Friday, May 13, 2022

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

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.

2022-05-20 / 16:00 ~ 17:30

학과 세미나/콜로퀴엄 - Face the World with Mathematical Mind:

by ()

2022-05-19 / 16:30 ~ 18:00

학과 세미나/콜로퀴엄 - 박사논문심사: 기하적 복소함수론을 이용한 내포의 모양 복원 및 중립물질 설계

by 최두성(KAIST)

심사위원장 : 임미경, 심사위원 : 김동환, 김용정, 권기운(동국대 수학과), 이현대(인하대 수학과)

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.

2022-05-19 / 14:30 ~ 15:45

SAARC 세미나 - SAARC 세미나:

by 김영헌(브리티시컬럼비아 대학)

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

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.

2022-05-19 / 12:00 ~ 12:50

대학원생 세미나 - 대학원생 세미나: Modular forms and transcendental questions

by 이원웅(KAIST)

Modular curves for Hecke congruence groups, or more generally, for Fuchsian groups of the first kind can be seen as the moduli spaces of the isomorphism classes of elliptic curves with torsion data in some sense. In this talk, I will introduce the notion of modular curves and modular forms. If time permits, I will also introduce their applications to some transcendental questions.

2022-05-19 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

by ()

Helly-type theorems and problems form a nice area of discrete geometry. I will start with the notable theorems of Radon and Tverberg and mention the following conjectural extension.

For a set X of points x(1), x(2),...,x(n) in some real vector space V we denote by T(X,r) the set of points in X that belong to the convex hulls of r pairwise disjoint subsets of X.
We let t(X,r) = 1 + dim(T(X,r)).

Radon's theorem asserts that
If t(X,1) < |X| then t(X, 2) > 0.

The first open case of the cascade conjecture asserts that
If t(X,1) + t(X,2) < | X | then t(X,3) >0.

In the lecture I will discuss connections with topology and with various problems in graph theory.
I will also mention questions regarding dimensions of intersection of convex sets.

Some related material:
1) A lecture (from 1999): An invitation to Tverberg Theorem: https://youtu.be/Wjg1_QwjUos
2) A paper on Helly type problems by Barany and me https://arxiv.org/abs/2108.08804
3) A link to Barany's book: Combinatorial convexity https://www.amazon.com/Combinatorial-Convexity-University-Lecture-77/dp/1470467097

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.

Events for the 취소된 행사 포함