Department Seminars & Colloquia

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The law of iterated logarithm (LIL) is a crowning achievement in classical probability theory that gives the sharp upper bound for the magnitude of fluctuations of a random walk. If each step has mean zero and variance one, then the upper bound (in certain sense) is given by \sqrt{2n\log\log n}, hence the name “iterated logarithm.” Despite being considered the “third fundamental limit theorem in probability” by some probabilists after the law of large numbers and the central limit theorem, its proof is not so accessible to non-experts. For instance, most textbooks either only consider special cases or use sophisticated machineries in their proofs. The purpose of this talk is to provide a relatively simple and elementary proof of the so-called Hartman—Wintner LIL. The idea is to generalize a proof of the central limit theorem (CLT), which will be also presented, to obtain a result on the rate of convergence in the CLT. First principles in probability (e.g. the second Borel—Cantelli lemma) are the only technical prerequisites.
Host: 폴정     Korean     2022-05-18 18:02:15
심사위원장 : 권순식, 심사위원 : 배명진, 남경식, Yoshio Tsutsumi(Kyoto University), Mamoru Okamoto(Osaka University)
To be announced     2022-05-11 18:05:38
Inside living cells, chemical reactions form a large web of networks and they are responsible for physiological functions. Understanding the behavior of complex reaction networks is a challenging and interesting task. In this talk, I would like to illustrate how the methods of algebraic topology can shed light on the properties of chemical reaction systems. In particular, we discuss the following two problems: (1) response of reaction systems to external perturbations and (2) simplification of complex reaction networks without altering the behavior of the system.
ZOOM Meeting ID: 868 7549 9085 Direct link:
Host: Jaekyoung Kim     To be announced     2022-03-14 09:37:36
심사위원장 : 김용정, 심사위원 : 강문진, 김재경, 임미경, 안인경(고려대학교)
To be announced     2022-05-18 17:36:02
심사위원장 : 김용정, 심사위원 : 강문진, 김재경, 임미경, 안인경(고려대학교)
To be announced     2022-05-18 17:37:29
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.
English     2022-05-15 00:50:30
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.
Host: 이창옥     To be announced     2022-05-11 15:09:04

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:
2) A paper on Helly type problems by Barany and me
3) A link to Barany's book: Combinatorial convexity
ZOOM Meeting ID: 868 7549 9085 Direct link:
Host: Andreas Holmsen     To be announced     2022-03-14 09:36:02
심사위원장 : 임미경, 심사위원 : 김동환, 김용정, 권기운(동국대 수학과), 이현대(인하대 수학과)
To be announced     2022-05-02 16:50:33
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.
Host: 박진현     Contact: 박진현 (2734)     To be announced     2022-03-07 16:41:18
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.
Host: Bo-Hae Im     To be announced     2022-05-02 09:22:13
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.
Host: 강문진     To be announced     2022-05-10 09:07:24
심사위원장 : 황강욱, 심사위원 : 강완모, 정연승, 전현호, 문일철(산업및시스템공학과)
To be announced     2022-05-02 16:47:58
심사위원장 : 이지운, 심사위원 : 강남규(겸직교수), 서인석(서울대학교 수리과학부), 폴정, 남경식
To be announced     2022-05-02 16:49:21
심사위원장 : 폴정, 심사위원 : 이지운, 남경식, 강남규(겸직교수), 서인석(서울대학교)
To be announced     2022-05-02 16:37:13
We study stability of a spherical vortex introduced by M. Hill in 1894, which is an explicit solution of the three-dimensional incompressible Euler equations. The flow is axi-symmetric with no swirl, the vortex core is simply a ball sliding on the axis of symmetry with a constant speed, and the vorticity in the core is proportional to the distance from the symmetry axis. We use the variational setting introduced by A. Friedman and B. Turkington (Trans. Amer. Math. Soc., 1981). As a consequence, the stability up to a translation is obtained by using a concentrated compactness method. As an application, we prove linear in time filamentation near Hill’s vortex: there exists an arbitrary small outward perturbation growing linearly for all times. These results rigorously confirm numerical simulations by Pozrikidis in 1986. The second part is joint work with In-Jee Jeong(SNU).
ZOOM Meeting ID: 868 7549 9085 Direct link:
Host: Myoungjean Bae     To be announced     2022-03-14 09:33:55

2011~현재 미국 국립 과학원 회원 2005~현재 수학 연보(Annals of Mathematics) 편집자/감사관 2010, 1990 국제 수학자 회의 초청 연사 2009 클레이상 2004 오스왈드 베블렌 기하학상 전 고등연구소 회원
Host: Hyung Ryul Baik     To be announced     2022-04-19 14:40:01
Ordinary differential equations are useful in modeling the periodic behavior of organisms, such as circadian rhythm, based on known biological knowledge and researchers' hypotheses. The theoretical mathematical models are calibrated to the experimental measurements by estimating a set of unknown model parameters. Traditional parameter estimation with mathematical models often focuses only on the point estimation relying on an optimization method such as simulated annealing, but it often neglects the uncertainty in point estimates and suffers from the local trap issue. This talk provides a gentle introduction to Bayesian analysis focusing on its usefulness in uncertainty quantification; introduces a Bayesian computing method with an advanced Markov chain Monte Carlo called the generalized multiset sampler; and illustrates the proposed Bayesian inference with circadian oscillations observed in a model filamentous fungus, Neurospora crassa.
ZOOM Meeting ID: 868 7549 9085 Direct link:
Host: Jaekyoung Kim     To be announced     2022-03-14 09:30:53
그래프 신경망은 그래프에서 높은 표현 능력과 함께 특징 정보를 추출하는 방법론으로 학계와 산업체에서 최근 폭발적인 관심을 받고 있다. 본 세미나에서는 그래프 신경망의 개요 및 주요 동작 원리를 다룬다. 구체적으로, message passing의 원리를 이해하고 state-of-the-art 알고리즘에서 사용한 다양한 message passing 함수를 소개한다. 그리고, 협업 필터링에 기반한 추천 시스템을 소개하고, 이러한 추천 시스템 설계에 그래프 신경망의 응용에 대해 학습한다. 경량화된 그래프 신경망을 사용한 state-of-the-art 추천 알고리즘을 소개하고, 해당 방법들이 가지는 challenge를 이해한다. 마지막으로, 발표자 연구실에서 제안한 그래프 신경망을 활용한 새로운 추천 시스템 방법을 간단히 소개한다.
Host: 이창옥     To be announced     2022-03-29 13:55:34
Morihiko Saito's theory of mixed Hodge modules is a far generalisation of classical Hodge theory, which is based on the theory of perverse sheaves, D-modules, variations of Hodge structures. One can think of mixed Hodge modules as a certain class of D-modules with Hodge structures. Naturally they are accompanied by perverse sheaves via the Riemann–Hilbert correspondence. This guide consists of about 8 talks, which may cover: review of classical Hodge theory, D-modules and filtered D-modules, nearby and vanishing cycles, etc. The main goal is to understand the notion of mixed Hodge modules and to explain two important theorems: the structure theorem and the direct image theorem. If time permits, we discuss recent applications of the theory in algebraic geometry.
Zoom 회의 ID: 352 730 6970; 암호: 1778 ; 실명으로 들어오시면 대기실에서 개별 승인해 드립니다.
Host: 박진현     Contact: 박진현 (2734)     Korean     2022-03-25 11:46:38
심사위원장: 이용남, 심사위원 : 곽시종, 백상훈, 최영욱(영남대 수학교육과), 최인송(건국대 수학과)
To be announced     2022-03-29 16:04:42