Dynamics Seminar 2022-2023: Difference between revisions

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The [[Dynamics]] seminar meets in room '''B309 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.  
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. 




Line 14: Line 14:
|September 12
|September 12
|[https://math.ou.edu/~jing/ Jing Tao] (OU)
|[https://math.ou.edu/~jing/ Jing Tao] (OU)
|[[# Jing Tao (OU) | ''TBA'']]
|[[#Jing Tao|Genericity of pseudo-Anosov maps]]
|Dymarz and Uyanik
|Dymarz and Uyanik
|-
|-
|September 19
|September 19
|[https://math.temple.edu/~tug67058/ Rebekah Palmer] (Temple)[VIRTUAL]
|[https://math.temple.edu/~tug67058/ Rebekah Palmer] (Temple)(virtual)
|[[# Rebekah Palmer (Temple)| ''TBA'']]
|[[#Rebekah Palmer|Totally geodesic surfaces in knot complements]]
|Loving
|VIRTUAL
|-
|-
|September 26
|September 26
|TBA
|[https://sites.google.com/view/beibei-liu/ Beibei Liu] (MIT)
|[[# TBA | ''TBA'']]
|[[#Beibei Liu|The critical exponent: old and new]]
|
| Dymarz
 
|-
|-
|October 3
|October 3
|[https://sites.google.com/view/beibei-liu/ Beibei Liu] (MIT)
|Grace Work (UW-Madison)
|[[# Beibei Liu (Georgia Tech) | ''TBA'']]
|[[#Grace Work |Discretely shrinking targets in moduli space]]
| Dymarz
|local
|-
|-
|October 10
|October 10
|[https://mutanguha.com/ Jean Pierre Mutanguha] (Princeton)
|[https://mutanguha.com/ Jean Pierre Mutanguha] (Princeton)
|[[# Jean Pierre Mutanguha (Princeton) | ''TBA'']]
|[[#Jean Pierre Mutanguha| Canonical forms for free group automorphisms]]
|Uyanik
|Uyanik
|-
|-
|October 17
|October 17
|[https://sites.google.com/ucsd.edu/ans032/ Anthony Sanchez] (UCSD)
|[https://sites.google.com/ucsd.edu/ans032/ Anthony Sanchez] (UCSD)
|[[# Anthony Sanchez (UCSD)| ''TBA'']]
|[[#Anthony Sanchez | Kontsevich-Zorich monodromy groups of translation covers of some platonic solids]]
|Uyanik
|Uyanik
|-
|-
|October 24
|October 24
|[https://you.stonybrook.edu/aerchenko/ Alena Erchenko] (Stony Brook)
|[https://you.stonybrook.edu/aerchenko/ Alena Erchenko] (U Chicago)
|[[# Alena Erchenko| ''TBA'']]
|postponed
|Uyanik and Work
|Uyanik and Work
|-
|-
|October 31
|October 31
|TBA
|[https://sites.google.com/view/zhufeng-math/home Feng Zhu] (UW Madison)
|[[# TBA| ''TBA'']]
|[[#Feng Zhu| ''Relatively Anosov representations: a dynamical notion of geometric finiteness'']]
|
|local
|-
|-
|November 7
|November 7
|[https://sites.google.com/bc.edu/ethan-farber/about-me?authuser=0/ Ethan Farber] (BC)
|[https://sites.google.com/bc.edu/ethan-farber/about-me?authuser=0/ Ethan Farber] (BC)
|[[# Ethan Farber (BC)| ''TBA'']]
|[[#Ethan Farber| ''Pseudo-Anosovs of interval type'']]
|Loving
|Loving
|-
|-
|November 14
|November 14
|TBA
|[https://www.math.montana.edu/geyer/ Lukas Geyer] (Montana)
|[[# TBA| ''TBA'']]
|[[#Lukas Geyer| ''Classification of critically fixed anti-Thurston maps'']]
|
|Burkart
|-
|-
|November 21
|November 21
|Harry Baik
|[http://www.hbaik.org/ Harry Hyungryul Baik] (KAIST)
|[[# TBA| ''TBA'']]
|[[#Harry Baik| ''Revisit the theory of laminar groups'']]
|Wu
|Wu
|-
|-
|November 28
|November 28
|TBA
|[https://mmontee.people.sites.carleton.edu MurphyKate Montee] (Carleton)
|[[# TBA| ''TBA'']]
|[[#MurphyKate Montee | ''Cubulation and Property (T) in random groups'']]
|
|Dymarz
|-
|-
|December 5
|December 5
|TBA
|[https://sites.google.com/view/lovingmath/home Marissa Loving] (UW Madison)
|[[# TBA| ''TBA'']]
|[[#Marissa Loving|Unmarked simple length spectral rigidity for covers]]
|
|local
|-
|-
|December 12
|December 12
|TBA
|[https://scholar.harvard.edu/tinatorkaman/home Tina Torkaman] (Harvard)
|[[# TBA| ''TBA'']]
|[[#Tina Torkaman| '' Intersection number and intersection points of closed geodesics on hyperbolic surfaces'']]
|
|Uyanik
|}
|}


Line 87: Line 86:


===Jing Tao===
===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===
===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===
===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.


===Jean Pierre Mutanguha===
===Jean Pierre Mutanguha===
The Nielsen–Thurston theory of surface homeomorphisms can be thought of as a surface analogue to the Jordan Canonical Form. I will discuss my progress in developing a similar canonical form for free group automorphisms. (Un)Fortunately, free group automorphisms can have arbitrarily complicated behaviour. This is a significant barrier to translating arguments that worked for surfaces into the free group setting; nevertheless, the overall ideas/strategies do translate!


===Anthony Sanchez===
===Anthony Sanchez===
Platonic solids have been studied for thousands of years. By unfolding a platonic solid we can associate to it a translation surface. Interesting information about the underlying platonic solid can be discovered in the cover where more (dynamical and geometric) structure is present. The translation covers we consider have a large group of symmetries that leave the global composition of the surface unchanged. However, the local structure of paths on the surface is often sensitive to these symmetries. The Kontsevich-Zorich mondromy group keeps track of this sensitivity.


===Alena Erchenko===
In joint work with R. Gutiérrez-Romo and D. Lee, we study the monodromy groups of translation covers of some platonic solids and show that the Zariski closure is a power of SL(2,R). We prove our results by finding generators for the monodromy groups, using a theorem of Matheus–Yoccoz–Zmiaikou that provides constraints on the Zariski closure of the groups (to obtain an "upper bound"), and analyzing the dimension of the Lie algebra of the Zariski closure of the group (to obtain a "lower bound").
 
===Feng Zhu===
 
Putting hyperbolic metrics on a finite-type surface S gives us linear representations of the fundamental group of S into PSL(2,R) with many nice geometric and dynamical properties: for instance they are discrete and faithful, and in fact stably quasi-isometrically embedded.
 
In this talk, we will introduce (relatively) Anosov representations, which generalise this picture to higher-rank Lie groups such as PSL(d,R) for d>2, giving us a class of (relatively) hyperbolic subgroups there with similarly good geometric and dynamical properties.
 
This is mostly joint work with Andrew Zimmer.


===Ethan Farber===
===Ethan Farber===


== Spring 2023 ==
A pseudo-Anosov (pA) is a homeomorphism of a compact connected surface S that, away from a finite set of points, acts locally as a linear map with one expanding and one contracting eigendirection. Ubiquitous yet mysterious, pAs have fascinated low-dimensional topologists and dynamicists for the past forty years. We show that any pA on the sphere whose associated quadratic differential has at most one zero, admits an invariant train track whose expanding subgraph is an interval. Concretely, such a pA has the dynamics of an interval map. As an application, we recover a uniform lower bound on the entropy of these pAs originally due to Boissy-Lanneau. Time permitting, we will also discuss potential applications to a question of Fried. This is joint work with Karl Winsor.
 
===Lukas Geyer===
 
Recently there has been an increased interest in complex dynamics of orientation-reversing maps, in particular in the context of gravitational lensing and as an analogue of reflection groups in Sullivan's dictionary between Kleinian groups and dynamics of (anti-)rational maps. Much of the theory parallels the orientation-preserving case, but there are some intriguing differences. In order to deal with the post-critically finite case, we study anti-Thurston maps (orientation-reversing versions of Thurston maps), and prove an orientation-reversing analogue of Thurston's topological classification of post-critically finite rational maps, as well as the canonical decomposition of obstructed maps, following Pilgrim and Selinger. Using these tools, we obtain a combinatorial classification of critically fixed anti-Thurston maps, extending a recently obtained classification of critically fixed anti-rational maps. If time allows, I will explain applications of this classification to gravitational lensing. Most of this is based on joint work with Mikhail Hlushchanka.
 
===Harry Baik ===
 
I will give a brief introduction to laminar groups which are groups of orientation-preserving homeomorphisms of the circle admitting invariant laminations. The term was coined by Calegari and the study of laminar groups was motivated by work of Thurston and Calegari-Dunfield. We present old and new results on laminar groups which tell us when a given laminar group is either fuchsian or Kleinian. This is based on joint work with KyeongRo Kim and Hongtaek Jung.
 
===MurphyKate Montee===
 
Random groups are one way to study "typical" behavior of groups. In the Gromov density model, we often find that properties have a threshold density above which the property is satisfied with probability 1, and below which it is satisfied with probability 0. Two properties of random groups that have been well studied are cubulation (and relaxations of this property) and Property (T). In this setting these are mutually exclusive properties, but threshold densities are not known for either property. In this talk I'll present the current state of the art regarding these properties in random groups, and discuss some ways to further these results.
 
===Marissa Loving===
A fundamental question in geometry is the extent to which a manifold M is determined by its length spectrum, i.e. the collection of lengths of closed geodesics on M. This has been studied extensively for flat, hyperbolic, and negatively curved metrics. In this talk, we will focus on surfaces equipped with a choice of hyperbolic metric. We will explore the space between (1) work of Otal (resp. Fricke) which asserts that the marked length spectrum (resp. marked ''simple'' length spectrum) determines a hyperbolic surface, and (2) celebrated constructions of Vignéras and Sunada, which show that this rigidity fails when we forget the marking. In particular, we will consider the extent to which the unmarked simple length spectrum distinguishes between hyperbolic surfaces arising from Sunada’s construction. This represents joint work with Tarik Aougab, Max Lahn, and Nick Miller.
 
===Tina Torkaman===
 
In this talk, I will talk about the (geometric) intersection number between closed geodesics on finite volume hyperbolic surfaces. Specifically, I will discuss the optimum upper bound on the intersection number in terms of the product of hyperbolic lengths. I also talk about the equidistribution of the intersection points between closed geodesics.
 
 
==Spring 2023==


{| cellpadding="8"
{| cellpadding="8"
!align="left" | date
! align="left" |date
!align="left" | speaker
! align="left" |speaker
!align="left" | title
! align="left" |title
!align="left" | host(s)
! align="left" |host(s)
|-
|-
|January 30
|January 30
|TBA
|[http://websites.umich.edu/~blayac/ Pierre-Louis Blayac] (Michigan)
|[[TBA| ''TBA'']]
|[[#Pierre-Louis Blayac| ''TBA'']]
|Zhu and Zimmer
|-
|February 6
|[http://www-personal.umich.edu/~kbutt/index.html Karen Butt] (Michigan)
|[[#Karen Butt| ''TBA'']]
|Zimmer
|-
|February 13
|[https://sites.google.com/view/elizabeth-field Elizabeth Field] (Utah)
|[[#Elizabeth Field| ''TBA'']]
|Loving
|-
|February 20
|[https://math.berkeley.edu/~chicheuk/ Chi Cheuk Tsang] (Berkeley)
|[[#Chi Cheuk Tsang| ''TBA'']]
|Loving
|-
|February 27
|[https://www.caglaruyanik.com/home Caglar Uyanik] (UW Madison)
|[[#Caglar Uyanik| ''TBA'']]
|local
|-
|March 6
|[https://filippomazzoli.github.io Filippo Mazzoli] (UVA)
|[[#Filippo Mazzoli| TBA]]
|Zhu
|-
|March 13
|Spring Break, No Seminar
|
|
|
|-
|March 20
|[https://www.rosemorriswright.com/ Rose Morris-Wright ] (Middlebury)
|[[#Rose Morris-Wright| ''TBA'']]
|Dymarz
|-
|-
|March 27
|March 27
|[https://www.carolynrabbott.com/ Carolyn Abbott] (Brandeis)
|[https://www.carolynrabbott.com/ Carolyn Abbott] (Brandeis)
|[[# Carolyn Abbott (Brandeis) | ''TBA'']]
|[[#Carolyn Abbott| ''TBA'']]
|Dymarz and Uyanik
|Dymarz and Uyanik
|-
|-
|April 24
|April 3
|Priyam Patel (Utah)
|[https://sites.google.com/view/sfairchild/home Samantha Fairchild] (Osnabrück)
|[[# Priyam Patel (Utah) | TBA ]]
|TBA
|Loving and Uyanik
|Apisa
|-
|April 10
|[https://www.math.utah.edu/~chaika/ Jon Chaika] (Utah)
|[[#Jon Chaika| ''TBA'']]
|Uyanik
|-
|April 17
|[https://sites.google.com/view/mikolaj-fraczyk/home Mikolaj Fraczyk] (Chicago)
|[[#Mikolaj Fraczyk| ''TBA'']]
|Skenderi and Zimmer
|-
||April 24
|[https://sites.google.com/view/tarikaougab/home/ Tarik Aougab] (Haverford)
|[[#Tarik Aougab| ''TBA'']]
|Loving
|-
|May 1
|[https://www.dmartinezgranado.com Didac Martinez-Granado] (UC Davis)
|[[#Didac Martinez-Granado| ''TBA'']]
|Uyanik
|-
|}
|}


== Spring Abstracts ==
==Spring Abstracts==
 
===Pierre-Louis Blayac===
 
===Karen Butt===
 
===Elizabeth Field===
 
===Chi Cheuk Tsang===
 
===Caglar Uyanik===
 
===Filippo Mazzoli===
 
===Rose Morris-Wright===


===Carolyn Abbott===
===Carolyn Abbott===


===Priyam Patel===
===Samantha Fairchild===
 
===Jon Chaika===
 
===Mikolaj Fraczyk===
 
===Tarik Aougab===
 
===Didac Martinez-Granado===


== Archive of past Dynamics seminars ==
== Archive of past Dynamics seminars==


2021-2022 [[Dynamics_Seminar_2021-2022]]
2021-2022 [[Dynamics_Seminar_2021-2022]]


2020-2021 [[Dynamics_Seminar_2020-2021]]
2020-2021 [[Dynamics_Seminar_2020-2021]]

Revision as of 20:56, 2 December 2022

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) Canonical forms for free group automorphisms Uyanik
October 17 Anthony Sanchez (UCSD) Kontsevich-Zorich monodromy groups of translation covers of some platonic solids Uyanik
October 24 Alena Erchenko (U Chicago) postponed Uyanik and Work
October 31 Feng Zhu (UW Madison) Relatively Anosov representations: a dynamical notion of geometric finiteness local
November 7 Ethan Farber (BC) Pseudo-Anosovs of interval type Loving
November 14 Lukas Geyer (Montana) Classification of critically fixed anti-Thurston maps Burkart
November 21 Harry Hyungryul Baik (KAIST) Revisit the theory of laminar groups Wu
November 28 MurphyKate Montee (Carleton) Cubulation and Property (T) in random groups Dymarz
December 5 Marissa Loving (UW Madison) Unmarked simple length spectral rigidity for covers local
December 12 Tina Torkaman (Harvard) Intersection number and intersection points of closed geodesics on hyperbolic surfaces 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.

Jean Pierre Mutanguha

The Nielsen–Thurston theory of surface homeomorphisms can be thought of as a surface analogue to the Jordan Canonical Form. I will discuss my progress in developing a similar canonical form for free group automorphisms. (Un)Fortunately, free group automorphisms can have arbitrarily complicated behaviour. This is a significant barrier to translating arguments that worked for surfaces into the free group setting; nevertheless, the overall ideas/strategies do translate!

Anthony Sanchez

Platonic solids have been studied for thousands of years. By unfolding a platonic solid we can associate to it a translation surface. Interesting information about the underlying platonic solid can be discovered in the cover where more (dynamical and geometric) structure is present. The translation covers we consider have a large group of symmetries that leave the global composition of the surface unchanged. However, the local structure of paths on the surface is often sensitive to these symmetries. The Kontsevich-Zorich mondromy group keeps track of this sensitivity.

In joint work with R. Gutiérrez-Romo and D. Lee, we study the monodromy groups of translation covers of some platonic solids and show that the Zariski closure is a power of SL(2,R). We prove our results by finding generators for the monodromy groups, using a theorem of Matheus–Yoccoz–Zmiaikou that provides constraints on the Zariski closure of the groups (to obtain an "upper bound"), and analyzing the dimension of the Lie algebra of the Zariski closure of the group (to obtain a "lower bound").

Feng Zhu

Putting hyperbolic metrics on a finite-type surface S gives us linear representations of the fundamental group of S into PSL(2,R) with many nice geometric and dynamical properties: for instance they are discrete and faithful, and in fact stably quasi-isometrically embedded.

In this talk, we will introduce (relatively) Anosov representations, which generalise this picture to higher-rank Lie groups such as PSL(d,R) for d>2, giving us a class of (relatively) hyperbolic subgroups there with similarly good geometric and dynamical properties.

This is mostly joint work with Andrew Zimmer.

Ethan Farber

A pseudo-Anosov (pA) is a homeomorphism of a compact connected surface S that, away from a finite set of points, acts locally as a linear map with one expanding and one contracting eigendirection. Ubiquitous yet mysterious, pAs have fascinated low-dimensional topologists and dynamicists for the past forty years. We show that any pA on the sphere whose associated quadratic differential has at most one zero, admits an invariant train track whose expanding subgraph is an interval. Concretely, such a pA has the dynamics of an interval map. As an application, we recover a uniform lower bound on the entropy of these pAs originally due to Boissy-Lanneau. Time permitting, we will also discuss potential applications to a question of Fried. This is joint work with Karl Winsor.

Lukas Geyer

Recently there has been an increased interest in complex dynamics of orientation-reversing maps, in particular in the context of gravitational lensing and as an analogue of reflection groups in Sullivan's dictionary between Kleinian groups and dynamics of (anti-)rational maps. Much of the theory parallels the orientation-preserving case, but there are some intriguing differences. In order to deal with the post-critically finite case, we study anti-Thurston maps (orientation-reversing versions of Thurston maps), and prove an orientation-reversing analogue of Thurston's topological classification of post-critically finite rational maps, as well as the canonical decomposition of obstructed maps, following Pilgrim and Selinger. Using these tools, we obtain a combinatorial classification of critically fixed anti-Thurston maps, extending a recently obtained classification of critically fixed anti-rational maps. If time allows, I will explain applications of this classification to gravitational lensing. Most of this is based on joint work with Mikhail Hlushchanka.

Harry Baik

I will give a brief introduction to laminar groups which are groups of orientation-preserving homeomorphisms of the circle admitting invariant laminations. The term was coined by Calegari and the study of laminar groups was motivated by work of Thurston and Calegari-Dunfield. We present old and new results on laminar groups which tell us when a given laminar group is either fuchsian or Kleinian. This is based on joint work with KyeongRo Kim and Hongtaek Jung.

MurphyKate Montee

Random groups are one way to study "typical" behavior of groups. In the Gromov density model, we often find that properties have a threshold density above which the property is satisfied with probability 1, and below which it is satisfied with probability 0. Two properties of random groups that have been well studied are cubulation (and relaxations of this property) and Property (T). In this setting these are mutually exclusive properties, but threshold densities are not known for either property. In this talk I'll present the current state of the art regarding these properties in random groups, and discuss some ways to further these results.

Marissa Loving

A fundamental question in geometry is the extent to which a manifold M is determined by its length spectrum, i.e. the collection of lengths of closed geodesics on M. This has been studied extensively for flat, hyperbolic, and negatively curved metrics. In this talk, we will focus on surfaces equipped with a choice of hyperbolic metric. We will explore the space between (1) work of Otal (resp. Fricke) which asserts that the marked length spectrum (resp. marked simple length spectrum) determines a hyperbolic surface, and (2) celebrated constructions of Vignéras and Sunada, which show that this rigidity fails when we forget the marking. In particular, we will consider the extent to which the unmarked simple length spectrum distinguishes between hyperbolic surfaces arising from Sunada’s construction. This represents joint work with Tarik Aougab, Max Lahn, and Nick Miller.

Tina Torkaman

In this talk, I will talk about the (geometric) intersection number between closed geodesics on finite volume hyperbolic surfaces. Specifically, I will discuss the optimum upper bound on the intersection number in terms of the product of hyperbolic lengths. I also talk about the equidistribution of the intersection points between closed geodesics.


Spring 2023

date speaker title host(s)
January 30 Pierre-Louis Blayac (Michigan) TBA Zhu and Zimmer
February 6 Karen Butt (Michigan) TBA Zimmer
February 13 Elizabeth Field (Utah) TBA Loving
February 20 Chi Cheuk Tsang (Berkeley) TBA Loving
February 27 Caglar Uyanik (UW Madison) TBA local
March 6 Filippo Mazzoli (UVA) TBA Zhu
March 13 Spring Break, No Seminar
March 20 Rose Morris-Wright (Middlebury) TBA Dymarz
March 27 Carolyn Abbott (Brandeis) TBA Dymarz and Uyanik
April 3 Samantha Fairchild (Osnabrück) TBA Apisa
April 10 Jon Chaika (Utah) TBA Uyanik
April 17 Mikolaj Fraczyk (Chicago) TBA Skenderi and Zimmer
April 24 Tarik Aougab (Haverford) TBA Loving
May 1 Didac Martinez-Granado (UC Davis) TBA Uyanik

Spring Abstracts

Pierre-Louis Blayac

Karen Butt

Elizabeth Field

Chi Cheuk Tsang

Caglar Uyanik

Filippo Mazzoli

Rose Morris-Wright

Carolyn Abbott

Samantha Fairchild

Jon Chaika

Mikolaj Fraczyk

Tarik Aougab

Didac Martinez-Granado

Archive of past Dynamics seminars

2021-2022 Dynamics_Seminar_2021-2022

2020-2021 Dynamics_Seminar_2020-2021