Speaker: Xuan Hien Nguyen (Iowa State University)

Title: The fundamental gap of horoconvex domains in hyperbolic space. 

Abstract: In this talk, we introduce the fundamental gap problem and its characteristics in hyperbolic space. We will spend some time recalling the special properties of hyperbolic geometry before showing that, unlike in the Euclidean or spherical cases, the product of their fundamental gap with the square of their diameter has no positive lower bound. The result follows from the study of the fundamental gap of geodesic balls as the radius goes to infinity, then comparing horoconvex domains to balls.