Approximate Equivalence Relations and Approximate Symmetries

Abstract: 

A k-approximate equivalence relation is a relation that can be represented as "distance at most 1" in a metric space with the property,
that any radius 2 ball is covered by k 1-balls.   This generalizes the notion of a k-approximate subgroup of a group.  Special examples include Cayley graphs of k-generated groups, and the distance-one relations in Riemannian homogeneous spaces; these play a special role among all approximate equivalence relations.  I will discuss some results and open 
problems, and the connection to stability. The talk will include a quick introduction to continuous logic and probability logic.