Timetable

Titles and abstracts

Nov. 19 (Wed), 4:30PM-5:15PM

speaker: Wontae Kim (HCMC)

title : Complex valued PDEs and its applications

abstract : 

In this talk, we will discuss the parametric problem of the Laplace equation, which serves as a model for various stochastic equations. Recently, the study of finding numerical solutions using AI has been extensive. In particular, we introduce the approach via complex extension to the parametric problem.

Nov. 19 (Wed), 5:30PM-6:15PM

speaker: Inhyeok Choi (KIAS)

title : Statistics in non-positively curved groups

abstract : 

In this talk, I will quickly introduce the theme of geometric group theory. Then I will explain some results regarding statistics in the mapping class group. Nothing is assumed beyond undergraduate group theory, 2x2 matrix theory and hyperbolic plane.

Nov. 20 (Thurs), 9:30AM-10:15AM

speaker: Jae-Hwan Choi (KIAS)

title : Bridges between Probability and Differential Equations

abstract : 

Probability and differential equations illuminate each other in surprising ways. In this talk, I will present on the mutual influence between them.

Nov. 20 (Thurs), 10:30AM-11:15AM

speaker: You-Cheng Chou (HCMC)

title : Permutation equivariant quantum K theory of a point

abstract : 

In this talk, I will start with two motivations for this project. The first is to establish a K-theoretic version of the Witten-Kontsevich theorem. The second comes from localization computation: localization computation for a general target usually reduced to the point case.

Then I will present ongoing work on two key aspects of this project. First is a pushforward formula applied to the universal cotangent line bundle and the pluri-Hodge bundle. This technique is combinatorially easier for not using Kawasaki-Hirzebruch-Riemann-Roch theorem. Second, I will discuss the permutation-equivariant string equation, which gives a recursive formula when forgetting multiple marked points with unit insertions. This talk is based on joint works (some in progress) with Y.-P Lee, Leo Herr, Irit Huq-Kuruvilla, and Kamyar Amini.

Nov. 20 (Thurs), 11:30AM-12:15PM

speaker: Hongtaek Jung (KIAS)

title : Introduction to higher Teichmuller spaces

abstract : 

I will explain how higher Teichmuller theory has emerged. It turns out that higher Teichmuller theory is deeply connected to the positive structures of semisimple Lie groups. After introducing the notion of positivity,  I will discuss several results and problems concerning higher Teichmuller spaces and positive representations.

Nov. 21 (Fri), 9:30AM-10:15AM

speaker: Doyoung Choi (KIAS)

title : Geometry of secant varieties

abstract : 

I will give an introduction to secant varieties. I begin with several equivalent definitions and basic geometric intuition. Concrete motivations with simple examples will be shown; for instance, connections to matrix multiplication complexity and the Waring rank of polynomials will be presented. Next I outline the situation for surfaces. In a short focused part I mention the main properties — normality, Du Bois (a mild class of singularities), and the expected linear behavior of syzygies — and give simple cohomological criteria to check Cohen–Macaulay or rational singularities. The talk finishes with an intuitive viewpoint from the Hilbert scheme and secant bundles: secants built from families of finite subschemes help to clarify their geometry.

Nov. 21 (Fri), 10:30AM-11:15AM

speaker: Se-Chan Lee (KIAS)

title : Time derivative estimates for parabolic $p$-Laplace equations

abstract : 

In this talk, I will introduce the $C^{p’}$-conjecture on the optimal regularity of solutions to elliptic and parabolic $p$-Laplace equations. Then I will establish the boundedness of time derivatives of solutions to parabolic $p$-Laplace equations, which is closely connected to the conjecture.

Nov. 21 (Fri), 11:30AM-12:15PM

speaker: Heejong Lee (HCMC)

title : Mod p representation theory of GL2(Qp) and beyond

abstract : 

The conjectural mod p Langlands correspondence predicts a close relationship between mod p representations of p-adic groups (e.g. GL2(Qp)) and of the absolute Galois group of Qp. In this talk, I will explain a concrete description of such a correspondence for GL2(Qp), emphasizing the parallel structures on two sides. After that, I will explain why it is difficult to obtain a similar correspondence for cases beyond GL2(Qp) by showing that the mod p representation theory of p-adic groups is surprisingly more complicated for such cases. This is based on a joint work with Zachary Feng, Ray Li, Vaughan McDonald, and Nischay Reddy.