Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

 

Past events in this series


Mon, 03 Nov 2025
15:30
L5

Prefactorisation algebras for superselection sectors and topological order

Pieter Naaijkens
(Cardiff University)
Abstract
In this talk I will explain the basics of topological order and superselection sector theory. The latter assigns a braided monoidal category to 2D topologically ordered quantum spin systems. The focus of this talk will be how this structure can be understood in terms of locally constant prefactorisation algebras over the category of cone-shaped regions. This naturally leads to a geometric origin for the braiding on the category of superselection sectors. Based on joint work with Marco Benini, Victor Carmona and Alexander Schenkel (arXiv:2505.07960).

 
Mon, 10 Nov 2025
15:30
L5

Ribbon concordance and fibered predecessors

Steven Sivek
(Imperial)
Abstract
Ribbon concordance defines an interesting relation on knots.  In his initial work on the topic, Gordon asked whether it is a partial order, and this question was open for over 40 years until Agol answered it affirmatively in 2022.  However, we still don’t know many basic facts about this partial order: for example, does any infinite chain of ribbon concordances $\dots \leq K_3 \leq K_2 \leq K_1$ eventually stabilize?  Even better, if we fix a knot $K$ in the 3-sphere, are there only finitely many knots that are ribbon concordant to $K$?  I’ll talk about joint work with John Baldwin toward these questions, in which we use tools from both Heegaard Floer homology and hyperbolic geometry to say that at the very least, there are only finitely many fibered hyperbolic knots ribbon concordant to $K$.

 
Mon, 17 Nov 2025
15:30
L5

On the congruence subgroup property for mapping class groups

Henry Wilton
(Cambridge University)
Abstract

I will relate two notorious open questions in low-dimensional topology.  The first asks whether every hyperbolic group is residually finite. The second, the congruence subgroup property, relates the finite-index subgroups of mapping class groups to the topology of the underlying surface. I will explain why, if every hyperbolic group is residually finite, then mapping class groups enjoy the congruence subgroup property. Time permitting, I may give some further applications to the question of whether hyperbolic 3-manifolds are determined by the finite quotients of their fundamental groups.

Mon, 01 Dec 2025
15:30
L5

Kazhdan‘s property T, waist inequalities, and some speculations

Roman Sauer
(Karlsruhe Institute of Technology)
Abstract

I will discuss a uniform waist inequality in codimension 2 for the family of finite covers of a Riemannian manifold whose fundamental group has Kazhdan‘s property T. I will describe a general strategy to prove waist inequalities based on a higher property T for Banach spaces. The general strategy can be implemented in codimension 2 but is conjectural in higher codimension. We speculate about the situation for lattices in semisimple Lie groups. Based on joint work with Uri Bader