PhD Dissertation Defense: “Descriptive Set Theory and Measure Theory in Locally Compact and Non-Locally Compact Groups” | Department of Mathematics
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PhD Dissertation Defense: “Descriptive Set Theory and Measure Theory in Locally Compact and Non-Locally Compact Groups”

Event Information
Speaker: 
Mike Cohen
Event Location: 
GAB 310
Event Date: 
Friday, March 29, 2013 - 2:00pm

Professors Robert Kallman and Su Gao invite you to attend the PhD dissertation defense of Michael Cohen on Friday, March 29th at 2:00 pm in GAB 310. Cake and coffee will be served in GAB 472 following this event.

"Descriptive Set Theory and Measure Theory in Locally Compact and Non-Locally Compact Groups"

Abstract:

In this thesis we examine a variety of descriptive-set-theoretic and measure-theoretic properties of Polish groups, with a thematic emphasis on the contrast between groups which are locally compact and those which are not. The work may be divided roughly into three major sections. In the first, working jointly with Robert R. Kallman, we resolve an old conjecture of A. M. Gleason regarding the Polish topologization of abstract (un-topologized) groups of homeomorphisms. In the second section we classify the Borel complexity of some subsets of the permutation group $S_\infty$ which arise naturally from the classical series rearrangement theorems of Riemann, Levy, and Steinitz. In the last section we study the phenomenon of Haar null sets a la Christensen, and the closely related notion of openly Haar null sets, which comprise measure-theoretic ``smallness notions'' in general Polish groups.