Teichmuller spaces are hyperbolic, well, statistically
Vaibhav Gadre (University of Glasgow)
Monday 5th October, 2020 16:00-17:00 Online
The notion of statistical hyperbolicity introduced by Duchin-Lelievre- Mooney encapsulates whether a space is hyperbolic "on average". A metric space is said to be statistically hyperbolic if the average distance between a pair of points on a large sphere divided by the radius approaches 2 as the radius approaches infinity. While Teichmuller spaces are not hyperbolic in the traditional sense, we show that they are statistically hyperbolic for a large class of measures, including the Lebesgue class measures for which statistical hyperbolicity was established by Dowdall-Duchin-Masur. This is joint work with Luke Jeffreys and Aitor Azemar.
The talk will be preceded by a 30 minute tea time. The Zoom link for the seminar is https://uofglasgow.zoom.us/j/91412568415 and the passcode is the genus of the two-dimensional sphere (4 letters).