Poster

Friday, October 18, 20139:30 amnote new timeSet theory seminarGC 6417Two talks for set theory seminar on this day

Canonical Ramsey theory on Polish spaces

Marcin Sabok

Instytut Matematyczny Uniwersytetu Wrocławskiego, Instytut Matematyczny Polskiej Akademii Nauk

Marcin Sabok

I would like to give an overview of recent results in canonical Ramsey theory in the context of descriptive set theory. This is the subject of a recent monograph joint with with Vladimir Kanovei and Jindra Zapletal. The main question we address is the following. Given an analytic equivalence relation on a Polish space, can one find a large subset of the space on which it has a simple form? Canonical Ramsey theory stems from finite combinatorics and is concerned with finding canonical forms of equivalence relations on finite (or countable) sets. We obtain canonization results for analytic and Borel equivalence relations and in cases when canonization is impossible, we prove ergodicity theorems. For a publisher’s book description see:

http://www.youtube.com/watch?v=ZPXBcKeepKk

Dr. Sabok (Ph.D. 2009 University of Wrocław) undertakes research in set theory, especially descriptive set theory, forcing and its applications.