Algebra

Monday 23rd June

15:10 – 15:50 Inna Capdeboscq (Warwick)
15:50 – 16:30 Matthew Fayers (Queen Mary)
16:30 – 17:10 Benjamin Briggs (Imperial)

Tuesday 24th June

15:40 – 16:20 Lewis Topley (Bath)
16:20 – 17:00 Ehud Meir (Aberdeen)
17:00 – 17:40 Ilaria Colazzo (Leeds)

Wednesday 25th June

Contributed talks (further details tbc)

Titles and Abstracts

Benjamin Briggs – Moment angle manifolds and linear free resolutions
This is a talk about some of the extremely close connections between the combinatorics of simplicial complexes, the homological algebra of monomial rings, and the topology of toric spaces. I’ll start by explaining how these three areas thread together by constructing the Stanley-Reisner ring and the moment angle space associated to a simplicial complex. Then I’ll survey some of the interactions between these objects, focusing on how linear resolutions affect the geometry of moment angle manifolds, as part of some joint work with Steve Amelotte.

Illaria Colazzo – Matched Pairs of Groups and Combinatorial Solutions to the Pentagon Equation
In this talk, I will present a complete classification of finite bijective set-theoretic solutions to the Pentagon Equation, uncovering a surprising connection with matched pairs of groups. We will introduce all necessary definitions. Next, we will focus on the fundamental components: the irretractable solutions, and we will examine how these solutions relate to matched pairs of groups. Finally, we will show how each irretractable solution can be lifted to classify all bijective solutions.

Matthew Fayers – Irreducible Specht modules
Given a finite group and a prime , it is an interesting question to ask which ordinary irreducible representations of remain irreducible in characteristic . For the symmetric groups this question was answered a while ago, and in the meantime there has been considerable activity in extending this question to other groups and algebras. I will give a survey of these results.

Ehud Meir – Geometric methods in braided vector spaces and their Nichols algebras
The Nichols algebra of a braided vector space is a generalization of both the symmetric algebra and the exterior algebra.It can be realized as a Hopf algebra in some braided monoidal category. By the process of Bosonization, Nichols algebras provide an abundance of examples of finite dimensional non-semisimple Hopf algebras. This raises the question of the finite-dimensionality of Nichols algebras. In this talk I will explain how to prove that certain Nichols algebras are infinite dimensional, by using geometric methods and in particular reductive group actions. This is based on a joint work with Istvan Heceknberger and Leandro Vendramin. If time permits, I will also talk about more recent work with Ben Martin, about the geometry of the space of braiding in a given dimension.