Nov 12 2019

Logic Seminar: Orbit equivalence relations of some classes of non-locally compact Polish groups, by Joseph Zielinski

November 12, 2019

3:30 PM - 4:20 PM

Location

427 SEO

Address

Chicago, IL

Joseph Zielinski: Orbit equivalence relations of some classes of non-locally compact Polish groups

By results of A.S. Kechris, whenever a locally compact Polish group acts continuously on a Polish space, the orbit equivalence relation of the action is essentially countableĀ—that is, Borel reducible to the orbit equivalence relation of an action of a countable group. It is unknown if this characterizes the locally compact Polish groups.
S. Solecki, after proving an analogous characterization for smooth actions of compact Polish groups, showed this to be true in the case where the group, G, is the additive group of a separable Banach space. The characterization also holds for abelian pro-countable groups, by results of M. Malicki. We discuss recent work on this problem, including an extension of this characterization to some important classes of Polish groups.
This is joint work with A.S. Kechris, M. Malicki, and A. Panagiotopoulos.

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Contact

Filippo Calderoni

Date posted

Nov 12, 2019

Date updated

Nov 12, 2019

Speakers

Joseph Zielinski