McGill Geometric Group Theory Seminar

A figure showing the dual to a Cayley graph in a set of lecture notes by Max Dehn.

McGill GGT research group

The seminar takes place on Wednesday at 3 PM in 1104 Burnside Hall, unless otherwise noted below.

Seminar organizers: William Chong, Katherine Goldman, Christopher Karpinski, Carl Kristof-Tessier, Piotr Przytycki, Daniel Wise


Upcoming talks:

September 17, 2025: Fabricio Dos Santos (McGill University) Garside shadows and biautomatic structures in Coxeter groups

In 2022, Osajda and Przytycki showed that any Coxeter group $W$ is biautomatic. Key to their proof is the notion of voracious projection of an element $g \in W$, which is used iteratively to construct a biautomatic structure for $W$: the voracious language. In this talk, I will generalize these two notions by defining them for any Garside shadow $B$ in a Coxeter system $(W,S)$. This leads to the result that any finite Garside shadow in $(W,S)$ can be used to construct a biautomatic structure for $W$. In particular, for the Garside shadow $L$ of low elements, the biautomatic structure obtained corresponds to the original voracious language of Osajda and Przytycki. These results answer a question of Hohlweg and Parkinson.

September 24, 2025: Maxwell Plummer (Rice University) TBD

October 1, 2025: Dani Wise (Weizmann Institute of Science) TBD

October 8, 2025: Jérémy Perazzelli (Université de Montréal) TBD

October 15, 2025: READING WEEK (No seminar)

October 22, 2025: Dani Wise (Weizmann Institute of Science) TBD

October 29, 2025: TBD

November 5, 2025: TBD

November 12, 2025: TBD

November 19, 2025: TBD

November 26, 2025: Jingyin Huang (The Ohio State University ) TBD

December 3, 2025: Monday schedule (No seminar)

December 10, 2025: Jon McCammon (UC Santa Barbara) TBD


Past talks:

September 10, 2025: Abdul Zalloum (Queen's University) Globally stable cylinders and fine structures for hyperbolic groups.

A hyperbolic group $G$ is said to have globally stable cylinders if there exist integers $K, m$ and a collection of equivariant $(1,K)$-quasi-geodesics connecting every pair of points in $G$ such that the following holds. For any $x,y,z\in G$; the (aforementioned) quasi-geodesics connecting them form a tripod, up to removing at most $m$ balls of radius $K$ centered along such quasi-geodesics. In short, the property asks for the existence of a bicombing on $G$ satisfying some very strong properties making the group look as close to a tree as possible. In 1995, Rips and Sela asked if torsion-free hyperbolic groups have this property, and in 2022 Sageev and Lazarovich established it for cubulated hyperbolic groups (hyperbolic groups with a geometric action on a CAT(0) cube complex). I will discuss recent work with Petyt and Spriano showing that residually finite hyperbolic groups admit globally stable cylinders.

September 3, 2025: Koichi Oyakawa (McGill University) Hyperfiniteness of the boundary action of virtually special groups

A Borel equivalence relation on a Polish space is called hyperfinite if it can be approximated by equivalence relations with finite classes. This notion has long been studied in descriptive set theory to measure complexity of Borel equivalence relations. Recently, a lot of research has been done on hyperfiniteness of the orbit equivalence relation on the Gromov boundary induced by various group actions on hyperbolic spaces. In this talk, I will explain my attempt to explore this connection of Borel complexity and geometric group theory for another intensively studied geometric object, which is CAT(0) cube complexes. More precisely, we prove that for any countable group acting virtually specially on a CAT(0) cube complex, the orbit equivalence relation induced by its action on the Roller boundary is hyperfinite.

July 23, 2025: Rachael Boyd (University of Glasgow) Diffeomorphisms of reducible 3-manifolds

I will talk about joint work with Corey Bregman and Jan Steinebrunner, in which we study the moduli space $\text{BDiff}(M)$, for M a compact, connected, reducible 3-manifold. We prove that when $M$ is orientable and has non-empty boundary, $\text{BDiff}(M\text{ rel } ∂M)$ has the homotopy type of a finite CW-complex. This was conjectured by Kontsevich and previously proved in the case where $M$ is irreducible by Hatcher and McCullough. The theory we develop to prove this theorem has other applications, and I'll provide an overview of these.


Seminar schedule archive