Wednesday, May 11, 2022

2022-05-11 / 16:00 ~ 17:00

by ()

A subset V of a domain Ω has the extension property if for every holomorphic function p on V there is a bounded holomorphic function φ on Ω that agrees with p on V and whose sup-norm on Ω equals the sup-norm of p on V. Within the talk, we shall study mutual relations between extension property and interpolations problems.

2022-05-13 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - PDE 세미나:

by 윤석배(성균관대)

Ellipsoidal BGK model (ES-BGK) is a generalized version of the Boltzmann-BGK model. In this model, the local Maxwellian in the relaxation operator is extended to an ellipsoidal Gaussian with a Prandtl parameter ν, so that the correct Prandtl number can be computed in the Navier-Stokes limit. In this talk, we review some of the recent results on ES-BGK model, such as the existence (stationary or non-stationary) theory and the entropy-entropy production estimates. A dichotomy is observed between −1/2 < v < 1 and ν=−1/2. In the former case, an equivalence relation between the local temperature and the temperature tensor enables one to apply theories developed for the original BGK model in a modified form. In the critical case (ν=−1/2), where the correct Prandtl number is achieved, such equivalence breaks down, and the structure of the flow has to be incorporated to estimate the temperature tensor from below. This is from joint works with Stephane Brull, Doheon Kim, and Son Sung Jun.

2022-05-16 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: A colorful version of the Goodman-Pollack-Wenger transversal theorem

by Andreas Holmsen(KAIST)

Hadwiger’s transversal theorem gives necessary and sufficient conditions for the existence of a line transversal to a family of pairwise disjoint convex sets in the plane. These conditions were subsequently generalized to hyperplane transversals in R d by Goodman, Pollack, and Wenger. Here we establish a colorful extension of their theorem, which proves a conjecture of Arocha, Bracho, and Montejano. The proof uses topological methods, in particular the Borsuk-Ulam theorem. The same methods also allow us to generalize some colorful transversal theorems of Montejano and Karasev.

2022-05-11 / 15:00 ~ 16:30

학과 세미나/콜로퀴엄 - 박사논문심사: 랜덤 행렬의 합과 곱의 극대 고유값

by 박재휘(KAIST)

심사위원장 : 이지운, 심사위원 : 강남규(겸직교수), 서인석(서울대학교 수리과학부), 폴정, 남경식

2022-05-12 / 16:00 ~ 17:30

학과 세미나/콜로퀴엄 - 박사논문심사: 가우시안 확률과정을 이용한 자료연관 기법과 특성 선택 기법

by 전영환(KAIST)

심사위원장 : 황강욱, 심사위원 : 강완모, 정연승, 전현호, 문일철(산업및시스템공학과)

2022-05-13 / 10:00 ~ 11:00

SAARC 세미나 - SAARC 세미나:

by 백진호()

The boundary of melting ice forms a random interface. So does the frontier of slowing burning pieces of paper. As time changes, the interface evolves in a random fashion. In probability theory, a collection of models often exhibits universal behaviors when the system size or time becomes large. The KPZ universality class comprises 1+1 dimensional probability models that mimic the random growth behavior mentioned above and display particular universal fluctuations.We will overview some of the development in this class that started about two decades ago.

2022-05-17 / 16:00 ~ 17:15

SAARC 세미나 - SAARC 세미나:

by 김영헌(브리티시컬럼비아 대학)

2022-05-12 / 14:30 ~ 15:45

SAARC 세미나 - SAARC 세미나:

by 김영헌(브리티시컬럼비아 대학)

2022-05-13 / 09:30 ~ 11:50

학과 세미나/콜로퀴엄 - 기타:

by ()

9:30-10:30am Title: Equations in Simple Groups Abstract: Given a word w in a free group on variables x_1,...,x_n, a finite group G, and an element g in G, we consider the question of whether the equation w = g has solutions where the x_i take values in G, and if so, how many. I am particularly interested in what happens when the word is fixed and G is a large finite simple groups. I will say something about the ideas which have led to progress for certain families of words, with emphasis on open problems. 10:50-11:50 Title: Elliptic curves and field arithmetic Abstract: Let E be an elliptic curve over a field K. When K is a number field, Mordell's theorem says that the points of E over K form a finitely generated group. We say a field is "anti-Mordellic" if the opposite is true for all E/K. I will discuss what is known about anti-Mordellic fields, with emphasis on a longterm joint project with Bo-Hae Im to understand the relation between the anti-Mordellic property and the absolute Galois group of K.

2022-05-17 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 정수론: Arithmetic of character variety of reductive groups

by 남경현(University of Queensland, Australia)

Counting the number of points on a variety is a historical method for investigating the variety, for example, in the Weil conjecture. Nowadays, it is known that the point count helps us determine the E-polynomial. This E-polynomial, in turn, gives arithmetic-geometric information on the variety such as the dimension, the number of irreducible components and Euler characteristic. In this talk, we will consider a specific type of variety, the character variety associated to the fundamental group of a surface. In short, we will discuss this variety for a punctured surface, with regular semisimple or regular unipotent monodromy at the punctures. This variety plays a crucial role in diverse areas of mathematics, including non-abelian Hodge theory, geometric Langlands program and mathematical physics. The complex representation theory of finite groups will be used to compute the number of points on such a variety.

2022-05-12 / 11:00 ~ 12:00

IBS-KAIST 세미나 - 수리생물학:

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I will first describe how to extend the theory of balanced networks to account for synaptic plasticity. This theory can be used to show when a plastic network will maintain balance, and when it will be driven into an unbalanced state. I will next discuss how this approach provides evidence for a novel form of rapid compensatory inhibitory plasticity. Experimental evidence for such plasticity comes from optogenetic activation of excitatory neurons in primate visual cortex (area V1) which induces a population-wide dynamic reduction in the strength of neuronal interactions over the timescale of minutes during the awake state, but not during rest. I will shift gears in the final part of the talk, and discuss how community detection algorithms can help uncover the large scale organization of neuronal networks from connectome data.

2022-05-12 / 10:30 ~ 10:55

IBS-KAIST 세미나 - 수리생물학:

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The idea of balance between excitation and inhibition is central in the theory of biological neural networks. I will give a brief introduction to the concept of such balance, and an overview of the mathematical ideas that can be used to study it.

Events for the 취소된 행사 포함