# Geometry and Topology Seminar

The Geometry and Topology seminar meets in room **901 of Van Vleck Hall** on **Fridays** from **1:20pm - 2:10pm**.

For more information, contact Shaosai Huang.

## Fall 2018

date | speaker | title | host(s) |
---|---|---|---|

Sept. 14 | Teddy Einstein (UIC) | Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes | (Dymarz) |

Oct. 12 | Marissa Loving | TBA | (Kent) |

Oct. 19 | Sara Maloni | TBA | (Kent) |

Nov. 16 | Xiangdong Xie | TBA | (Dymarz) |

## Fall Abstracts

### Teddy Einstein

"Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes"

Non-positively curved (NPC) cube complexes are important tools in low dimensional topology and group theory and play a prominent role in Agol's proof of the Virtual Haken Conjecture. Constructing a hierarchy for a NPC cube complex is a powerful method of decomposing its fundamental group essential to the theory of NPC cube complex theory. When a cube complex admits a hierarchy with nice properties, it becomes possible to use the hierarchy structure to make inductive arguments. I will explain what a quasiconvex hierarchy of an NPC cube complex is and briefly discuss some of the applications. We will see an outline of how to construct a quasiconvex hierarchy for a relatively hyperbolic NPC cube complex and some of the hyperbolic and relatively hyperbolic geometric tools used to ensure the hierarchy is indeed quasiconvex.

## Archive of past Geometry seminars

2017-2018 Geometry_and_Topology_Seminar_2017-2018

2016-2017 Geometry_and_Topology_Seminar_2016-2017

2015-2016: Geometry_and_Topology_Seminar_2015-2016

2014-2015: Geometry_and_Topology_Seminar_2014-2015

2013-2014: Geometry_and_Topology_Seminar_2013-2014

2012-2013: Geometry_and_Topology_Seminar_2012-2013

2011-2012: Geometry_and_Topology_Seminar_2011-2012

2010: Fall-2010-Geometry-Topology