Self-similar groups are groups of automorphisms of infinite rooted trees obeying a simple but powerful rule. Under this rule, groups with exotic properties can be generated from very basic starting data, most famously the Grigorchuk group which was the first example of a group with intermediate growth.

Nekrashevych introduced a groupoid and a C*-algebra for a self-similar group action on a tree as models for some underlying noncommutative space for the system. Our goal is to compute the K-theory of the C*-algebra and the homology of the groupoid. Our main theorem provides long exact sequences which reduce the problems to group theory. I will demonstrate how to apply this theorem to fully compute homology and K-theory through the example of the Grigorchuk group.

This is joint work with Benjamin Steinberg.

The Seventeenth Brooke Benjamin Lecture 2024

The Elusive Singularity

I will describe the open problems of singularity formation in incompressible fluids. I will discuss a list of related models, some results, and some more open problems.

Date: Monday, 11 November 2024 

Time: 5pm GMT

Location: Lecture Theatre 1, Mathematical Institute 

Speaker: Professor Peter Constantin        

More information about The Brooke Benjamin Lecture.

The Bruhat-Tits building is a crucial combinatorial tool in the study of reductive p-adic groups and their representation theory. Given a p-adic group, its Bruhat-Tits building is a simplicial complex upon which it acts with remarkable properties. In this talk I will give an introduction to the Bruhat-Tits building by sketching its definition and going over some of its basic properties. I will then show the usefulness of the Bruhat-Tits by determining the maximal compact subgroups of a p-adic group up to conjugacy by using the Bruhat-Tits building.