Organizers: Spencer Dowdall, Dan Margalit, Denis Osin

Time: Wednesdays, 4:10–5:00pm  

Location: SC 1432

Mailing List: If you would like to be added to the seminar mailing list and receive regular announcements, please contact one of the organizers.

Fall 2025 - Spring 2026

Wednesday, September 10

Dan Margalit (Vanderbilt)

Title:  Algorithms for pseudo-Anosov maps

Abstract: In joint work with Strenner, Taylor, and Yurttas, we give an algorithm whose input is a product of Dehn twists and whose output is the Nielsen-Thurston type of the associated mapping class, along with the associated data: period, reducing curves, stretch factor, and foliations.  Our main theorem explains why Mark Bell's program Flipper works. We aim to make the talk accessible to students learning about mapping class groups.

Wednesday, September 17

Denis Osin (Vanderbilt)

Title: Simple p-adic Lie groups with abelian Lie algebras

Abstract: For each prime p and each positive integer d, we construct the first examples of second countable, topologically simple, p-adic Lie groups of dimension d with abelian Lie algebras. This answers a question asked by P.-E. Caprace and N. Monod. In my talk, I will survey the necessary background material and explain why this question is of fundamental importance in the theory of p-adic Lie groups. Perhaps surprisingly, the proof of the main result makes use of small cancellation techniques in groups acting on hyperbolic spaces. Geometric ideas come into play through a general construction that associates a non-discrete, totally disconnected topological group with any discrete group satisfying a certain algebraic condition. The talk is based on joint work with P.-E. Caprace and A. Minasyan.

Wednesday, September 24

Shuxian Song (Vanderbilt)

Title: Generating the Mapping Class Group

Abstract: Generating sets of mapping class groups have been a central theme in the study of surfaces and low dimensional topology. In this survey talk, I will begin with Dehn twist generators. We gave a short, self-contained proof that the Humphries generators indeed form a generating set for mapping class groups. Unlike other proofs, our argument did not introduce extraneous generators. I will then turn to generating sets consisting of torsion elements and pseudo-Anosov maps, surveying results on small generating sets by elements of a certain order or by pseudo-Anosov maps. 

Wednesday, October 1

Nic Brody (UC Santa Cruz) 

Title: Presentations for Linear Groups

Abstract: Suppose S is a finite set of invertible matrices over the field of algebraic numbers. Immediately, this offers a plethora of perspectives we can use to shed light on the group these matrices generate, and there is a rich interplay between these topics. In this talk we will survey three known methods for constructing subgroups of linear groups, and propose that there may not be any other possibilities! Furthermore, we will discuss the circumstances in which one can efficiently compute a presentation for a given finitely generated matrix group. We propose that there is always an algorithm for computing a presentation for a finitely generated subgroup of PGL_2 over the algebraic closure of Q. To study this, we devote special attention to the case in which the group is discrete in PSL_2(C); that is, the world of Kleinian groups and 3-manifolds.  

Host: Talia Fernos

Wednesday, October 15

Yash Lodha (Purdue University) 

Title: TBA

Abstract: TBA

Host: Denis Osin

Wednesday, October 22

Thomas Hill (University of Utah)

Title: TBA

Abstract: TBA

Host: Spencer Dowdall

Wednesday, October 29

Talia Fernos (Vanderbilt)

Title: A plethora of examples, AU-acylindricity in higher rank

Abstract: This talk will be an overview of the class of groups (and associated subdirect products) that admit acylindrical actions of Ambiguous Uniformity on finite products of delta-hyperbolic spaces. The primary focus will be the semi-simple case, i.e. when the factor actions are of general type. While based on joint work with Balasubramanya, this talk is a survey.

Wednesday, November 5

Daniel Groves (University of Illinois, Chicago)

Title: TBA

Abstract: TBA

Host: Talia Fernos

Wednesday, November 12

Kevin Pilgrim (Indiana University)

Title: TBA

Abstract: TBA

Host: Dan Margalit

Wednesday, November 19

Tina Torkaman (University of Chicago)

Title: TBA

Abstract: TBA

Host: Spencer Dowdall

Wednesday, December 3

TBA

Wednesday, January 14

TBA

Wednesday, January 21

TBA

Wednesday, January 28

TBA

Wednesday, February 4

TBA

Wednesday, February 11

TBA

Wednesday, February 18

Anush Tserunyan (McGill University)

Title: TBA

Abstract: TBA

Host: Denis Osin

Wednesday, February 25

TBA

Wednesday, March 4

TBA

Wednesday, March 18

TBA

Wednesday, March 25

TBA

Wednesday, April 1

TBA

Wednesday, April 8

TBA

Wednesday, April 15

TBA