Descriptive set theory and Polish groups

01 January 2018 to 30 June 2018


Justin Moore, Cornell University
Christian Rosendal, University of Illinois at Chicago
Todor Tsankov, Université Paris Diderot

Descriptive set theory is classically defined as the study of definable (e.g. Borel, analytic) sets in Polish spaces -- separable, completely metrizable spaces. It has long thrived in its connections with classical areas of mathematics such as harmonic and functional analysis and logic (set theory and computability theory in particular). Over the course of the last 25 years, however, a vast number of new interactions have opened up the field to novel and exciting directions. The principal goal of the semester long program is to organize a number of activities in and around modern aspects of descriptive set theory and its links with other areas of mathematics. An important focus is to facilitate research on the structure of Polish topological groups, which recently has gathered momentum partially due to work in descriptive set theory.

The program is focused on three themes which span much of the current research in descriptive set theory: Borel graphs, Borel equivalence relations and Borel reducibility; nonlocally compact Polish groups, their geometry, and their actions; regular ideals of small sets Polish spaces. We also emphasize connections with other areas of mathematics.