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: Two new constructions of finitely presented infinite simple groups

Abstract: I will describe two new constructions of finitely presented infinite simple groups. First, I will present a construction of finitely presented (and type F∞) simple groups that act by orientation preserving homeomorphisms on the real line. These are the first such examples. Next, I will present a construction of a family of finitely presented infinite uniformly simple groups, where the Ulam width can get arbitrarily large. Among the class of finitely generated (but not finitely presentable) groups, the existence of such examples was demonstrated in the work of Muranov from 2007. Our construction provides the first such family of examples in the class of finitely presented infinite groups. This is joint work with James Hyde. 

Host: Denis Osin

Wednesday, October 22

Thomas Hill (University of Utah)

Title: Mapping class groups of infinite graphs 

Abstract: The group of topological symmetries of a surface, known as the mapping class group, provides a powerful lens for studying the geometry and topology of surfaces. The outer automorphism groups of a free group, Out(Fn​), can be thought of as a graph-theoretic analog of the mapping class group.  Although results do not translate directly between the surface and graph settings, their structural parallels inspire questions and techniques between these areas. Over the past decade, there has been growing interest in studying big mapping class groups, namely those of infinite type surfaces.  In this talk, I will discuss recent progress on the analog of Out(Fn​) for infinite graphs, including an Ivanov-type rigidity theorem and results about the algebraic properties of their asymptotically rigid subgroups.

Host: Spencer Dowdall

Wednesday, October 29

Annie Holden (Notre Dame)

Title: Cohomology of Handlebody Torelli Groups

Abstract: We begin by introducing the Torelli subgroup of the mapping class group of a surface and outlining known results and its low-dimensional cohomology. We then present recent work extending these results to two Torelli subgroups of the mapping class group of a handlebody.

Host: Dan Margalit

Wednesday, November 5

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 12

Spencer Dowdall (Vanderbilt)

Title: Complexity length and lattice point counting in Teichmüller space

Abstract: This talk expands on the mini-colloquium I gave on September 25. I will discuss the key geometric features of Teichmüller space that are relevant for counting problems. These include thin regions and their inherent product structure, curve complex subsurface projections, and Rafi's distance formula. I will then introduce a new notion of "complexity length" in Teichmüller space that carefully accounts for how geodesics move through product regions and lends itself to counting problems. Using this tool, we are able to count the number of mapping class group lattice points for various types of types of elements. Joint work with Howard Masur.

Wednesday, November 19

Tina Torkaman (University of Chicago)

Title: TBA

Abstract: TBA

Host: Spencer Dowdall

Wednesday, December 3

Darren Creutz (Vanderbilt)

Title: Harmonic Functions on Groups

Abstract: Implicit in the work of Mok (1995) and Kleiner (2010) is the statement that a finitely generated group is infinite if and only if there exists a nonconstant harmonic (with respect to the counting measure on a generating set) function on the group. I will present (sort of) recent work generalizing this to locally compact groups under a more general class of measures: such a group is noncompact if and only if it admits a nonconstant Lipschitz-bounded harmonic function (for any/every reasonable probability measure). The proof involves an improvement of Mok/Kleiner's energy argument.  I will also present how this improvement makes progress towards the Margulis-Zimmer conjecture on commensurated subgroups of lattices in higher-rank semisimple groups.

Wednesday, January 14

Sarah Maloni (University of Virginia)

Title: TBA

Abstract: TBA

Host: Spencer Dowdall

Wednesday, January 21

Lvzhou Chen (Purdue University)

Title: The Wiegold problem and the weight of free products

Abstract: The weight (or normal rank) of a group G is the smallest number of elements that normally generate G. This notion plays an important role in 3-manifold topology, but it is poorly understood. It is extremely difficult to give lower bounds apart from looking at the abelianization. The Wiegold problem asks if there is a finitely generated perfect group that has weight greater than one, namely the group cannot be normally generated by any single element. In a joint work with Yash Lodha, we show that free products of nontrivial left-orderable groups all have weight greater than one, which solves the Wiegold problem. I will explain the topological and dynamical ingredients in the proof of our theorem.

Host: Denis Osin

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