Queen's College

Symplectic reflection algebras are an important class of algebras related to an incredibly high number of different topics such as combinatorics, noncommutative geometry and resolutions of singularities and have themselves a rich representation theory. We will recall their definition and classification coming from symplectic reflection groups and outline some of the results that have characterised their representation theory over the last decade, focusing on the link with representations of quivers.

Saturated fusion systems are both a convenient language in which to formulate p-local finite simple group theory and interesting structures in their own right. In this talk, we will start by explaining what is meant by a 'tree of fusion systems' and give conditions on such an object for there to exist a saturated completion. We then describe how this theory can be used to understand a class of fusion systems first considered by Bob Oliver, which are determined by modular representations of finite groups. If time permits, we will discuss joint work with David Craven towards a complete classification of such fusion systems. The talk is aimed at a general mathematical audience with some background in algebra.

Concepts such as infinitesimal numbers and fluxions have been used by Leibnitz and Newton for the initial development of calculus. However, their non-rigorous nature has caused a lot of controversy and they have eventually been phased out by epsilon-delta definitions. In early 60s Abraham Robinson realised that methods of mathematical logic can be used to provide rigorous meaning to such concepts. This talk is a gentle introduction to some of Robinson's ideas.

In this talk, I will discuss homotopy limits: The basics, and why you should care about them if you are a topologist, an algebraic geometer, or an algebraist (have I missed anyone?).

Categorification is a fancy word for a process that is pretty ubiquitous in mathematics, though it is usually not referred to as "a thing". With the advent of higher category theory it has, however, become "a thing". I will explain what people mean by this "thing" (sneak preview: it involves replacing sets by categories) and hopefully convince you it is not quite as alien as it may seem and maybe even tempt you to let it infect some of your maths. I'll then explain how this fits into the context of higher categories.

I shall talk about Subgroup Membership Problem for amalgamated products of finite rank free groups. I'm going to show how one can solve different versions of this problem in amalgams of free groups and give an estimate of the complexity of some algorithms involved.  This talk is based on a joint paper with A. J. Duncan.

Following the recent paper of Ogasa, we attempt to construct Boy's surface using only paper and tape. If this is successful we hope to address such questions as:

Is that really Boy's surface?

Why should we care?

Do we have any more biscuits?

We'll provide some motivation for the appearance of factorization algebras in physics, before discussing the definition of a factorization monoid. We'll then review the definition of a principal G-bundle and show how a factorization monoid can help us understand the moduli stack Bun_G of principal G-bundles.

I will give an introduction to The McKay Correspondence, relating the irreducible representations of a finite subgroup Γ ≤ SL2 (C), minimal resolutions of the orbit space C2 /Γ, and affine Dynkin diagrams.