Jay Williams : Group embeddability and countable Borel quasi-orders

Posted by , part of the Logic Seminar.

At

Oct. 27, 2011, 3 p.m.

In

SEO 1227

Abstract

Descriptive set theory gives us a framework for analyzing the relative complexity of quasi-orders (i.e. reflexive transitive relations) arising in many areas of mathematics, such as Turing reducibility of sets of natural numbers or embeddability of countable groups, using the notion of a Borel reduction. I will discuss a special class of quasi-orders, the countable Borel quasi-orders, and focus in particular on embeddability of finitely-generated groups, answering a question of Louveau and Rosendal. The ideas in this case will apply to the more general case of embeddability of countable groups.