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 Francesca Fedele, Ilaria Colazzo and Peter Huston) 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.
Results 11 to 20 of 50
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.
Abstract:
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.
I will talk about a joint work with Tyrone Crisp and Uri Onn about the complex representation theory of the groups GL_n(Z/p^r). Following the work of Zelevinsky, we know that when r=1 the complex representation theory of the groups GL_n(Z/p) decomposes nicely into a combinatorial part and an arithmetic part. The representation theory of GL_n(Z/p^r) where r>1 seems to be much more complicated. We conjecture that a similar decomposition exists there. In this talk I will explain how we tackle this conjecture, using tools from symmetric monoidal categories and from classical representation theory. The main insight from symmetric monoidal categories is that the languages of finite groups and finite rings intertwine here, and that studying the representation theory of GL_n(Z/p^r) naturally contains the study of groups of the form Aut_R(M) for general finite rings R and finite modules M. This much more general framework, together with classical tools from representation theory, gives much better insight into the conjecture.
In a 2019 paper, Kadar, Martin, and Yu, introduced the notion of left height for a Brauer diagram, and used it to define a family of subalgebras of the Brauer algebra which interpolate between the Temperley-Lieb (sub)algebra, and the full Brauer Algebra. Early calculations indicated that for intermediate height values, these algebras exhibited novel semi-simplicity criteria distinct from the classical criteria in the Temperley-Lieb case (roots of unity), and Brauer case (integers). In this talk, we present ongoing work aimed characterising these criteria; rules for computing Gram-matrix determinants for all standard modules are given in some low height cases, leading to a general conjecture. This conjecture involves introducing a Chebyshev series of polynomials for each integer partition, the roots of which seem to “resemble” roots of unity for large n. Time permitting, we will discuss some of the representation theoretic consequences of our calculations for the Kadar-Yu algebras in low rank.
Finding Morita invariants of fusion categories enriched over a fixed modular tensor category is important because, by a form of the cobordism hypothesis, they correspond (2+1)D twice-extended framed TQFTs, and therefore to physical characteristics of topological phases of matter. In this talk, we will introduce the notions of fusion 1- and 2-category and see how they appear naturally in higher linear algebra. We will then see how the Morita 3-category of fusion categories, bimodule categories, bimodule functors, and natural transformations can be equivalently described by concrete Morita invariants, so that choices of representatives of Morita class need not be made.
I start with the definition of cluster integrable systems a la Goncharov and Kenyon, defined by convex Newton polygons, up to the action of $SA(2,\mathbb{Z})$. There are several arguments requiring that to complete the picture, this class should be extended by their Hamiltonian reductions, which can be performed preserving the structure of cluster variety.