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"
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.