Seminars & Colloquia Calendar
Brian Pinsky - Rutgers University
Date & time: Tuesday, 29 March 2022 at 2:00PM - 3:00PM
Abstract : Like many areas of group theory, the study of branch groups began with burnside’s problem: whether every finitely generated torsion group is finite. One of the first counterexamples was Grigorchuck’s group, a group of self-similar automorphisms of cantor space. Self similarity is a powerful tool for working with these groups, and they are among the most useful examples in geometric group theory. I will illustrate this technique by proving Grigorchuck’s group is torsion, this is very elegant and requires no group theory background. Afterwards, I’d like to go over a generalization of Grigorchuck’s construction using coding theory; one I thought I’d invented, but Zoron Sunic actually beat me by 15 years. I’d also like to talk about generalizations acting on infinite type surfaces, rather than cantor space, as according to my enthusiastic office-neighbor and some papers I still need to read, this is fruitful.