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.
Tue, 17 Nov 2026
15:00
15:00
L6
Rigidity properties of mapping class groups and their random quotients
Giorgio Mangioni
(Heriot-Watt University, Edinburgh)
Abstract
A theorem of Ivanov states that the mapping class group G of a finite-type surface is also the automorphism group of the curve graph, which encodes the intersection patterns of simple closed curves on the surface. In other words, simplicial automorphisms of the curve graph are "rigid": they all come from homeomorphisms of the surface. This fact can then be used to prove other "rigidity" results, such as quasi-isometric rigidity (if a group is quasi-isometric to G, it is commensurable to G) and the fact that every automorphism of G is inner.
In this talk, we first introduce the various characters in our story, and review the literature on these results. Then we show that the same type of properties are enjoyed by "random" quotients of mapping class groups, defined by modding out the n-th steps of certain random walks. Some of this talk is based on joint work with Abbott, Berlyne, Ng, and Rasmussen.
Tue, 24 Nov 2026
15:00
15:00
L6
The ideal Poisson–Voronoi tessellation and some applications
Amanda Wilkens
(University of North Carolina)
Abstract
We motivate and define the ideal Poisson–Voronoi tessellation (IPVT), a new random object with intriguing geometric properties when considered on a semisimple symmetric space (the hyperbolic plane, for example). In joint work with Mikolaj Frączyk and Sam Mellick, we use the IPVT to prove a result on the relationship between the volume of a manifold and the number of generators of its fundamental group (for higher rank semisimple Lie groups, the minimum number of generators in a lattice is sublinear in the covolume). In this talk we give some ideas of the proof. Time permitting, we will discuss related percolation results, joint with Matteo D'Achille, Jan Grebik, Ali Khezeli, and Konstantin Recke.
Tue, 01 Dec 2026
15:00
15:00
L6
The conjugacy problem in twisted right-angled Artin groups
Gemma Crowe
(Manchester)
Abstract
There exists a vast literature around the idea of constructing groups (and monoids) via some correspondence with finite simple graphs. One well-known example is right-angled Artin groups (RAAGs), where edges in our graph correspond to commuting generators in our group.
In this talk, we will discuss an adaptation of this group, known as twisted RAAGs (T-RAAGs), where we introduce the option of ‘Klein-bottle’ relations, to correspond to directed edges of our graph. We will then survey some results about these groups (including many open questions!) and show T-RAAGs have a decidable conjugacy problem. This is based on joint work with Islam Foniqi.