Geometry and Topology

Please contact Saul Schleimer, Davide Spriano, or Robert Kropholler if you would like to speak or to suggest a speaker. A picture of a cat that is made out of cubes

We will also attempt to maintain an up-to-date listing at researchseminars.org.

The seminar will be hybrid, and will be run weekly. The talk is in B3.02 Zeeman Buildingon Thursdays, times below. We will open and close the Zoom session on the hour. All of the talks will be streamed at this link.

Click on a title to view the abstract!

Upcoming Seminars

27 November 2025 at 13:30 in B3.02
Speaker: Jing Tao (University of Oklahoma)
Title: TBA

Abstract: TBA

04 December 2025 at 13:30 in B3.02
Speaker: TBA (TBA)
Title: TBA

Abstract: TBA

11 December 2025 at 13:30 in B3.02
Speaker: Philipp Bader (University of Glasgow)
Title: TBA

Abstract: TBA

Past Seminars

20 November 2025 at 13:30 in B3.02
Speaker: Sebastian Hensel (LMU Munich)
Title: Dynamics of torus homeomorphisms and the fine curve graph

Abstract: The fine curve graph is a Gromov hyperbolic graph on which the homeomorphism group of a surface acts. In this talk we will discuss joint work with Frédéric Le Roux which relates the surface dynamics of a torus homeomorphism to its action on the fine curve graph. We show in particular that the shape of a “big" rotation set is determined by the fixed points on the Gromov boundary of the graph. A key ingredient is a metric version of the WPD property for the homeomorphism group of the torus.

13 November 2025 at 13:30 in B3.02
Speaker: Will Cohen (University of Cambridge)
Title: Improving acylindrical actions on trees

Abstract: Loosely speaking, an action of a group on a tree is acylindrical if long enough paths must have small stabilisers. Groups admitting such actions form a natural subclass of acylindrically hyperbolic groups, and an interesting feature of acylindrical actions on trees is that many properties of groups are inherited from their vertex stabilisers. In order to make use of this, it is important to have some degree of control over these stabilisers. For example, can we ask for these stabilisers to be finitely generated? Even stronger, if our group is hyperbolic, can we ask for the stabilisers to be quasiconvex?

In this talk, I will introduce acylindrical actions and some stronger and related concepts, and discuss a method known as the Dunwoody—Sageev resolution that we can use to move between these concepts and provide positive answers to the above questions in some cases.

06 November 2025 at 13:45 in b3.02
Speaker: Islam Foniqi (University of East Anglia)
Title: Submonoid Membership Problems in One-Relator Groups and Monoids, Surface Groups, and Beyond.

Abstract: The word problem for one-relator monoids remains one of the long-standing open questions in combinatorial algebra. One way to approach it is by studying related decision problems, in particular the submonoid membership problem, in both monoids and groups. In this talk, I will discuss how these problems are connected, drawing on classical work by Adian and Guba. I will also highlight the role of embeddings of right-angled Artin groups and trace monoids, which offer useful insights into the structure of these questions. Finally, I will present recent joint results with Robert D. Gray on the submonoid membership problem in surface groups, and in the broader hyperbolic setting.

23 October 2025 at 13:30 in B3.02
Speaker: Mahan Mj (Tata Institute of Fundamental Research)
Title: Hyperbolic and elliptic commensurations

Abstract: A group G is said to commensurate a subgroup H, if for all g in G, H^g \cap H is of finite index in H and H^g, where H^g denotes the conjugate of H by g. The commensuration action of G on H can be studied dynamically. This gives rise to two extreme behaviors: hyperbolic and elliptic. We will discuss what these mean and survey a range of theorems and conjectures in this context, starting with work of Mostow and Margulis, and coming to the present day.

16 October 2025 at 13:30 in B3.02
Speaker: Davide Spriano (University of Warwick)
Title: Curtains, walls and stable cylinders.

Abstract: In this talk we will discuss a generalization of Sageev’s wallspace construction that allows to study the geometry of certain spaces by combinatorial properties of certain walls. Specifically, we’ll look at the interactions with hyperbolicity and focus on two applications. In CAT(0) spaces, these techniques allow to construct a “universal hyperbolic quotient”, called the curtain model, that is analogous to the curve graph of a surface. When focusing on a space that is already hyperbolic, the construction can be used to improve its fine properties, and in particular we address a conjecture of Rips and Sela and show that residually finite hyperbolic groups admit globally stable cylinders. This is joint work with Petyt and Zalloum.