Topology Seminar (Introductory Talk): Univalent functions, surfaces in hyperbolic space and Schwarzian derivatives

Seminar | February 28 | 2-3 p.m. | 740 Evans Hall

 Ken Bromberg, University of Utah

 Department of Mathematics

An elegant construction of C. Epstein associates a surface in hyperbolic space to a univalent (injective, holomorphic) function. One can use this Epstein surface to derive properties of the univalent function and conversely use properties of the univalent function to study surfaces in hyperbolic space. The key tool to translate between them is the Schwarzian derivative. We will define both the Epstein surface and the Schwarzian derivative along with some of their properties. If time permits we will discuss an estimate on Thurston’s projective metric coming from G. Anderson’s 1998 Berkeley thesis.