Some modern open problems on polytopes with symmetries and regularities
Martin Winter (Warwick)
Abstract: Polytope theory has itself established as a modern field of mathematics with deep connections to geometry, combinatorics, and algebra. Convex polytopes with many symmetries and regularities however have thereby played only a secondary role and are often considered as a fascinating, yet esoteric subject of the past. In this talk I want to rectify this by presenting up to three modern open problems that connect the study of such polytopes to representation theory, hyperplane arrangements and Weyl groupoids, as well as spectral graph theory. More specifically, the three topics are the possible symmetries of orbit polytopes, inscribed and simple zonotopes, and the reconstruction of polytopes from graphs via spectral graph theory.
combinatorics
Audience: researchers in the topic
Series comments: This is the online combinatorics seminar at Warwick.
| Organizers: | Jan Grebik, Oleg Pikhurko |
| Curator: | Hong Liu* |
| *contact for this listing |