Friday, June 6, 2025

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

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

by 김태균(KAIST)

2025-06-10 / 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.

2025-06-10 / 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