Ilijas Farah : Abstract and concrete classification problems

Posted by Mihnea Popa , part of the Departmental Colloquium.

At

April 5, 2013, 3 p.m.

In

SEO 636

Abstract

G. Mackey introduced the notion of smooth equivalence relation in the context of unitary group representations. Over the last two decades Mackey's notion was extended to an abstract framework for analyzing classification problems in mathematics. Methods developed by Hjorth, Kechris and others enable one to precisely define when one classification problem is more difficult than another. Classification problems are compared using the relation of Borel-reducibility. I will outline some of the recent results, putting a particular emphasis on applications to Elliott's program for classification of nuclear C*-algebras. This is a joint work with a number of coauthors.