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.