Welcome to the One-day Festival of Group actions, Geometry and Dynamics!

Date:  August 6th (Wed), 2025

Venue: KIAS building 8 (Rm 8101), Seoul, Korea (Google map)

Registration link  please submit your registration by noon, Aug 4.

Schedule

      9:30-10 am Coffee

10-11  Wooyeon Kim (KIAS)

11:30-12:30 Inhyeok Choi (KIAS)

Lunch at KIAS (4th floor)

2:30-3:30 Dongryul Kim (Yale)

Tea time

4:30-5:30 Gye-Seon Lee (SNU)

6:00- Dinner at 샹그라

Titles and Abstracts

Wooyeon Kim

Title: Distribution of determinants at lattice points of matrices

Abstract: In this talk, we study the distribution of determinant values taken by lattice points in the space of real matrices. Specifically, given a lattice  that is not equivalent to a rational lattice, we investigate the asymptotic behavior of the number of elements in the lattice of norm at most T whose determinant lies in a fixed interval, as T tends to infinity. Our approach relies on techniques from homogeneous dynamics, in particular the behavior of certain unipotent flows, to analyze the distribution of these lattice points. This is joint work in progress with Hee Oh.

Inhyeok Choi

Title: Dynamics of semigroups of circle homeomorphisms

Abstract: The circle homeomorphism group Homeo(S^1) is a huge group that contains a variety of subgroups and subsemigroups. Because of its richness, the Tits alternative does not hold in general for Homeo(S^1). Still, a dynamical Tits alternative, asked by Ghys and proved by Margulis, holds for Homeo(S^1): every subgroup of Homeo(S^1) either preserves an invariant probability measure or contains a Schottky pair that enables ping-pong argument. A similar dichotomy holds for subsemigroups of Homeo(S^1) thanks to Malicet’s theory of random walks on Homeo(S^1). In this talk, I will explain an alternative approach to the dynamical Tits alternative for semigroups that is inspired by Margulis’ original method.

Dongryul Kim

Title: Rigidity of Kleinian groups via dynamics on Anosov homogeneous spaces

Abstract: A deformation of a convex cocompact Kleinian group is given by a boundary map on its limit set. We present a rigidity dichotomy for the set of "conformal points" of this boundary map: it either has zero Hausdorff measure, or coincides with the entire limit set. In the latter case, the deformation is trivial. We prove this rigidity by considering the associated self-joining subgroup in higher rank, which turns out to be an Anosov subgroup. We focus on how we use the dynamics on the higher rank Anosov homogeneous space to prove the rigidity theorem for Kleinian groups. This is joint work with Hee Oh. 

Gye-Seon Lee

Title: Discrete Coxeter groups

Abstract: Coxeter groups are a special class of groups generated by involutions and play important roles in many areas of mathematics. This survey talk focuses on how Coxeter groups can be used to construct interesting examples of discrete subgroups of Lie groups.

Organizer:  Hee Oh (Yale University) hee.oh(AT)yale(DOT)edu