Date: 2nd December 2019
Time: 16:00–18:00
Location: Glasgow University Maths Building
Speakers: Alex Evetts (Heriot-Watt), James Rowe (Glasgow)
Alex Evetts — Assorted BS
The Baumslag-Solitar groups BS(n,m) are an interesting class of finitely generated infinite groups. I will define them and discuss a few different ways to understand them. In particular, I’ll talk about their word growth and recent results regarding their conjugacy growth series.
James Rowe — Sheaves of Triangulated Categories
Tensor triangulated categories appear naturally in various areas of mathematics including algebraic geometry, modular representation theory and stable homotopy theory. The work of Balmer establishes prime ideals and a spectrum to a tensor triangulated category which acts as an invariant: an example of its strength is that it can reconstruct nice schemes from their derived category of perfect complexes. Central to this construction is a “sheaf” of triangulated categories used to capture local information. We use this to investigate the reverse of modern geometry: instead of using categories to study geometric objects can we use natural geometric constructions to tell us something about our categories?
Date: 21st August 2020
Time: 16:00–18:30
Location: Virtual
Speaker: Martyn Quick (St Andrews)
Graduate level talk — An introduction to profinite groups and the just infinite property
I will explain what is meant by a profinite group, some of their basic properties, and the situations in which they arise in group theory. I will also introduce the concept of a just infinite group and explain why this is of significance in the context of profinite groups.
Research level talk — The structure of groups with specified quotients
A group is called “just infinite” if it is infinite and every proper quotient is finite. I shall review the background on the topic and describe some ways in which the concept has been generalized. I shall, in particular, present some new results concerning groups with all proper quotients abelian-by-finite and explain why this is a natural class of groups to consider.