Monday, November 22, 2021

2021-11-24 / 17:00 ~ 19:00

학과 세미나/콜로퀴엄 - 해외 석학 특별 강연 시리즈:

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Geometric and functional inequalities play a crucial role in several problems arising in analysis and geometry. Proving the validity of such inequalities, and understanding the structure of minimizers, is a classical and important question. In these lectures I will first give an overview of this beautiful topic and discuss some recent results.

2021-11-23 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Ramsey numbers of Boolean lattices

by Casey Tompkins(IBS 이산수학그룹)

The poset Ramsey number $R(Q_{m},Q_{n})$ is the smallest integer $N$ such that any blue-red coloring of the elements of the Boolean lattice $Q_{N}$ has a blue induced copy of~$Q_{m}$ or a red induced copy of $Q_{n}$. Axenovich and Walzer showed that $n+2\le R(Q_{2},Q_{n})\le2n+2$. Recently, Lu and Thompson improved the upper bound to $\frac{5}{3}n+2$. In this paper, we solve this problem asymptotically by showing that $R(Q_{2},Q_{n})=n+O(n/\log n)$. Joint work with Dániel Grósz and Abhishek Methuku.

2021-11-26 / 13:30 ~ 15:00

학과 세미나/콜로퀴엄 - 박사논문심사: 특별한 입방다양체의 준등장 불변량

by 오상록(KAIST)

심사위원장: 백형렬, 심사위원: 최서영, 박정환, 김상현(겸직교수), 이상진(건국대 수학과)

2021-11-24 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 정수론: On the Brumer-Stark conjecture

by Prof Mahesh Kakde(Indian Institute of Science)

The talk with start with an introduction to Stark’s conjectures. We will then specialise to the situation of Brumer-Stark conjecture and its various refinements. I will then sketch a proof of the conjecture. This is a joint work with Samit Dasgupta.

2021-11-25 / 12:25 ~ 12:45

대학원생 세미나 - 대학원생 세미나: Eigenvalues and parity factors in graphs

by 김동규(KAIST & IBS)

Let $G$ be a graph and let $g, f$ be nonnegative integer-valued functions defined on $V(G)$ such that $g(v) \le f(v)$ and $g(v) \equiv f(v) \pmod{2}$ for all $v \in V(G)$. A $(g,f)$-parity factor of $G$ is a spanning subgraph $H$ such that for each vertex $v \in V(G)$, $g(v) \le d_H(v) \le f(v)$ and $f(v)\equiv d_H(v) \pmod{2}$. In this paper, we prove sharp upper bounds for certain eigenvalues in an $h$-edge-connected graph $G$ with given minimum degree to guarantee the existence of a $(g,f)$-parity factor; we provide graphs showing that the bounds are optimal. This is a joint work with Suil O.

2021-11-25 / 12:00 ~ 12:20

대학원생 세미나 - 대학원생 세미나: A new elementary proof of the central limit theorem

by 진우영(KAIST)

The proof of the central limit theorem (CLT) is often deferred to a graduate course in probability because the notion of characteristic functions is sometimes considered too advanced. I’ll start the talk by reviewing the past efforts to provide an elementary proof of the CLT which is not based on characteristic functions. Then I will explain a new proof of the CLT that derives it from the de Moivre-Laplace theorem, which is the CLT for Bernoulli random variables. The de Moivre-Laplace theorem is the first instance of the CLT in the history, and can be proved directly by computation.

2021-11-22 / 16:30 ~ 18:00

학과 세미나/콜로퀴엄 - 계산수학 세미나: Multigrid Methods for Vector Field Problems

by 오덕순(충남대학교)

We design and analyze V‐cycle multigrid methods for problems posed in H(div) and H(curl). Due to the fact that traditional smoothers do not work well for the vector field problems, special approaches for smoothers in the multigrid methods are essential. We introduce new smoothing techniques which involve non-overlapping domain decomposition preconditioners based on substructuring. We prove uniform convergence of the V‐cycle methods on bounded convex hexahedral domains. Numerical experiments that support the theory are also presented.

2021-11-25 / 18:00 ~ 19:00

IBS-KAIST 세미나 - 수리생물학:

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Simple mathematical models have had remarkable successes in biology, framing how we understand a host of mechanisms and processes. However, with the advent of a host of new experimental technologies, the last ten years has seen an explosion in the amount and types of quantitative data now being generated. This sets a new challenge for the field – to develop, calibrate and analyse new models to interpret these data. In this talk I will use examples relating to intracellular transport and cell motility to showcase how quantitative comparisons between models and data can help tease apart subtle details of biological mechanisms.

2021-11-26 / 15:00 ~ 16:00

학과 세미나/콜로퀴엄 - PDE 세미나:

by 옥지훈(서강대학교)

In recent years, local regularity theory for weak solutions to nonlocal equations with fractional orders has been studied extensively. In this talk, we discuss on local regularity for weak solutions to nonlocal equations with nonstandard growth and differentiability. In particular, we consider nonlocal equations of a variable exponent type, a double phase type and an Orlicz type.

2021-11-25 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄: Mathematical modeling for infectious disease using epidemiological data

by 이효정(경북대학교 통계학과)

The new infectious disease are emerging around the world. Coronavirus disease 2019 (COVID-19) caused by a novel coronavirus has emerged and has been rapidly spreading. The World Health Organization (WHO) declared the COVID-19 outbreak a global pandemic on March 11, 2020. Mathematical modelling plays a key role in interpreting the epidemiological data on the outbreak of infectious disease. Moreover, mathematical modeling can give us an early warning about the size of the outbreak. First, we construct a mathematical model to estimate the effective reproduction numbers, which assess the effect of control interventions. Second, we forecast the COVID-19 cases according to the different effect of control interventions. Finally, the most effective intervention can be suggested in terms of modeling approach. In this talk, I’d like to briefly introduce the main results of recent research on the mathematical modeling for various infectious diseases.

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