During term-time, we hold an Algebra Seminar at 3pm on Tuesdays.
In this page, you can find all the information on the seminar (currently organised by Peter Huston, previously organised by Ilaria Colazzo and Francesca Fedele) since September 2025.
Unless otherwise specified, Algebra seminars take place during term time on Tuesdays at 3.00pm in the MALL, School of Mathematics, University of Leeds.
Abstract - Dehn’s famous decision problems for finitely presented groups have been studied for over a century by combinatorial and geometric group theorists. In recent years, a variant of one of these classical problems, namely the twisted conjugacy problem, has been studied. The motivation for this problem comes from Bogopolski, Martino and Ventura who, in 2009, proved an equivalence between conjugacy in group extensions and twisted conjugacy.
In this talk I will give a brief survey of this lesser-known decision problem, and discuss some of the latest results in this area. This includes a framework which can be applied to dihedral Artin groups.
Abstract: With (almost) every finite mutation class of quivers we associate two groups: an extended affine Weyl group of type A or D, and a certain quotient of a Coxeter group which behaves nicely with respect to mutations (in most cases, the latter can also be obtained as a quotient of certain surface braid group). I will discuss a connection between these groups and a (still conjectural) characterization of mutation-finite quivers in terms of positive semidefinite symmetric matrices. The talk is based on joint works (some still in progress) with Anna Felikson, John Lawson and Michael Shapiro.
Classical knot theory associates to a combinatorial knot diagram a knot embedding in the 3-sphere. The fundamental group (and peripheral system) of the complement give rise to powerful, combinatorially computable invariants. This talk explores an analogous construction for welded knots, a diagrammatic extension of classical knot theory corresponding to ribbon knotted tori in 4-space via the tube map.
We introduce a new topological invariant, the fundamental \pi-module (built using the first and second homotopy groups), and show how it can be computed combinatorially from a diagram. We then define a natural topological generalisation of the peripheral system, using the free loop space of the complement, and again show how this admits a simple combinatorial description.
Cluster ensembles were introduced by Fock and Goncharov to encode seed data for cluster algebras in terms of certain lattices, enabling the definition of cluster varieties by gluing the associated tori. We will explain aspects of two pieces of joint work, with Gratz and Pressland respectively, in which we show that categorifications of cluster algebras yield cluster ensembles, that these categorifications are often quantizable and that there is also a category governing interactions between cluster ensembles. Furthermore, these structures can help us understand mirror symmetry for cluster varieties.
Abstract: In this talk, I will review the basic notions of Fomin-Kirillov algebras and discuss some open problems. I will explain how these algebras arise in combinatorial Schubert calculus and in the theory of Hopf algebras. Finally, I will present some crazy numerology that seems to connect Fomin-Kirillov algebras with various topics in representation theory.
Abstract - The main aim of affinization (in the sense discussed here) is to formulate and analyse (additive or linear) algebraic structures in a way in which no selection of a specific element is necessary. In this talk I will explain the main motivation and various aspects of affinization and illustrate the process by affinization of familiar algebraic structures such as groups, vector spaces, and associative and Lie algebras.
Module categories have two types of generators: projective modules and simple modules. Abstractions of projective modules have led to (tau-)tilting theory and cluster-tilting theory. Cluster-tilting theory is well suited to positive Calabi-Yau categories. However, there are natural examples of negative Calabi-Yau categories, such as the stable module category of a symmetric algebra. Projective generators are less useful in this context because they are killed by stabilisation, making understanding the simple-like generators an important question.
In this talk I will explain how simple-minded systems are negative Calabi-Yau analogues of cluster-tilting objects and give an overview of aspects of their theory for hereditary algebras.
In a Riemannian manifold, the first filling function $F(l)$ measures the least area needed to fill all null-homotopic loops of length at most $l$ using minimal discs. In this talk I will focus on the first filling function for large loops in Riemannian Lie groups. This function is also known as the Dehn function and quantifies the complexity of the word problem from combinatorial group theory. I will review results of Cornulier and Tessera showing it is either exponential or polynomially bounded, and discuss some recent progress on the problem of estimating the degree of polynomial growth when it is polynomially bounded. This is joint work with Ido Grayevsky (Bristol).
While an affine algebraic group is a subgroup of the general linear group that is defined by some polynomial equations, an affine difference algebraic group is a subgroup of the general linear group that is defined by difference polynomial equations. In this talk I will introduce difference algebra and difference algebraic geometry, before explaining how we can use difference algebraic groups to find a class of difference ideals that are finitely difference generated.
Long before having taken their name, thus earned their distinguished place in an area in the intersection of algebra, Knots Theory and combinatorics now a days, Fully Commutative Elements served in the shadows for years, being used as element of basis of the known Temperley-Lieb algebras. It turns out that "they" have their own story. I shall enter by the pure algebra door by giving the general definition, which is simple "by definition". It is a fact that 55 minutes would not be enough to tell the importance of such a class of elements, yet I hope having enough time to talk about the present rather than the past and and so to present some interesting open problems. Please enjoy.
