"Polyhedra inscribed in quadrics, their geometry and quasicircles"

Abstract: In 1832 Steiner asked for a characterization of polyhedra which can be inscribed in quadrics. In 1992 Rivin answered in the case of the sphere by classifying ideal polyhedra in hyperbolic space. In this talk, I will describe the complete answer to Steiner's question, which involves the study of ideal polyhedra inscribed in anti de Sitter and half-pipe geometry. Time permitting, I will also discuss future directions in the study of (a universal version of) Thurston and Mess' conjectures about convex hulls of quasicircles in quasi-Fuchsian manifolds. (This is joint work with J. Danciger and J.-M. Schlenker and partially F. Bonsante.)

Host: Steven Frankel