Working Seminar in Orbit Equivalence and Measured Group Theory

Date: October 23, 2020

Time: 11:00AM - 12:00PM

Location: Zoom

Speaker: Konrad Wrobel

Title: An introduction to arithmetic groups and some facts about semisimple Lie groups

Abstract: The goal of this seminar is to study arithmetic subgroups of semisimple Lie groups. By definition, the subject combines algebra(groups of matrices) with number theory(groups of integers). There are also many important connections to geometry(fundamental groups of locally symmetric spaces) and various properties that geometric group theorists find interesting. The tools used come from several of these fields, but surprisingly enough, many of the tools come from ergodic theory. Some of the ultimate goals of the seminar include Margulis Superrigidity, Mostow Rigidity, and the classification of arithmetic subgroups of classical groups. This first lecture will give an outline of the goals and tools involved and start giving several definitions as well as discuss some basics about Lie groups. We will be reading from Dave Witte Morris's "An Introduction to Arithmetic Groups." Please contact Konrad Wrobel for the zoom link.