Wednesday, November 1, 2023

2023-11-07 / 13:30 ~ 14:30

SAARC 세미나 - SAARC 세미나:

by 지홍창()

The spectrum of a general non-Hermitian (non-normal) matrix is unstable; a tiny perturbation of the matrix may result in a huge difference in its eigenvalues. This instability is often quantified as eigenvalue condition numbers in numerical linear algebra or as eigenvector overlap in random matrix theory. In this talk, we show that adding a smoothly random noise matrix regularizes this instability, by proving a nearly optimal upper bound of eigenvalue condition numbers. If time permits, we will also discuss the effect of the noise matrix on a macroscopic scale in terms of the Brown measure of free circular Brownian motion. This talk is based on joint works with László Erdős.

2023-11-02 / 14:30 ~ 15:30

학과 세미나/콜로퀴엄 - 정수론:

by 신석우()

(KAI-X Distinguished Lecture Series) We have multiple approaches to vanishing theorems for the cohomology of Shimura varieties, via either algebraic geometry or automorphic forms. Such theorems have been of interest with either complex or torsion coefficients. Recently, results have been obtained under various genericity hypotheses by Caraiani-Scholze, Koshikawa, Hamann-Lee et al. I will survey different approaches. If time permits, I may discuss an ongoing project with Koshikawa to understand the non-generic case.

2023-11-01 / 16:00 ~ 17:00

IBS-KAIST 세미나 - 수리생물학:

by ()

The Hypothalamic-Pituitary-Adrenal (HPA) axis is the key regulatory pathway responsible for maintaining homeostasis under conditions of real or perceived stress. Endocrine responses to stressors are mediated by adrenocorticotrophic hormone (ACTH) and corticosteroid (CORT) hormones. In healthy, non-stressed conditions, ACTH and CORT exhibit highly correlated ultradian pulsatility with an amplitude modulated by circadian processes. Disruption of these hormonal rhythms can occur as a result of stressors or in the very early stages of disease. Despite the fact that misaligned endocrine rhythms are associated with increased morbidity, a quantitative understanding of their mechanistic origin and pathogenicity is missing. Mathematically, the HPA axis can be understood as a dynamical system that is optimised to respond and adapt to perturbations. Normally, the body copes well with minor disruptions, but finds it difficult to withstand severe, repeated or long-lasting perturbations. Whilst a healthy HPA axis maintains a certain degree of robustness to stressors, its fragility in diseased states is largely unknown, and this understanding constitutes a critical step toward the development of digital tools to support clinical decision-making. This talk will explore how these challenges are being addressed by combining high-resolution biosampling techniques with mathematical and computational analysis methods. This interdisciplinary approach is helping us quantify the inter-individual variability of daily hormone profiles and develop novel “dynamic biomarkers” that serve as a normative reference and to signal endocrine dysfunction. By shifting from a qualitative to a quantitative description of the HPA axis, these insights bring us a step closer to personalised clinical interventions for which timing is key.

2023-11-07 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Some Variants of the Erdős-Sós Conjecture

by Bruce A. Reed(Academia Sinica)

Determining the density required to ensure that a host graph G contains some target graph as a subgraph or minor is a natural and well-studied question in extremal combinatorics. The celebrated 50-year-old Erdős-Sós conjecture states that for every k, if G has average degree exceeding k-2 then it contains every tree T with k vertices as a subgraph. This is tight as the clique with k-1 vertices contains no tree with k vertices as a subgraph. We present some variants of this conjecture. We first consider replacing bounds on the average degree by bounds on the minimum and maximum degrees. We then consider replacing subgraph by minor in the statement.

2023-11-02 / 11:50 ~ 12:40

대학원생 세미나 - 대학원생 세미나: Complex Geometry Arising from Quaternionic Kähler Manifolds

by 권민성(Dept. of Mathematical Sciences, KAIST)

In this talk, I will introduce twistor theory, which connects complex geometry, Riemannian geometry, and algebraic geometry by producing a complex manifold, called the twistor space, from a quaternionic Kähler manifold. First, I will explain why quaternionic Kähler manifolds have to be studied in view of holonomy theory in Riemannian geometry, and how twistor theory enables us to use algebraic geometry in studying their geometry. Next, based on the realization of homogeneous twistor spaces as adjoint varieties, I will present a description of the compactified spaces of conics in adjoint varieties, which is motivated by twistor theory.

2023-11-02 / 14:30 ~ 15:45

학과 세미나/콜로퀴엄 - 기타:

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(information) "Introduction to Oriented Matroids" Series Thursdays 14:30-15:45

2023-11-02 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

by 신석우()

2023-11-02 / 13:00 ~ 15:00

학과 세미나/콜로퀴엄 - 박사논문심사: 스파이크 랜덤 행렬 모형들에서의 신호 감지 문제

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Events for the 취소된 행사 포함