# Andre Nies: The complexity of isomorphism between profinite groups

Invitation to the Logic Seminar at the National University of Singapore

Date: Thursday, 25 February 2016, 17:00 hrs

Room: S17#04-06, Department of Mathematics, NUS

Speaker: Andre Nies, The University of Auckland

Title: The complexity of isomorphism between profinite groups

URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html

A topological group G is profinite if it is compact and totally
disconnected. Equivalently, G is the inverse limit of a surjective
system of finite groups carrying the discrete topology. An example is
We discuss how to represent a countably based profinite group as a
point in a Polish space. Thereafter, we study the complexity of their
isomorphism using the theory of Borel reducibility in descriptive set
theory. For topologically finitely generated groups this complexity is
the same as the one of identity for reals. In general, it is the same
as the complexity of isomorphism for countable graphs.