**Date & Time:** Wednesday, July 23, 2014, 16:30-17:30.

**Venue:** Ramanujan Hall

**Speaker:** Vamsi Pingali, Johns Hopkins University

**Title:** Computing Teichmüller maps between polygons

**Abstract:** By the Riemann mapping theorem, one can bijectively map the interior of an *n*-gon *P* to that of another *n*-gon conformally. However, (the boundary extension of) this mapping need not necessarily map the vertices of *P* to those *Q*. In this case, one wants to find the "best" mapping between these polygons, i.e., one that minimizes the maximum angle distortion (the dilatation) over *all* points in *P*. I shall discuss this problem in the continuous and the discrete settings. This topic lies on the interface of complex analysis and theoretical computer science.