Difference between revisions of "Dynamics Seminar 2020-2021"

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(Fall 2020)
(Chenxi Wu)
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===Chenxi Wu===
 
===Chenxi Wu===
  
"Asymptotic translation lengths on free factor complex"
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"Asymptotic translation lengths on curve complexes and free factor complexes"
  
The free factor complex is a graph theoretic analogy of the curve complex of surfaces. I will review some results about the asymptotic translation length of pseudo-Anosov action on curve complexes, in particular, the estimate of asymptotic translation lengths for pseudo-Anosovs with the same mapping torus, and the analogous results in the setting of free factor complexes. This will include prior works with Hyungryul Baik, Eiko Kin and Hyunshik Shin, as well as ongoing work with Hyungryul Baik and Dongryul Kim.
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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.

Revision as of 13:27, 29 September 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

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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) Asymptomatic translation lengths on curve complexes and free factor complexes (local)
October 7 Kathryn Lindsey TBA (Boston College)

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.