Thursday, April 24, 2025

2025-05-01 / 11:50 ~ 12:40

대학원생 세미나 - 대학원생 세미나: Introduction to Mathematical Modeling for Heterogeneous Diffusion

by 박준성(카이스트 수리과학과)

In undergraduate PDE course, one may have learned that the (classical) diffusion equation can be expressed as $u_t=D \Delta u$, where $D$ is a constant diffusivity. This is true for homogeneous environment. However, for (spatially) heterogeneous environment, $D$ is no longer a constant, and diffusion phenomena in those environments such as fractionation, or Soret effect, cannot be explained with the classical diffusion equation. In this talk, I will first discuss how to model and derive some of the diffusion equations in heterogeneous environment by using basic random walk theory. We will see that the heterogeneity of components, such as speed, walk length, sojourn time, etc, can explain the diffusion phenomena. Then, I will give some specific examples how such models can be applied in science, based on my recent works.

2025-04-30 / 16:30 ~ 18:00

학과 세미나/콜로퀴엄 - 미분기하 세미나:

by 엄기윤()

I will provide a brief introduction to the canonical metric problem in Kähler geometry and related objects. Then I'll explain how generalizations of these objects naturally appear in the context of partition functions of determinantal point processes on polarized Kähler manifolds. The talk will be aimed at beginning geometry students and I will be rather pedagogical. Especially, I will focus on geometric aspects of the topic, so probabilistic or physical discussion will be postponed or omitted. This is based on my recent preprint.

2025-04-24 / 15:00 ~ 16:30

학과 세미나/콜로퀴엄 - 위상수학 세미나:

by 박종일()

A normal projective surface with the same Betti numbers of the projective plane CP2 is called a rational homology projective plane (briefly Q-homology CP2 or QHCP2). People working in algebraic geometry and topology have long studied a Q-homology CP2 with possibly quotient singularities. It has been known that it has at most five such singular points, but it is still mysterious so that there are many unsolved problems left. In this talk, I’ll review some known results and open problems in this field which might be solved and might not be solved in near future. In particular, I’d like to review the following two topics and to report some recent progress: 1. Algebraic Montgomery-Yang problem. 2. Classification of Q-homology CP2 with quotient singularities. This is a joint work with Woohyeok Jo and Kyungbae Park..

2025-04-29 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Approximation Algorithms for the Geometric Multimatching Problem

by Eunjin Oh(Dept. of Computer Science and Engineering, POSTECH)

Let S and T be two sets of points in a metric space with a total of n points. Each point in S and T has an associated value that specifies an upper limit on how many points it can be matched with from the other set. A multimatching between S and T is a way of pairing points such that each point in S is matched with at least as many points in T as its assigned value, and vice versa for each point in T. The cost of a multimatching is defined as the sum of the distances between all matched pairs of points. The geometric multimatching problem seeks to find a multimatching that minimizes this cost. A special case where each point is matched to at most one other point is known as the geometric many-to-many matching problem. We present two results for these problems when the underlying metric space has a bounded doubling dimension. Specifically, we provide the first near-linear-time approximation scheme for the geometric multimatching problem in terms of the output size. Additionally, we improve upon the best-known approximation algorithm for the geometric many-to-many matching problem, previously introduced by Bandyapadhyay and Xue (SoCG 2024), which won the best paper award at SoCG 2024. This is joint work with Shinwoo An and Jie Xue.

2025-04-24 / 13:30 ~ 14:30

학과 세미나/콜로퀴엄 - 위상수학 세미나: An invitation to combinatorial semigroup theory IV

by (고등과학원)

In this series of talks, I'll present the basics of combinatorial semigroup theory, starting with elementary results and ending in recent research using high-powered tools. I'll begin by giving an overview of the elements of semigroup theory, including the analogue of Cayley's theorem, eggbox diagrams, Green's relations, inverse semigroups, and a famous result due to Green & Penrose. In the subsequent talk, I'll present the elements of presentations of semigroups, free (inverse) semigroups, Munn trees, and rewriting systems, leading into the fundamental problem central to combinatorial semigroup theory: the word problem. In the next talk, I'll dive into a particular class of semigroups called "special" monoids, and give proofs via rewriting systems due to Zhang (1990s) of famous results due to Adian (1960s), giving a solution to the word problem in all monoids given by a single defining relation of the form w=1. In the final talk (if there is time) I will dip our toes into how rewriting systems can compute the (co)homology of a monoid, and give new proofs via the spectral sequence of certain rewriting systems (forthcoming) of homological results due to Gray & Steinberg (2023).

2025-04-24 / 10:00 ~ 11:00

학과 세미나/콜로퀴엄 - 위상수학 세미나: An invitation to combinatorial semigroup theory III

by (고등과학원)

2025-04-25 / 14:00 ~ 16:00

IBS-KAIST 세미나 - 수리생물학:

by ()

In this talk, we discuss the paper “Boolean modelling as a logic-based dynamic approach in systems medicine” by Ahmed Abdelmonem Hemedan et al., Computational and Structural biotechnology journal (2022).

2025-04-25 / 15:00 ~ 17:00

학과 세미나/콜로퀴엄 - 기타: Grothendieck groups of regular schemes 1

by 우태윤(KAIST)

This is a reading seminar presented by the graduate student, Mr. Taeyoon Woo. Following the lecture note of Yuri Manin, he will study K_0 of schemes, and its essential properties, such as functoriality, projective bundle formula, filtrations, relationship to Picard group, blow-up squares, Chern classes, Todd classes and the Grothendieck-Riemann-Roch theorem.

Events for the 취소된 행사 포함