Monday, May 16, 2022

2022-05-23 / 16:00 ~ 17:00

by ()

This talk is concerned with the bifurcation and stability of the compresible Taylor vortex. Consider the compressible Navier-Stokes equations in a domain between two concentric infinite cylinders. If the outer cylinder is at rest and the inner one rotates with sufficiently small angular velocity, a laminar flow, called the Couette flow, is stable. When the angular velocity of the inner cylinder increases, beyond a certain value of the angular velocity, the Couette flow becomes unstable and a vortex pattern, called the Taylor vortex, bifurcates and is observed stably. This phenomena is mathematically formulated as a bifurcation and stability problem. In this talk, the compressible Taylor vortex is shown to bifurcate near the criticality for the incompressible problem when the Mach number is sufficiently small. The localized stability of the compressible Taylor vortex is considered under sufficiently small axisymmetric perturbations; and it is shown that the large time behavior of solutions around the Taylor vortex is described by solutions of a system of diffusion equations.

2022-05-23 / 16:30 ~ 18:00

학과 세미나/콜로퀴엄 - 계산수학 세미나:

by 최민석()

Despite of great progress over the last decades in simulating complex problems with the numerical discretization of (stochastic) partial differential equations (PDEs), solving high-dimensional problems governed by parameterized PDEs remains challenging. Machine learning has emerged as a promising alternative in scientific computing community by enforcing the physical laws. We review some of machine learning approaches and present a novel algorithm based on variational inference to solve (stochastic) systems. Numerical examples are provided to illustrate the proposed algorithm.

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)

2022-05-19 / 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)

2022-05-23 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: The precise diameter of reconfiguration graphs

by Stijn Cambie(IBS 극단 조합 및 확률 그룹)

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