Friday, March 8, 2024

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2024-03-15 / 11:00 ~ 12:00
학과 세미나/콜로퀴엄 - 응용 및 계산수학 세미나: 인쇄
by 이은정(연세대학교)
This talk presents mathematical modeling, numerical analysis and simulation using finite element method in the field of electromagnetics at various scales, from analyzing quantum mechanical effects to calculating the scattering of electromagnetic wave in free space. First, we discuss and analyze the Schrodinger-Poisson system of quantum transport model to calculate electron states in three-dimensional heterostructures. Second, the electromagnetic vector wave scattering problem is solved to analyze the field characteristics in the presence of stealth platform. This talk also introduces several challenging issues in these applications and proposes their solutions through mathematical analysis.
2024-03-15 / 10:00 ~ 11:30
학과 세미나/콜로퀴엄 - 위상수학 세미나: ARC.dim of Julia sets 인쇄
by Dylan Thurston(University of Indiana, Bloomington)
The Julia set of a (hyperbolic) rational map naturally comes embedded in the Riemann sphere, and thus has a Hausdorff dimension. But the Hausdorff dimension varies if we tweak the parameters slightly. Is there a "best" representative or more invariant dimension? One answer comes from looking at quasi-symmetries; the \emph{conformal dimension} of the Julia set is the minimum Hausdorff dimension of any metri quasi-symmetric to the original. We characterize the Ahlfors-regular conformal dimension of Julia sets of rational maps using graphical energies arising from a natural combinatorial description. (Ahlfors-regular is a dynamically natural extra condition on the metric.) This is joint work with Kevin Pilgrim.
2024-03-12 / 16:30 ~ 18:30
IBS-KAIST 세미나 - 수리생물학: 인쇄
by (IBS 의생명수학그룹)
"Reduced model for female endocrine dynamics: Validation and functional variations", Mathematical Biosciences (2023) will be discussed in this Journal Club. A normally functioning menstrual cycle requires significant crosstalk between hormones originating in ovarian and brain tissues. Reproductive hormone dysregulation may cause abnormal function and sometimes infertility. The inherent complexity in this endocrine system is a challenge to identifying mechanisms of cycle disruption, particularly given the large number of unknown parameters in existing mathematical models. We develop a new endocrine model to limit model complexity and use simulated distributions of unknown parameters for model analysis. By employing a comprehensive model evaluation, we identify a collection of mechanisms that differentiate normal and abnormal phenotypes. We also discover an intermediate phenotype—displaying relatively normal hormone levels and cycle dynamics—that is grouped statistically with the irregular phenotype. Results provide insight into how clinical symptoms associated with ovulatory disruption may not be detected through hormone measurements alone. If you want to participate in the seminar, you need to enter IBS builiding (https://www.ibs.re.kr/bimag/visiting/). Please contact if you first come IBS to get permission to enter IBS building.
2024-03-08 / 11:00 ~ 12:00
학과 세미나/콜로퀴엄 - 응용 및 계산수학 세미나: 인쇄
by 최재웅()
Optimal Transport (OT) problem investigates a transport map that bridges two distributions while minimizing a specified cost function. OT theory has been widely utilized in generative modeling. Initially, the OT-based Wasserstein metric served as a measure for assessing the distance between data and generated distributions. More recently, the OT transport map, connecting data and prior distributions, has emerged as a new approach for generative models. In this talk, we will introduce generative models based on Optimal Transport. Specifically, we will present our work on a generative model utilizing Unbalanced Optimal Transport. We will also discuss our subsequent efforts to address the challenges associated with this approach.
2024-03-08 / 11:00 ~ 12:00
IBS-KAIST 세미나 - 수리생물학: 인쇄
by ()

2024-03-15 / 14:00 ~ 16:00
학과 세미나/콜로퀴엄 - 기타: Introduction to étale cohomology 1 인쇄
by 이제학(KAIST)
This is an introductory reading seminar presented by a senior undergraduate student, Jaehak Lee, who is studying the subject.
2024-03-14 / 11:50 ~ 12:40
대학원생 세미나 - 대학원생 세미나: Towards a high-dimensional Dirac's theorem 인쇄
by 이현우(KAIST, IBS 극단 조합 및 확률 그룹)
TBA
2024-03-12 / 16:00 ~ 17:00
SAARC 세미나 - SAARC 세미나: 인쇄
by 류경석(서울대학교)
Momentum-based acceleration of first-order optimization methods, first introduced by Nesterov, has been foundational to the theory and practice of large-scale optimization and machine learning. However, finding a fundamental understanding of such acceleration remains a long-standing open problem. In the past few years, several new acceleration mechanisms, distinct from Nesterov’s, have been discovered, and the similarities and dissimilarities among these new acceleration phenomena hint at a promising avenue of attack for the open problem. In this talk, we discuss the envisioned goal of developing a mathematical theory unifying the collection of acceleration mechanisms and the challenges that are to be overcome.
2024-03-14 / 16:15 ~ 17:15
학과 세미나/콜로퀴엄 - 콜로퀴엄: 인쇄
by ()
A rational map, like f(z) = (1+z^2)/(1-z^2), gives a map from the (extended) complex plane to itself. Studying the dynamics under iteration yields beautiful Julia set fractals with intricate nested structure. How can that structure be best understood? One approach is combinatorial or topological, giving concrete models for the Julia set and tools for cataloguing the possibilities.
2024-03-12 / 16:30 ~ 17:30
IBS-KAIST 세미나 - 이산수학: On polynomial degree-boundedness 인쇄
by Linda Cook(IBS 이산수학그룹)
We prove a conjecture of Bonamy, Bousquet, Pilipczuk, Rzążewski, Thomassé, and Walczak, that for every graph $H$, there is a polynomial $p$ such that for every positive integer $s$, every graph of average degree at least $p(s)$ contains either $K_{s,s}$ as a subgraph or contains an induced subdivision of $H$. This improves upon a result of Kühn and Osthus from 2004 who proved it for graphs whose average degree is at least triply exponential in $s$ and a recent result of Du, Girão, Hunter, McCarty and Scott for graphs with average degree at least singly exponential in $s$. As an application, we prove that the class of graphs that do not contain an induced subdivision of $K_{s,t}$ is polynomially $\chi$-bounded. In the case of $K_{2,3}$, this is the class of theta-free graphs, and answers a question of Davies. Along the way, we also answer a recent question of McCarty, by showing that if $\mathcal{G}$ is a hereditary class of graphs for which there is a polynomial $p$ such that every bipartite $K_{s,s}$-free graph in $\mathcal{G}$ has average degree at most $p(s)$, then more generally, there is a polynomial $p'$ such that every $K_{s,s}$-free graph in $\mathcal{G}$ has average degree at most $p'(s)$. Our main new tool is an induced variant of the Kővári-Sós-Turán theorem, which we find to be of independent interest. This is joint work with Romain Bourneuf (ENS de Lyon), Matija Bucić (Princeton), and James Davies (Cambridge),
2024-03-08 / 14:00 ~ 16:00
학과 세미나/콜로퀴엄 - 기타: Introduction to complex algebraic geometry and Hodge theory #1 인쇄
by 김재홍(KAIST)
This is part of an informal seminar series to be given by Mr. Jaehong Kim, who has been studying the book "Hodge theory and Complex Algebraic Geometry Vol 1 by Claire Voisin" for a few months. There will be 6-8 seminars during Spring 2024, and it will summarize about 70-80% of the book.
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