## Dynamics, Geometry, & Groups Seminar

### Friday, September 20th, 2019

**Time:** 10:30 a.m** Place:** Jeffery Hall 319

**Speaker:** Ian Frankel (Queen's University)

**Title:** Local geometry of Teichmüller space: flat and quasiconformal.

**Abstract:** The Teichmüller distance between two homeomorphic Riemann surfaces X and Y is a number that quantifies the following question: Given a homeomorphism from X to Y, how non-conformal does the map have to be?

The optimal quasiconformal maps, i.e. those with smallest quasiconformal constant, are characterized by choices of special singular flat metrics on X and Y, and in fact fit into a large familes of maps, and the dynamics of SL(2,R) acting on this family have been the subject of many celebrated results in the past decade.

Now, suppose we are given X and Y but with singular flat metrics that are not related to the optimal map. We will describe how we can still estimate the Teichmüller distance from X to Y.