Virtual Seminar on
Geometry and Topology
How to join
Zoom Meeting ID 739-035-2844
Password Zero minus the Euler characteristic of a closed oriented surface of genus 4000
Time Wed 4 pm or Thursday 9 am (or so) in KST (Korea Standard Time)
December 9 and 10 (W, Th), 5 pm Korea = 9 am Switzerland
Yash Lodha (EPFL)
Spaces of countable groups
In this mini course I will describe two spaces of groups. The first is the Grigorchuk space of marked groups, and the second is the Polish space of enumerated groups. Both spaces provide a useful framework for the study of countable, discrete groups. After a gentle introduction, I shall describe some recent results in the field, such as the work of Minasyan, Osin and Witzel on quasi-isometric diversity, and the work of Elayavalli and Goldbring on the generic version of the von Neumann-Day problem. I shall also describe how some of my past and also some recent work (in part with coauthors) fits into the picture.
December 17 (Th) 10 am, Zoom 739-035-2844
(= December 16 (W) 8 pm Indiana)
David Fisher (Indiana University)
January 7, 11, 13 (Th, M, W), 4 pm Korea
Yash Lodha (KIAS, expected)
Amenability and paradoxical decompositions.
The notion of Amenability has its roots in the seminal work of von Neumann from the early 20th century. Since then, it has become a well studied subfield of modern group theory. In this mini course shall describe amenability from a rather algebraic point of view. In the first lecture we shall define amenability via the notion of Folner sets. The second lecture shall be focused on paradoxical decompositions and Tarski numbers. The third lecture shall focus on some recent results in the field, including new solutions to the von Neumann-Day problem.