An Invitation to Descriptive Group Theory

by Dr Srivatsav Kunnawalkam Elayavalli (Vanderbilt U and UCLA)

Tuesday 19 Jul 2022, 15:00 → 16:00 Asia/Kolkata

Math. Seminar Room (A-369)

Abstract: I will present joint work with I. Goldbring and Y. Lodha where we study the space of enumerated groups which is a topological Polish space consisting of enumerations of countable groups. We also study Polish subspaces of this space consisting of groups with desired properties such as amenability, orderability etc. The fundamental problem of proving or disproving existence of co-meager isomorphism classes in these spaces is surprisingly mysterious. We settle this problem for a family of subspaces including the space of all countable enumerated groups and the space of all left orderable enumerated groups. Our work crucially uses tools from descriptive set theory, combinatorial group theory and model theoretic forcing, especially ideas of Hodges.