Matthew Harrison-Trainor : Effective Gelfand Duality and a Scott Analysis for Topological Spaces

Posted by Matthew Harrison-Trainor , part of the Logic Seminar.

At

Oct. 24, 2023, 4 p.m.

In

636 SEO

Abstract

I will talk about an Effective Gelfand Duality between a compact topological space X and its algebra of functions. We can use that to reduce the homeomorphism problem for compact topological spaces to the isomorphism problem for C*-algebras, which is known to be Borel. One can then ask, for a particular space X, what is the complexity of the set of homeomorphic copies of X?