PhD Dissertation Defense: “The relative complexity of various classification problems among compact metric spaces” | Department of Mathematics

PhD Dissertation Defense: “The relative complexity of various classification problems among compact metric spaces”

Event Information
Event Location: 
GAB 105
Event Date: 
Wednesday, March 30, 2016 - 3:30pm

Professor Su Gao invites you to attend the PhD dissertation defense of Jeff Chang next Wednesday, March 30th, at 3:30 pm in GAB 105. Cake and coffee will be served in GAB 472 following this event.

"The relative complexity of various classification problems among compact metric spaces"

Abstract:

One of the topics of descriptive set theory is to compare the complexity of various classification problems, many of them can be shown to be Borel bireducible to a universal orbit equivalence relation. In this work, we present that the homeomorphic equivalence relation among connected compact metric spaces is also Borel bireducible to a universal orbit equivalence relation. Then we consider the class of all locally compact two-sided invariant non-Archimedean Polish groups and present a topological characterization of these groups. Using one of the characterizations, we present that there does not exist a universal group in the class, but there exists a surjectively universal group.

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