Wesleyan Dynamics and Analysis (DnA) Seminar

Fall 2016

Tuesdays at 12:10p in Exley 638

Organizers: Ilesanmi Adeboye, Dave Constantine, Adam Fieldsteel, Han Li, Felipe Ramirez

Date Speaker Title and Abstract
Sept 13

Sept 20

Sept 27

Oct 4

Oct 11 Russell Ricks
Binghamton University
Flat Strips and Bowen-Margulis Measures for Rank One CAT(0) Spaces

For compact, negatively curved manifolds, the measure of maximal entropy provides an important tool for understanding the dynamics of the geodesic flow. This measure, constructed independently by Bowen and Margulis using different methods, is called the Bowen-Margulis measure. Sullivan later provided another method to construct this measure for real hyperbolic space; this method has since been generalized to many geometric settings, including compact, rank one nonpositively curved manifolds and CAT(-1) spaces under proper isometric actions. We will discuss a generalization to the setting of certain rank one CAT(0) spaces and identify precisely which CAT(0) spaces are mixing.

Our construction of the Bowen-Margulis measure hinges on establishing a new structural result of independent interest: Almost no geodesic (under the Bowen-Margulis measure) bounds a flat strip of any positive width. We also show that almost every point in the boundary of X (under the Patterson-Sullivan measure) is isolated in the Tits metric.

Many of the techniques we use extend beyond the Bowen-Margulis measure, and work without compactness.

Oct 18 Ian Adelstein
Trinity College

Oct 25 No meeting (Fall Break)

Nov 1

Nov 8

Nov 15

Nov 22 No meeting (faculty meeting)

Nov 29

Dec 6