Wednesday, June 4, 2025

2025-06-04 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Strict Erdős-Ko-Rado Theorems for Simplicial Complexes

by Denys Bulavka(Hebrew University of Jerusalem)

The now classical theorem of Erdős, Ko and Rado establishes the size of a maximal uniform family of pairwise-intersecting sets as well as a characterization of the families attaining such upper bound. One natural extension of this theorem is that of restricting the possiblechoices for the sets. That is, given a simplicial complex, what is the size of a maximal uniform family of pairwise-intersecting faces. Holroyd and Talbot, and Borg conjectured that the same phenomena as in the classical case (i.e., the simplex) occurs: there is a maximal size pairwise-intersecting family with all its faces having some common vertex. Under stronger hypothesis, they also conjectured that if a family attains such bound then its members must have a common vertex. In this talk I will present some progress towards the characterization of the maximal families. Concretely I will show that the conjecture is true for near-cones of sufficiently high depth. In particular, this implies that the characterization of maximal families holds for, for example, the independence complex of a chordal graph with an isolated vertex as well as the independence complex of a (large enough) disjoint union of graphs with at least one isolated vertex. Under stronger hypothesis, i.e., more isolated vertices, we also recover a stability theorem. This talk is based on a joint work with Russ Woodroofe.

2025-06-05 / 17:00 ~ 18:00

학과 세미나/콜로퀴엄 - 박사논문심사: 내포물 문제에 대한 기하적 시리즈 해 방법과 물리 정보 신경망 방법 연구 및 역문제 응용

by 조대희(KAIST)

2025-06-10 / 14:00 ~ 15:00

학과 세미나/콜로퀴엄 - 박사논문심사: 두꺼운 꼬리 구조를 갖는 구면 스핀글래스의 새로운 보편성 구조

by 김태균(KAIST)

2025-06-05 / 16:15 ~ 18:30

학과 세미나/콜로퀴엄 - 기타:

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Lecture 1: Artem Pulemotov (University of Queensland), 4:15-5:15PM
Title: The prescribed Ricci curvature problem on homogeneous spaces
Abstract: We will discuss the problem of recovering the ``shape" of a Riemannian manifold $M$ from its Ricci curvature. After reviewing the relevant background material and the history of the subject, we will focus on the case where $M$ is a homogeneous space for a compact Lie group. Based on joint work with Wolfgang Ziller (The University of Pennsylvania).

Lecture 2: Mikhail Feldman (University of Wisconsin-Madison), 5:30-6:30PM
Title: Self-similar solutions to two-dimensional Riemann problems with transonic shocks
Abstract: Multidimensional conservation laws is an active research area with open questions about existence, uniqueness, and stability of properly defined weak solutions, even for fundamental models such as the compressible Euler system. Understanding particular classes of weak solutions, such as Riemann problems, is crucial in this context. This talk focuses on self-similar solutions to two-dimensional Riemann problems involving transonic shocks for compressible Euler systems. Examples include regular shock reflection, Prandtl reflection, and four-shocks Riemann problem. We first review the results on existence, regularity, geometric properties and uniqueness of global self-similar solutions of regular reflection structure in the framework of potential flow equation. A significant open problem is to extend these results to compressible Euler system, i.e. to understand the effects of vorticity. We show that for the isentropic Euler system, solutions of regular reflection structure have low regularity. We further discuss existence, uniqueness and stability of renormalized solutions to the transport equation for vorticity in this low regularity setting.

***Tea Time 3:45PM-4:15PM in Room 1410***

2025-06-10 / 16:00 ~ 17:00

편미분방정식 통합연구실 세미나 - 편미분방정식: Geometry effects on the boundary-layer profiles of the Keller-Segel system

by 문상혁()

We consider a nonlocal semilinear elliptic equation in a bounded smooth domain with the inhomogeneous Dirichlet boundary condition, which arises as the stationary problem of the Keller-Segel system with physical boundary conditions describing the boundary-layer formation driven by chemotaxis. This problem has a unique steady-state solution which possesses a boundary-layer profile as the nutrient diffucion coefficient tends to zero. Using the Fermi coordinates and delicate analysis with subtle estimates, we also rigorously derive the asymptotic expansion of the boundary-layer profile and thickness in terms of the small diffusion rate with coefficients explicitly expressed by the domain geometric properties including mean curvature, volume and surface area. By these expansions, one can explicitly find the joint impact of the mean curvature, surface area and volume of the spatial domain on the boundary-layer steepness and thickness.

2025-06-11 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 대수기하학:

by ()

Computing obstructions is a useful tool for determining the dimension and singularity of a Hilbert scheme at a given point. However, this task can be quite challenging when the obstruction space is nonzero. In a previous joint work with S. Mukai and its sequels, we developed techniques to compute obstructions to deforming curves on a threefold, under the assumption that the curves lie on a "good" surface (e.g., del Pezzo, K3, Enriques, etc.) contained in the threefold. In this talk, I will review some known results in the case where the intermediate surface is a K3 surface and the ambient threefold is Fano. Finally, I will discuss the deformations of certain space curves lying on a complete intersection K3 surface, and the construction of a generically non-reduced component of the Hilbert scheme of P^5.

2025-06-04 / 16:30 ~ 18:00

학과 세미나/콜로퀴엄 - 미분기하 세미나:

by ()

The investigation of $G_2$-structures and exceptional holonomy on 7-dimensional manifolds involves the analysis of a nonlinear Laplace-type operator on 3-forms. We will discuss the existence of solutions to the Poisson equation for this operator. Based on joint work with Timothy Buttsworth (The University of New South Wales).

2025-06-04 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 기타: Second-order learning in confidence bounds, contextual bandits, and regression

by 전광성()

Confidence sequence provides ways to characterize uncertainty in stochastic environments, which is a widely-used tool for interactive machine learning algorithms and statistical problems including A/B testing, Bayesian optimization, reinforcement learning, and offline evaluation/learning.In these problems, constructing confidence sequences that are tight and correct is crucial since it has a significant impact on the performance of downstream tasks. In this talk, I will first show how to derive one of the tightest empirical Bernstein-style confidence bounds, both theoretically and numerically. This derivation is done via the existence of regret bounds in online learning, inspired by the seminal work of Raklin& Sridharan (2017). Then, I will discuss how our confidence bound extends to unbounded nonnegative random variables with provable tightness. In offline contextual bandits, this leads to the best-known second-order bound in the literature with promising preliminary empirical results. Finally, I will turn to the $[0,1]$-valued regression problem and show how the intuition from our confidence bounds extends to a novel betting-based loss function that exhibits variance-adaptivity. I will conclude with future work including some recent LLM-related topics.

2025-06-04 / 16:00 ~ 18:00

학과 세미나/콜로퀴엄 - 확률론:

by 김영헌(브리티시컬럼비아대학)

Given a distribution, say, of data or mass, over a space, it is natural to consider a lower dimensional structure that is most “similar” or “close” to it. For example, consider a planning problem for an irrigation system (1-dimensional structure) over an agricultural region (2-dimensional distribution) where one wants to optimize the coverage and effectiveness of the water supply. This type of problem is related to “principal curves” in statistics and “manifold learning” in AI research. We will discuss some recent results in this direction that employ optimal transport approaches. This talk will be based on joint projects with Anton Afanassiev, Jonathan Hayase, Forest Kobayashi, Lucas O’Brien, Geoffrey Schiebinger, and Andrew Warren.

2025-06-10 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Minors of non-hamiltonian graphs

by On-Hei Solomon Lo(Tongji University)

A seminal result of Tutte asserts that every 4-connected planar graph is hamiltonian. By Wagner’s theorem, Tutte’s result can be restated as: every 4-connected graph with no $K_{3,3}$ minor is hamiltonian. In 2018, Ding and Marshall posed the problem of characterizing the minor-minimal 3-connected non-hamiltonian graphs. They conjectured that every 3-connected non-hamiltonian graph contains a minor of $K_{3,4}$, $\mathfrak{Q}^+$, or the Herschel graph, where $\mathfrak{Q}^+$ is obtained from the cube by adding a new vertex and connecting it to three vertices that share a common neighbor in the cube. We recently resolved this conjecture along with some related problems. In this talk, we review the background and discuss the proof.

Events for the 취소된 행사 포함