## Topology Seminar

Date: October 21, 2020

Time: 4:00PM - 5:00PM

Location: Zoom

Speaker: Sara Maloni, University of Virginia

Title: Convex hulls of quasicircles in hyperbolic and anti-de Sitter space.

Abstract: Thurston conjectured that quasi-Fuchsian manifolds are determined by the induced hyperbolic metrics on the boundary of their convex core and Mess generalized those conjectures to the context of globally hyperbolic AdS spacetimes. In this talk I will discuss a universal version of these conjectures (and prove the existence part) by considering convex sets spanning quasicircles in the boundary at infinity of hyperbolic and anti-de Sitter space. This work generalizes Alexandrov and Pogorelov's results about the characterization metrics induced on the boundary of a compact convex subset of hyperbolic space. Time permitting, we will discuss why in hyperbolic space quasicircles can't be characterized by the width of their convex hulls, except when the convex hulls have small width. This is different than the anti-de Sitter setting, as Bonsante and Schlenker showed. (This is joint work with Bonsante, Danciger and Schlenker.)