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 2026

Wednesday, September 2

Insung Park (Stony Brook University) 

Title: Forgetting punctures in measured foliations and dynamics on the universal curve over Teichmüller space

Abstract: Puncture-forgetting maps have been studied for various objects, including Teichmüller spaces, mapping class groups, and closed curves. In this talk, we will introduce an idea of forgetting punctures in measured foliations, giving rise to upper semicontinuous maps between spaces of measured foliations. We will then discuss applications to Teichmüller dynamics on the universal curve over Teichmüller space and the dynamics of post-critically finite rational maps. This is joint work with Jeremy Kahn.

Host: Dan Margalit

Wednesday, September 9

Ekaterina Rybak (Vanderbilt)

Title: Boundary dynamics and algebraic properties in weakly hyperbolic groups

Abstract: Groups admitting a general type action on a hyperbolic space are called weakly hyperbolic. This broad class includes all non-elementary hyperbolic and relatively hyperbolic groups, all acylindrically hyperbolic groups, and many others. I will describe a division of weakly hyperbolic groups into two subclasses, determined by a dynamical property of their boundary actions, and discuss the contrasting algebraic properties of the groups in these subclasses.

Wednesday, September 16

Noah Caplinger (University of Chicago)

Title: Groups acting on horocyclic products

Abstract:  Horocyclic products are a well-studied class of metric spaces that provide models for various solvable groups. Key examples include the universal cover of mapping tori of expanding maps or Anosov maps on nilmanifolds. Horocyclic products have played a key role in many quasi-isometric rigidity results in the past few decades. In this talk, I will give lots of examples of groups acting on horocyclic products and explain a theorem of mine and Daniel Levitin's, which says that essentially all examples of finitely presented groups acting on horocyclic products come from expanding or Anosov maps.

Host: Denis Osin

Wednesday, September 23

Darren Creutz (Vanderbilt)

Title: Structure of the (stabilized, inert) automorphism group of the shift 

Abstract: The automorphism group of the shift on X = A^Z for a finite set A is the set of all homeomorphisms on X which commute with the shift map and the stabilized automoprhism group are those which commute with some power of the shift. 

It is known that every finite group and every free (abelian and nonabelian) group embeds faithfully into the stabilized automorphism group, as do Thompson's group and related groups (for a subshift), and in fact it is conjectured that every countable group may embed faithfully (though it is also conjectured that (T) groups do not embed faithfully). There is no known example of a countable group which does not embed in the stabilized automorphism group. I will discuss these and related groups, including various open problems and conjectures, and present joint work with Scott Schmeiding on some structural results which shed light on these groups. In particular, I will discuss the analogues to lattices in semisimple groups and why one might expect normal subgroup theorem-like results to hold.

Wednesday, September 30

Summer Sun (Vanderbilt)

Title: A minimal generating set for the level-four braid group

Abstract: The level-four braid group is a congruence subgroup of the braid group arising from the Burau representation. By a theorem of Brendle and Margalit, it is also the kernel of the mod 2 abelianization of the pure braid group. Kordek and Margalit computed its first rational homology and asked whether its dimension could be realized as the size of a generating set for the group. In this talk, we will introduce the level-four braid group, discuss this earlier work, and describe an explicit generating set attaining this lower bound. We will explain the main ideas of the construction and discuss consequences for the integral first homology.

Wednesday, October 7

TBA

Wednesday, October 14

TBA

Wednesday, October 28

Nick Salter (Notre Dame)

Title: The isoresidual fibration 

Abstract: It is a wonderful fact that a meromorphic differential form on a Riemann surface admits a geometric incarnation as a translation surface (a special kind of flat metric on a surface with conical singularities) - this opens up a rich point of interaction between algebraic geometry, dynamics, and topology. The set of all such differentials is organized into spaces called strata, which are closely related to things like configuration spaces and moduli spaces, and from there to braid and mapping class groups. In the meromorphic setting, one can ask how residues fit into this picture. The main result of my talk will be recent work with D. Chen and G. Tahar showing that the residue map realizes a stratum of meromorphic differentials on the Riemann sphere as a "stratified fibration" over the space of residues; time permitting, I will also discuss how this relates to "stratified braid groups" as studied a few years ago by myself and P. Huxford. Ultimately I hope to show you how this theory gives rise to a broad class of groups closely related to, but conjecturally distinct from, (subgroups of) braid groups. 

Host: Spencer Dowdall

Wednesday, November 4

Abdul Zalloum (Queen's University)

Title: TBA

Abstract: TBA

Host: Dan Margalit 

Wednesday, November 11

TBA

Wednesday, November 18

TBA

Wednesday, December 2

TBA

Spring 2027

Wednesday, January 20

TBA

Wednesday, January 27

TBA

Wednesday, February 3

TBA

Wednesday, February  10

Waltraud Lederle (Bielefeld University)

Title: TBA

Abstract:  TBA

Host: Denis Osin

Wednesday, February 17

TBA

Wednesday, February 24

TBA

Wednesday, March 3

TBA

Wednesday, March 10

Jing Tao (University of Oklahoma)

Title: TBA

Abstract: TBA

Host: Spencer Dowdall

Wednesday, March 24

TBA

Wednesday, March 31

TBA

Wednesday, April 7

TBA

Wednesday, April 14

TBA

Wednesday, April 21

TBA