Algebra

Monday 23rd June, Forum Seminar Rooms 1-3

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, Forum Seminar Rooms 1-3

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

Wednesday 25th June, Peter Chalk Centre Newman Red

Contributed talks

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.#

Inna Capdeboscq – Chevalley groups over non-archemadian local fields: some subgroups
In this talk we discuss  the structure and generation of some subgroups of Chevalley groups over non-archimedean local fields. This is a  joint work with Bertrand Remy.

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.

Lewis Topley – Quantizations of conjugacy classes in positive characteristic
Poisson algebras provide a basic algebraic framework for Hamiltonian dynamics, and quantization is the process of finding a non-commutative algebra which approximates a Poisson algebra in a precise sense. In recent years it has become apparent that large families of rather complicated Poisson varieties in characteristic zero admit rigid quantization theories: their global quantizations can be classified. Over fields of positive characteristic the appearance of such phenomena has not even been enunciated as a conjecture. In this talk I will explain a work in progress with Filippo Ambrosio and Matt Westaway which classifies the quantizations of conjugacy classes of matrices, using methods from representation theory.