Title: Polyhedra inscribed in quadrics
Speakers：Jean-Marc Schlenker, Anton Thalmaier
Time：2020/11/12，21:00-22:00
Link：https://zoom.com.cn/j/67532621800
Code：929725
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.)
