Abstract:
This will be an introductory talk in a two part series. This talk will focused on an area of mathematics referred to as measured group theory, which is the study of infinite groups from a measure theoretic perspective and the impact of the group structure on the ergodic theory of their actions. I will introduce Gromov's Measure Equivalence from both a group theoretic and measure theoretic perspective and explain their connections and the problems studied in the area.