Colloquium

Date: October 12, 2022

Time: 4:00PM - 5:00PM

Location: Bloc 117

Speaker: Chris Bishop, Stony Brook University

Description: Title: Conformal Mapping in Linear Time
Abstract:  What do hyperbolic 3-manifolds have to do with the Riemann mapping theorem?  In this talk, I will explain how a theorem of Dennis Sullivan (based on an observation of Bill Thurston) about  convex sets in hyperbolic 3-space leads to a fast algorithm for computing conformal maps. The conformal map from the unit disk to the interior of a polygon is given by the Schwarz-Christoffel formula, but this formula is stated in terms of parameters that are hard to compute.  I will explain a fast way to approximate these parameters: the speed comes from the medial axis,  a type of Voronoi diagram from computational geometry, and the accuracy is proven using Sullivan's theorem.  At the end of the lecture, I will mention various  applications to discrete geometry and optimal meshing; one of these  will be the subject of the second lecture.