# Difference between revisions of "Dynamics Seminar 2020-2021"

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"Asymptotic translation lengths on curve complexes and free factor complexes" | "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. | + | 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] |

## Revision as of 14:31, 30 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

## 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 | 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. Slides