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.