Lecture:2020/11/12,21:00-22:00,Jean-Marc Schlenker, Anton Thalmaier,University of Luxemburg


Title: Polyhedra inscribed in quadrics
Speakers:Jean-Marc Schlenker, Anton Thalmaier 


Abstract:In 1832, Jakob Steiner published a book which opened new perspectives on geometry, and in particular on polyhedra. Among other questions, he asked: what are the combinatorial types of polyehdra that can be  realized in $\RR^3$ with their vertices on a quadric? The question is projectively invariant and, up to projective transformation, there are only three quadrics in $\RR^3$. The question was first answered in the 1990s for polyhedra inscribed in an ellipsoid, using hyperbolic geometry. I will explain this result and how the question can be answered for the other two quadrics using anti-de Sitter and Half-pipe geometry. (New results are joint work with Jeff Danciger and Sara Maloni.)