Pure Maths Colloquium: Yash Lodha

In this talk 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.