##### Department of Mathematics,

University of California San Diego

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### Math 211B - Group Actions Seminar

## Jinho Jeoung

#### Seoul National University

## $\operatorname{PGL}_2(\mathbb{Q}_p)$-orbit closures on a $p$-adic homogenenous space of infinite volume

##### Abstract:

We proved closed/dense dichotomy of $\operatorname{PGL}_2(\mathbb{

Let $\mathbb{K}$ be an unramified quadratic extension of $\mathbb{Q}_p$. Our homogeneous space is a quotient space of $\operatorname{\mathbb{K}}$ by a certain class of Schottky subgroups. Using the main tools of McMullen, Mohammadi, and Oh, we introduced the necessary properties of Schottky subgroups and used the Bruhat-Tits tree $\operatorname{PGL}_2$. In this talk, we introduce the highly-branched Schottky subgroups and steps for the proof of the main theorem.

This is a joint work with Seonhee Lim.

Host: Brandon Seward

### February 1, 2024

### 4:00 PM

Zoom ID 967 4109 3409

Research Areas

Ergodic Theory and Dynamical Systems****************************