Dynamics Seminar 2022-2023

The Dynamics seminar meets in room B329 of Van Vleck Hall on Mondays from 2:30pm - 3:20pm. To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu. For more information, contact Paul Apisa, Marissa Loving, Caglar Uyanik, or Chenxi Wu. Contact Caglar Uyanik with your wisc email to get the zoom link for virtual talks.

Fall 2022

date	speaker	title	host(s)
September 12	Jing Tao (OU)	Genericity of pseudo-Anosov maps	Dymarz and Uyanik
September 19	Rebekah Palmer (Temple)(virtual)	Totally geodesic surfaces in knot complements	VIRTUAL
September 26	Beibei Liu (MIT)	The critical exponent: old and new	Dymarz
October 3	Grace Work (UW-Madison)	Discretely shrinking targets in moduli space	local
October 10	Jean Pierre Mutanguha (Princeton)	TBA	Uyanik
October 17	Anthony Sanchez (UCSD)	TBA	Uyanik
October 24	Alena Erchenko (U Chicago)	TBA	Uyanik and Work
October 31	Feng Zhu (UW Madison)	TBA	local
November 7	Ethan Farber (BC)	TBA	Loving
November 14	Lukas Geyer (Montana)	TBA	Burkart
November 21	Harry Hyungryul Baik (KAIST)	TBA	Wu
November 28	Marissa Loving (UW Madison)	TBA	local
December 5	MurphyKate Montee (Carleton)	TBA	Dymarz
December 12	Tina Torkaman (Harvard)	TBA	Uyanik

Fall Abstracts

Jing Tao

By Nielsen-Thurston classification, every homeomorphism of a surface is isotopic to one of three types: finite order, reducible, or pseudo-Anosov. While there are these three types, it is natural to wonder which type is more prevalent. In any reasonable way to sample matrices in SL(2,Z), irreducible matrices should be generic. One expects something similar for pseudo-Anosov maps. In joint work with Erlandsson and Souto, we define a notion of genericity and show that pseudo-Anosov maps are indeed generic. More precisely, we consider several "norms" on the mapping class group of the surface, and show that the proportion of pseudo-Anosov maps in a ball of radius r tends to 1 as r tends to infinity. The norms can be thought of as the natural analogues of matrix norms on SL(2,Z).

Rebekah Palmer

Studying totally geodesic surfaces has been essential in understanding the geometry and topology of hyperbolic 3-manifolds.  Recently, Bader--Fisher--Miller--Stover showed that containing infinitely many such surfaces compels a manifold to be arithmetic.  We are hence interested in counting totally geodesic surfaces in hyperbolic 3-manifolds in the finite (possibly zero) case.  In joint work with Khánh Lê, we expand an obstruction, due to Calegari, to the existence of these surfaces.  On the flipside, we prove the uniqueness of known totally geodesic surfaces by considering their behavior in the universal cover.  This talk will explore this progress for both the uniqueness and the absence.

Beibei Liu

The critical exponent is an important numerical invariant of discrete groups acting on negatively curved Hadamard manifolds, Gromov hyperbolic spaces, and higher-rank symmetric spaces. In this talk, I will focus on discrete groups acting on hyperbolic spaces (i.e., Kleinian groups), which is a family of important examples of these three types of spaces. In particular, I will review the classical result relating the critical exponent to the Hausdorff dimension using the Patterson-Sullivan theory and introduce new results about Kleinian groups with small or large critical exponents.

Grace Work

The shrinking target problem characterizes when there is a full measure set of points that hit a decreasing family of target sets under a given flow. This question is closely related to the Borel Cantilli lemma and also gives rise to logarithm laws. We will examine the discrete shrinking target problem in a general and then more specifically in the setting of Teichmuller flow on the moduli space of unit-area quadratic differentials.

Spring 2023

date	speaker	title	host(s)
January 30	Pierre-Louis Blayac (Michigan)	TBA	Zhu and Zimmer
March 27	Carolyn Abbott (Brandeis)	TBA	Dymarz and Uyanik
April 10	Jon Chaika (Utah)	TBA	Apisa and Uyanik
April 24	Priyam Patel (Utah)	TBA	Loving and Uyanik

Archive of past Dynamics seminars

2021-2022 Dynamics_Seminar_2021-2022

2020-2021 Dynamics_Seminar_2020-2021