2025

Dec 12 (Fri) 11 am - 12 pm

SNU (Room TBA) & Zoom https://kimsh.kr/vz

Donggyun Seo (Seoul National University) 

Title: Dehn twists on a doubled handlebody

Abstract: A double of a three-dimensional handlebody, often called a doubled handlebody, has been the subject of study for several decades. The mapping class group of a doubled handlebody is known to be virtually isomorphic to the outer automorphism group of a free group.  In this talk, we will focus on the properties of Dehn twists in the mapping class group of a doubled handlebody, with attention to their analogies and differences with Dehn twists on surfaces.

Dec 16 (Tue) 11 am - 12 pm

KIAS (Room 1423) & Zoom https://kimsh.kr/vz

Sunhyuk Lim (SKKU)

Title: TBA

Abstract: TBA

Dec 22 (Mon) 10:30 am - 12 pm

KIAS (Room 1423) & Zoom https://kimsh.kr/vz

Dongryul M. Kim (Yale)

Title: Measure classification via geometric group theory

Abstract: In this talk, I will present my joint work with Inhyeok Choi that develops geometric group theoretic approaches to classifying invariant Radon measures on various dynamical systems arising from Teichmüller dynamics and homogeneous dynamics.

First, given a non-elementary subgroup of the mapping class group of a hyperbolic surface, we construct an invariant Radon measure on the space of measured laminations and prove that any ergodic invariant Radon measure on the recurrent measured laminations coincides with this measure. When the subgroup is the full mapping class group, this measure is the Thurston measure, and in this case the uniqueness on recurrent measured laminations was independently proved by Lindenstrauss--Mirzakhani and Hamenstädt.

Next, we classify all horospherical-invariant Radon measures on higher-rank Anosov and relatively Anosov homogeneous spaces. Our approaches towards both Teichmüller and homogeneous settings are based on geometric properties of certain geodesics, which we call squeezing.