Difference between revisions of "Dynamics Seminar 2020-2021"

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(Kathryn Lindsey)
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|October 7
 
|October 7
 
|Kathryn Lindsey
 
|Kathryn Lindsey
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|Slices of Thurston's Master Teapot
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|October 14
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|Daniel Thompson
 
|TBA
 
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The curve complex of a closed surface is a simplicial complex where the vertices are simple closed curves up to isotopy and faces are curves that are disjoint, and an analogy for the curve complex in the setting of Out(F_n) is the free factor complex. A pseudo-Anosov map induces a map from the curve graph to itself, and a basic question is to study the asymptotic translation length which is known to be a non-zero rational number. I will review some prior results on the study of this asymptotic translation length, as well as some of their analogies in the setting of free factor complexes. The latter part is an ongoing project with Hyrungryul Baik and Dongryul Kim. [https://wuchenxi.github.io/graph.pdf Slides]
 
The curve complex of a closed surface is a simplicial complex where the vertices are simple closed curves up to isotopy and faces are curves that are disjoint, and an analogy for the curve complex in the setting of Out(F_n) is the free factor complex. A pseudo-Anosov map induces a map from the curve graph to itself, and a basic question is to study the asymptotic translation length which is known to be a non-zero rational number. I will review some prior results on the study of this asymptotic translation length, as well as some of their analogies in the setting of free factor complexes. The latter part is an ongoing project with Hyrungryul Baik and Dongryul Kim. [https://wuchenxi.github.io/graph.pdf Slides]
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===Kathryn Lindsey===
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"Slices of Thurston's Master Teapot"
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Thurston's Master Teapot is the closure of the set of all points $(z,\lambda) \in \mathbb{C} \times \mathbb{R}$ such that $\lambda$  is the growth rate of a critically periodic unimodal self-map of an interval and $z$ is a Galois conjugate of $\lambda$.  I will present a new characterization of which points are in this set.  This characterization gives a way to think of each horizontal slice of the Master Teapot as an analogy of the Mandelbrot set for a "restricted iterated function system." An application of this characterization is that the Master Teapot is not invariant under the map $(z,\lambda) \mapsto (-z,\lambda)$.  This presentation is based on joint work with Chenxi Wu.

Revision as of 15:37, 1 October 2020

The Dynamics Seminar meets virtually on Wednesdays from 2:30pm - 3:20pm.
For more information, contact Chenxi Wu. To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu

Hawk.jpg


Fall 2020

date speaker title host(s)
September 16 Andrew Zimmer (Wisconsin) An introduction to Anosov representations I (local)
September 23 Andrew Zimmer (Wisconsin) An introduction to Anosov representations II (local)
September 30 Chenxi Wu (Wisconsin) Asymptoic translation lengths on curve complexes and free factor complexes (local)
October 7 Kathryn Lindsey Slices of Thurston's Master Teapot (Boston College)
October 14 Daniel Thompson TBA (Ohio State)

Fall Abstracts

Andrew Zimmer

"An introduction to Anosov representations"

Anosov representations are a special class of representations of finitely generated groups into Lie groups, which are defined using ideas from dynamics (namely, the theory of Anosov flows). In this talk, I will explain the definition (in a special case), give some examples, and describe some properties. I will focus on the case of representations into the general linear group where no background knowledge about Lie groups is required.


Chenxi Wu

"Asymptotic translation lengths on curve complexes and free factor complexes"

The curve complex of a closed surface is a simplicial complex where the vertices are simple closed curves up to isotopy and faces are curves that are disjoint, and an analogy for the curve complex in the setting of Out(F_n) is the free factor complex. A pseudo-Anosov map induces a map from the curve graph to itself, and a basic question is to study the asymptotic translation length which is known to be a non-zero rational number. I will review some prior results on the study of this asymptotic translation length, as well as some of their analogies in the setting of free factor complexes. The latter part is an ongoing project with Hyrungryul Baik and Dongryul Kim. Slides


Kathryn Lindsey

"Slices of Thurston's Master Teapot"

Thurston's Master Teapot is the closure of the set of all points $(z,\lambda) \in \mathbb{C} \times \mathbb{R}$ such that $\lambda$ is the growth rate of a critically periodic unimodal self-map of an interval and $z$ is a Galois conjugate of $\lambda$. I will present a new characterization of which points are in this set. This characterization gives a way to think of each horizontal slice of the Master Teapot as an analogy of the Mandelbrot set for a "restricted iterated function system." An application of this characterization is that the Master Teapot is not invariant under the map $(z,\lambda) \mapsto (-z,\lambda)$. This presentation is based on joint work with Chenxi Wu.