MW, 12-1:30p1, MS 6221.
Instructor: MS 7340. W: 10-11, F: 11-1.
This course will roughly fall into two parts. The first part will have very few prerequisites, mainly just a general understanding of certain basic facts about Borel structure which I will review as needed. It will deal with the theory of countable Borel equivalence relations: I plan to prove Feldman-Moore, the Glimm-Effros dichotomy for countable Borel equivalence relations, and discuss hyperfinite and non-hyperfinite countable Borel equivalence relations.
The second part of the course will be less elementary and require some knowledge of effective descriptive set theory. I will introduce the Gandy-Harrington forcing/topology and use this to prove Silver's theorem and the Harrington-Kechris-Louveau generalization of Glimm-Effros to arbitrary Borel equivalence relations. We will also have the opportunity to explore further dichotomy theorems we can be established using the same techniques.
If there is time remaining, I may also spend some time discussing equivalence relations with many ends and connections with superrigidity.
Homeworks: There will be homeworks posted on this web page for the students who want a letter grade. Probably about three or four in all.
The first homework is due Monday, November 5.
The second homework is due Wednesday, November 21.
The third and final homework is due Wednesday, December 5.