Geometric Analysis and Topology Seminar

Spring 2017

The seminar's usual time is Wednesday at 11:00am in 1314 Warren Weaver Hall (Directions). Special times and dates are marked in red. Click on the title of a talk for the abstract (if available).

Jan 25,  11am
1314 WWH
Mario Bonk
Parabolicity of leaves
Feb 22,  11am
1314 WWH
Brandon Seward
The Geometric Burnside's Problem

Organizers: Sylvain Cappell, Jeff Cheeger, Bruce Kleiner, and Robert Young.


Parabolicity of leaves, Mario Bonk.  Certain dynamical systems give rise to foliations where the leaves are quasi-isometric to open simply connected surfaces. The question arises whether these leaves are parabolic or hyperbolic (equivalent to recurrence or transience of a random walk). This is related, for example, to Cannon's conjecture in geometric group theory or to Thurston's characterization of postcritically-finite rational maps. I will discuss this in my talk and also mention some open problems in the area.
The Geometric Burnside's Problem, Brandon Seward.  Burnside's Problem and the von Neumann Conjecture are classical problems from group theory which were long ago answered in the negative. In 1999, Kevin Whyte defined geometric analogs of these problems and proved the Geometric von Neumann Conjecture. In this talk, I will present a solution to the Geometric Burnside's Problem. I will also present a strengthening of Whyte's result and draw conclusions about the existence of regular spanning trees of Cayley graphs.

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