Max Dehn Seminar
on Geometry, Topology, Dynamics, and Groups
Fall 2024 and Spring 2025
LCB 222
Wednesdays at 3:15 pm
Date  Speaker  Title click for abstract (if available) 

August 28 
Noy Soffer Aranov
University of Utah 
One way to study the distribution of quadratic number fields is through the evolution of continued fraction expansions. In the function field setting, it was shown by de Mathan and Teullie that given a quadratic irrational $\Theta$, the degrees of the periodic part of the continued fraction of $t^n\Theta$ are unbounded. Paulin and Shapira improved this by proving that quadratic irrationals exhibit partial escape of mass. Moreover, they conjectured that they must exhibit full escape of mass. We show that the Thue Morse sequence is a counterexample to their conjecture. In this talk we shall discuss the technique of proof as well as the connection between escape of mass in continued fractions, Hecke trees, and number walls. This is part of ongoing work joint with Erez Nesharim.

September 18 
Nathan Geer
Utah State University 
In this talk, I will explore two methods for constructing
Topological Quantum Field Theories (TQFTs). The first method is known
as the universal construction, which traces its origins to the work of
Blanchet, Habegger, Masbaum, and Vogel in 1995. The second method
involves a generator and relation presentation of the category of
cobordisms, as developed by Juhasz in 2018. I will introduce a concept
called a chromatic morphism and demonstrate how it generates numerous
examples for both construction methods. These examples yield
interesting representations of mapping class groups and open new
avenues for studying 4manifolds. This talk is designed to be
introductory and suitable for graduate students.

September 25 
Paige Hillen
UC Santa Barbara 
Given an irreducible element of Out(Fn), there is a graph
and an irreducible "train track map" on this graph, which induces (a
representative of) the outer automorphism on the fundamental group of
the graph. The stretch factor of an outer automorphism measures the
rate of growth of words in Fn under applications of the automorphism,
and appears as the leading eigenvalue of the transition matrix of a
train track representative. I'll present work showing a lower bound
for the stretch factor in terms of the edges in the graph and the
number of folds in the fold decomposition of the train track map.
Moreover, in certain cases, a notion of the latent symmetry of the
graph gives a lower bound on the number of folds required for any
train track map on a given graph. We use this to classify all single
fold train track maps.

October 9  No seminar, Fall Break  
October 16 
Scott Schmieding
Penn State 
TBD

October 30 
Thomas O'Hare
The Ohio State University 
TBD

November 6 
Marlies Gerber
Indiana University 
TBD

November 13 
Patrick DeBonis
Purdue University 
TBD

November 27  No seminar, Thanksgiving 
Archive of past talks
You may also be interested in the RTG Seminar
Max Dehn Seminar is organized by Mladen Bestvina, Ken Bromberg, Jon Chaika, Elizabeth Field,
Priyam Patel, Rachel Skipper, Domingo Toledo, Kurt Vinhage and Kevin Wortman.
This web page is maintained by Rachel Skipper.