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.
|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)|
|Oct. 26||Dingxin Zhang (Harvard)||TBA||(Huang)|
|Nov. 9||Zhongshan An (Stony Brook)||Ellipticity of the Bartnik Boundary Conditions||(Huang)|
|Nov. 16||Xiangdong Xie||TBA||(Dymarz)|
"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.
"Ellipticity of the Bartnik Boundary Conditions"
The Bartnik quasi-local mass is defined to measure the mass of a bounded manifold with boundary, where a collection of geometric boundary data — the so-called Bartnik boundary data— plays a key role. Bartnik proposed the open problem whether, on a given manifold with boundary, there exists a stationary vacuum metric so that the Bartnik boundary conditions are realized. In the effort to answer this question, it is important to prove the ellipticity of Bartnik boundary conditions for stationary vacuum metrics. In this talk, I will start with an introduction to the Bartnik quasi-local mass and the moduli space of stationary vacuum metrics. Then I will explain the ellipticity result for the Bartnik boundary conditions and, as an application, give a partial answer to the existence question.
Archive of past Geometry seminars