2026-27
Seminars are held on Thursdays at 12:00 in B3.02
Organisers: Sean Eberhard and Gareth Tracey
We welcome suggestions for speakers. Please email the organisers.
Term 1:
8th October: Ernesto Ingrosso (Napoli)
Title: Groups with dual classes of subgroups
Abstract: We completely characterize insoluble groups whose subgroups are pronormal or pronormalize every subgroup. We also completely describe p-groups with this property, and prove many structural results in the soluble case (for example, such groups are always of length at most 3 and have Sylow towers). This is joint work with M. Trombetti and A. Zitouni.
15th October: Marie Roth (UEA)
Title: On the subregular and submaximal p-cells of classical Weyl groups.
Abstract: The Kazhdan-Lusztig basis of a Hecke algebra and the associated cell structure is a fundamental tool in representation theory in characteristic zero. In the last ten years, a modular version of the Kazhdan-Lusztig basis (the p-canonical basis) and the corresponding p-cells have been defined. However, the description is very chaotic and not much is known.
We report on some recent progress towards a better understanding, focusing on the subregular and submaximal cells. This is joint work with V. Miemietz and D. Tubbenhauer.
22nd October: Veronica Kelsey (Manchester)
Title: Puzzles, Pestilence and Pseudogroups
Abstract: The Fifteen Puzzle has 15 numbered tiles in a 4x4 grid and the aim is to slide the tiles around to obtain particular configurations. It became a craze in the 1880s with The New York Times reporting:
"No pestilence has ever visited this or any other country which has spread with the awful celerity of what is popularly called the 'Fifteen Puzzle'.”
We’ll begin the talk with the maths behind the original, and then discuss some less pestilent versions of this puzzle. The first variant was described by Conway and then studied by Conway, Elikes and Martin. This construction was used to produce the “pseudogroup” M_{13} (also called a groupoid). In some joint work with Peter Rowley, Conway’s modification has been extended to a family of puzzles each with their own groupoid which we will discuss for the remainder of the talk.
29th October: Hans Wenzl (UCSD)
Title: Reconstructing tensor categories of type $G_2$
Abstract: We show that any ribbon tensor category with the fusion rules of the compact Lie group of type $G_2$ has to be equivalent to the Drinfeld-Jimbo quantum group of the same type, for q not a root of unity. A similar statement also holds for the corresponding finite fusion categories.
5th November: Álvaro Guttierez (Bristol)
Title: Algebraic functions in log-space
Abstract: Countless constants in algebra are positive by construction, and hard to compute in general. A combinatorial understanding of these often unlocks theoretical methods and computational tools. A philosophy of Mulmuley (in his quest towards P vs NP) and later flagshipped by Pak equates the notions of "combinatorial interpretation" with a certain computational complexity class #P (poly-time verifiable).
We study algebraic functions from representation theory, number theory, and enumerative combinatorics in a different class #L (log-space verifiable), which is as good of a candidate to formalise "combinatorial interpretation". Instead, we propose a new candidate formalisation.
12th November: Robert Laugwitz (Nottingham)
Title: Fully dualizable module categories
Abstract: Finite module categories over a braided finite tensor category form a monoidal 2-category with respect to the relative Deligne product. In this talk, I will discuss the new monoidal 2-subcategories of fully exact and perfect module categories. Fully exact module categories lead to a natural generalization of the concept of a separable algebra in a non-semisimple tensor category. Perfect module categories are precisely the fully dualizable module categories in the sense of the cobordism hypothesis. I will present examples obtained from representations of finite groups and Hopf algebras.
19th November: James Taylor (Bristol)
Title: Revisiting Dyson's Tenfold Way.
Abstract: Semilinear representations are a natural generalisation of linear representations, where now there is also an action of the group G on the coefficient field L. In this talk I will introduce the basic theory of semilinear representations, and describe recent work on a classification of semilinear representations in the simplest non-trivial case, when the action of G on L is through an order two automorphism. In the case that L = C, I will explain what Dyson's Tenfold Way is, and how our classification recovers it. This is joint work with Dmitriy Rumynin.
26th November: Andrew Darlington (VUB)
3rd December: Rachel Quinlan (Galway)
10th December: Dan Ciubotaru (Oxford)