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.

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

February 2, 2026

Xiaolei Wu (Fudan University)

February 9, 2026 (on zoom)

Yongsheng Jia (University of Manchester)

February 16, 2026

Bin Sun (MSU)

March 2, 2026

Hongbin Sun (Rutgers)

March 16, 2026 (No talk due to Spring break)