Jingyin Huang
The Ohio State Uniervsity
Title
Introduction to measure equivalence classification of countable groups
Abstract
Recall that two countable groups are measure equivalent, if they admit commuting, measure preserving, free actions on the same measure space with finite measure fundamental domains. This notion was first proposed by Gromov as a measure-theoretical version of quasi-isometry, and it is closely related to the notion of orbit equivalence of groups acting on probability measure spaces. Given a countable group G, one may ask what are other groups which are measure equivalent to G. This question has generated many interesting mathematics, and there was rather strong rigidity results proved in the case when G is a higher rank lattice or the mapping class group of a surface. In this talk, we will cover some backgrounds on measure equivalence classification of groups, and survey some measure equivalence invariants and rigidity results.