Logic Seminar

Sumun IyerCornell University
Generic actions of free groups

Friday, September 1, 2023 - 2:55pm
Malott 205

Let $G$ be a countable free group, possibly with infinitely many generators. We can consider the Polish space $\textrm{Act}(G)$ of all continuous $G$-actions on compact Polish spaces. Any particular action of $G$ on a compact Polish space generates a countable Borel equivalence relation. The main theorem will be that the generic element of $\textrm{Act}(G)$ generates a hyperfinite equivalence relation. The proof uses a projective Fraisse limit result due to Kwiatkowska as well as the theory of Borel asymptotic dimension due to Conley, Jackson, Marks, Seward, and Tucker-Drob. This is joint work with Forte Shinko.