We are glad to inform you that our first KMGS will start on November 18th, Thursday, via Zoom and Gather Town.
We invite Ho-Youn Kim from Dept. of Mathematical Sciences, KAIST and Doyoung Choi from Dept. of Mathematical Sciences, KAIST and IBS Center for Complex Geometry (CCG).
The abstracts of two talks are as follows.
1st slot (PM 12:00~12:20)
Speaker: Ho-youn Kim (김호연) from Dept. of Mathematical Sciences, KAIST, supervised by Prof. Yong Jung Kim (김용정 교수님)
Title: What is the correct diffusion equation in heterogeneous mediums
Discipline: PDE
Abstract: In the classical diffusion theory, the diffusivity has been regarded as an intrinsic property of particles. However, it can’t explain diffusion phenomena in heterogeneous medium, one of the most famous example is Soret effect. The diffusivity can be changed along different mediums and it arises a question: how can we express heterogeneous diffusion. In this talk, I’ll introduce the heterogeneous diffusion equation we found and give some experimental data verifying this work.
Language: Korean
2nd slot (PM 12:25~12:45)
Speaker: Doyoung Choi (최도영) from Dept. of Mathematical Sciences, KAIST and IBS Center for Complex Geometry (CCG), supervised by Prof. Yongnam Lee (이용남 교수님)
Title: Chern classes of tautological sheaves on Hilbert schemes of points on surface
Discipline: Algebraic Geometry
Abstract: I will introduce some concepts of Chern classes, Hilbert schemes and tautological sheaves on Hilbert scheme of points which is associated to a line bundle on surfaces. Also, I will provide a brief description of Lehn’s work which gives an algorithmic approach of the action of the Chern classes of tautological bundles on the cohomology of Hilbert schemes of points on a smooth surface. His work is based on the framework of Nakajima’s oscillator algebra. At the end, I will present the computation of the top Segre classes of tautological bundles associated to line bundles on $Hilb^n$ up to $n \leq 7$, extending computations of Severi, LeBarz, Tikhomirov and Troshina.
Language: Korean