Wednesday, March 13, 2024

2024-03-15 / 11:00 ~ 12:00

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

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.

2024-03-15 / 14:00 ~ 16:00

학과 세미나/콜로퀴엄 - 기타: Introduction to étale cohomology 1

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

by 이현우(KAIST, IBS 극단 조합 및 확률 그룹)

TBA

2024-03-14 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

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.

2024-03-19 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - 정수론:

by 이정인(아주대학교)

Motivated by the Cohen-Lenstra heuristics, Friedman and Washington studied the distribution of the cokernels of random matrices over the ring of p-adic integers. This has been generalized in many directions, as well as some applications to the distribution of random algebraic objects. In this talk, first we give an overview of random matrix theory over the ring of p-adic integers, together with their connections to conjectures in number theory. After that, we investigate the distribution of the cokernels of random p-adic matrices with given zero entries. The second part of this talk is based on work in progress with Gilyoung Cheong, Dong Yeap Kang and Myungjun Yu.

Events for the 취소된 행사 포함