Geometric Group Theory Seminar

In Spring 2026, we are starting to organize the Purdue Geometric Group Theory (GGT) Seminar. It will be held on Mondays 1:30-2:30pm Eastern Time in SCHM 123 if we meet in person. Some talks will be on zoom and the link will be included in the email announcement.

We are maintaining an email list for this seminar, through which we send notifications regarding talks and seminar lunches/dinners. You can subscribe to the list (choose "regular" role) by the link here: https://lists.purdue.edu/scripts/wa.exe?SUBED1=GGT-SEMINAR&A=1

Lvzhou Chen, Yash Lodha, Ben McReynolds are organizing this seminar in Spring 2026.

Spring 2026

January 12, 2026

Arya Vadnere (University of Buffalo)

Title: Gromov Boundary of the Grand Arc Graph

Abstract: In 1999, E. Klarreich found a very intriguing correspondence between the Gromov boundary of the curve graph for closed surfaces (a very GGT object) with the space of ending laminations on the surface (a very geometric object). Since then, Hamendstädt, Schleimer and Pho-On have thought about various proofs for this result, and generalizations to the arc graph / the arc-and-curve graph for finite-type surfaces. The grand arc graph is a type of arc graph associated with certain infinite-type surfaces, which is also an infinite-diameter hyperbolic graph. In this talk, we shall talk about a couple of ways to define “laminations that should correspond to points on the Gromov boundary of the grand arc graph”. This work is joint with Carolyn Abbott and Assaf Bar-Natan.

January 14, 2026 (special time, Wed. 1:30-2:30pm at SCHM 123, joint with Geometry and Geometric Analysis Seminar)

Aleksander Skenderi (UW Madison)

Title: Asymptotically large free semigroups in Zariski dense discrete subgroups of Lie groups

Abstract: An important quantity in the study of discrete groups of isometries of Riemannian manifolds, Gromov hyperbolic spaces, and other interesting geometric objects is the critical exponent. For a discrete subgroup of isometries of the quaternionic hyperbolic space or octonionic projective plane, Kevin Corlette established in 1990 that the critical exponent detects whether a discrete subgroup is a lattice or has infinite covolume. Precisely, either the critical exponent equals the volume entropy, in which case the discrete subgroup is a lattice, or the critical exponent is less than the volume entropy by some definite amount, in which case the discrete subgroup has infinite covolume. In 2003, Leuzinger extended this gap theorem for the critical exponent to any discrete subgroup of a Lie group having Kazhdan’s property (T) (for instance, a discrete subgroup of SL(n,R), where n is at least 3).

In this talk, I will present a result which shows that no such gap phenomenon holds for discrete semigroups of Lie groups. More precisely, for any Zariski dense discrete subgroup of a Lie group, there exist free, finitely generated, Zariski dense subsemigroups whose critical exponents are arbitrarily close to that of the ambient discrete subgroup.

As an application, we show that the critical exponent is lower semicontinuous in the Chabauty topology whenever the Chabauty limit of a sequence of Zariski dense discrete subgroups is itself a Zariski dense discrete subgroup.

January 19, 2026 (No talk due to MLK day)

January 29, 2026 (special time, Thu. 1:30-2:30pm at BRNG 1206, joint with Automorphic Forms and Representation Theory Seminar)

Yash Lodha (Purdue)

Title: A solution to the Wiegold problem on perfect groups

Abstract: One of the most fundamental notions in group theory is the notion of the normal rank of a group. This is the smallest size of a set of elements, which if included in the set of relations, render the group trivial. The smallest number of factors in the direct sum decomposition of the group abelianization provides a natural lower bound for the normal rank. The 1976 Wiegold problem on perfect groups asks whether there exist finitely generated perfect groups whose normal rank is greater than one. We demonstrate that free products of finitely generated perfect left orderable groups have normal rank greater than one. This solves the Wiegold problem in the affirmative, since a plethora of such examples exist. This is joint work with Lvzhou Chen.

February 2, 2026

Xiaolei Wu (Fudan University)

Title: Embedding groups into acyclic groups

Abstract: We first discuss various embedding results for groups in the literature. Then we talk about how one could embed a group of type F_n into an acyclic group of type F_n. The embedding we have uses the labelled Thompson group which goes back to Thompson's Splinter group in the 1980s. We explain how one can show that the labeled Thompson groups are always acyclic. This also allows us to build the first acyclic groups of type F_n but not F_{n+1} for any n >=2. If time permited, I will also discuss related results in the simple setting using the twisted Brin--Thompson groups. This is based on a joint work in progress with Martin Palmer.

February 5, 2026 (special time, Thu. 1:30-2:30pm at BRNG 1206, joint with Automorphic Forms and Representation Theory Seminar)

Lvzhou Chen (Purdue)

Title: The Wiegold problem and the normal rank of free products

Abstract: This is a continuation of the talk by Yash Lodha last week. I will explain our main results in more detail, and in connection to Dehn surgeries of 3-manifolds. Our main results involve two main ingredients: one topological and one dynamical. I will show you the topological side and also explain the dynamical side in more detail (if Yash didn't have time to cover it).

February 9, 2026 (on zoom)

Yongsheng Jia (University of Manchester)

February 16, 2026

Bin Sun (MSU)

March 2, 2026

Hongbin Sun (Rutgers)

March 9, 2026

Thomas Koberda (Virginia)