Title: Thurston's metric on Teichmueller spaces of flat n-tori

Date: 09/07/2017

Time: 2:00 PM - 3:00 PM

Place: C304 Wells Hall

Speaker: Mark Greenfield, University of Michigan

Several interesting metrics have been defined for Teichmueller spaces of hyperbolic surfaces. However, analogous metrics on the Teichmueller space of flat n-tori have not been as well studied. After reviewing some background on Teichmueller theory, we will define an analog of Thurston's metric for these spaces. We find that in dimension n=2, it agrees with the hyperbolic metric. In particular, this gives a new way to realize the hyperbolic plane as the moduli space of marked flat tori. Time permitting, we will describe the corresponding situation in dimension n>2. This work is joint with Lizhen Ji.