 경희대학교 이상준 교수

제목 : Introduction to random graphs and properties of random intersection graphs related to MERS

초록 : Random graph는 graph들의 모임을 확률적인 공간으로 생각하는 것으로서 1959년에 Erdos-Renyi에 의해 정의되었고, 현재는 조합론의 기초연구와 실생활로부터 정의되는 그래프 모델링 등 다양한 분야에 이용되고 있다.

본 강연에서는 먼저 random graph를 쉽게 정의한 후, 두 가지 결과를 소개하고자 한다. 첫째로는 random graph가 주어진 그래프들을 포함하는 문제인 containment problem과 universality의 개념을 설명하고 새로운 결과를 설명한다. 둘째로는 메르스의 확산 모델인 random intersection graph를 소개하고 그 모델을 random graph와 비교한 새로운 결과를 소개한다.

본 강연은 학부생도 쉽게 이해할 수 있는 강연입니다.

2019년 1학기 인천대학교 수학과 Colloquium

4월 9일 (화) 5시, 5호관 102호

연사 : 성균관대 허지선 박사

제목 : Counting self-conjugate simultaneous core partitions

초록 : In this talk, we consider counting self-conjugate simultaneous core partitions based on my recent works with Hyunsoo Cho and Jaebum Sohn:

- A bijection between ordinary partitions and self-conjugate partitions with same disparity

-Counting self-conjugate (s,s+1,s+2)-core partitions

For each box in the Young diagram of a partition, we define its hook length by counting the number of boxes directly to its right or below, including the box itself. For a positive integer t, a partition is called a t-core if none of its hook lengths are multiples of t. Since the work [1] of Anderson, the topic counting simultaneous cores has received growing attention. By using several methods, we count the number of simultaneous core partitions with some restrictions and found closed formulae for these numbers.

[1] Jaclyn Anderson. Partitions which are simultaneously $t_1$- and $t_2$-core. Discrete Math., 248(1-3):237-243,2002.

4월 30일 (화) 5시, 5호관 102호

연사 : University of Waterloo, Rose McCarty

제목 : Structural graph theory, vertex minors, and circle graphs​

초록 : A graph H is a vertex minor of a graph G if H can be obtained from G by a sequence of vertex deletions and local complementations; locally complementing at a vertex v replaces the induced subgraph on the neighbourhood of v by its complement. Classes of graphs that are closed under taking vertex minors and do not contain all graphs oftentimes can be described in a simple way. A natural class of graphs with geometric representations, called circle graphs, arises. We discuss this connection and how to further decompose circle graphs.

5월 10일 (금) 4시, 5호관 104호

연사 : 숭실대 김수정 교수

제목 : Nonlinear diffusion PDEs between curved spaces

초록 : A variety of nonlinear diffusion phenomena appear in nature such as heat conduction, spreading of ink in water, diffusion of populations. Nonlinear diffusion can be described by elliptic and parabolic partial differential equations (PDEs). In this talk, we discuss two topics within the theory of elliptic and parabolic PDEs in connection with non-Euclidean geometry. We first explain a regularity theory of elliptic and parabolic PDEs defined on Riemannian manifolds. The second part concerns the Ericksen-Leslie theory for the hydrodynamic flow of liquid crystals taking values in the 2-sphere, which has applications to liquid crystal displays (LCDs).

5월 17일 (금) 4시, 5호관 104호

연사 : 경희대 김명호 교수

제목: Representation theory, quantum affine algebras, and quiver Hecke algebras

초록 : In this talk, I will explain first what is the representation theory with an easy example from groups. Next, I will introduce certain algebraic objects called the quantum affine algebras and the quiver Hecke algebras. I will explain a connection between those objects via representation theory of associative algebras.

2018년 2학기 인천대학교 수학과 Colloquium

시간 : 금요일 4시

장소 : 5호관 103호

11월 2일 : 고등과학원 박철 박사

제목 : Introduction to mod p Langlands program

초록 : 링크

11월 16일 : 경남대 수학교육과 서샛별 교수

제목 : A Mathematical Model of Synaptic Transmission for Independent Currents

초록 : Synapse plays a key role of communication in our brain. Presynaptic terminals release neurotransmitters either in response to action potential or spontaneously independent of presynaptic activity. Spontaneous neurotransmission has an independent role in neuronal communication that is distinct from that of evoked release. However, the process of spontaneous neurotransmitter release is still unclear. We develop a mathematical model in 3-D to emulate spontaneous and evoked neurotransmissions resulted from glutamate release within a single synapse. In order to identify the spatial relation between spontaneous and evoked glutamate releases, we consider quantitative factors, such as the size of synapses, inhomogeneity of diffusion coefficients, the geometry of synaptic cleft, and the release rate of neurotransmitter, that will affect postsynaptic currents. We conclude quantitatively when a synaptic size is larger, the cleft space is less diffusive in the central area than the edge area, if the geometry synaptic cleft has a narrower gap in the center and if glutamate release is slower, then there is a better chance for independence of two modes of currents from spontaneous and evoked release. The computed results match well with existing experimental findings and provide a quantitative map of boundaries of physical constraints for having independent synaptic fusion events.

11월 30일 : 인천대 수학교육과 최우철 교수 (4시), 고등과학원 최종근 박사 (5시).

1. 최우철 교수

제목 : Introduction to the Control Theory with applications to Mechanical Engineering.

초록 : 제어이론은 수학과 공학의 접점에 있는 분야로 20세기를 거치며 광범위하게 발전해 왔다. 특히 기계공학에서의 필수적인 역할을 하고 있다. 현대에는 에너지, 반도체 등의 기술 발전으로 드론과 다양한 로봇들이 상용화 되었고, 필요한 제어기술의 수요도 증가해왔다. 이번 발표에서는 제어 이론의 몇가지 기본적인 아이디어들과 예들을 소개하고, 최근 발전 동향을 살펴본다. 특히 최적화와 관련된 수학적인 이슈들과 관련 알고리즘 개발의 중요성에 대하여 이야기해 본다.

2. 최종근 박사

제목 : Mixed boundary value problem for elliptic equation

초록 : A boundary value problem is called a mixed problem if the boundary condition is characterized by a combination of Dirichlet and conormal derivative boundary conditions along at least one boundary. The regularity theory for such mixed problem has important applications in mathematical physics and engineering. In this talk, I will review classical regularity theory for the mixed problem, and then, I will talk about recent results on $L^p$ regularity theory, a problem posed by Calos Kenig.