Sebastian Manecke : Inscribable fans, zonotopes, and reflection arrangements

Abstract: Steiner posed the question if any 3-dimensional polytope had a
realization with vertices on a sphere. Steinitz constructed the first
counter example and Rivin gave a complete resolution. In
dimensions 4 and up, universality theorems by Mnev/Richter-Gebert
render the question for inscribable combinatorial types hopeless.

However, for a given complete fan F, we can decide in polynomial time
if there is an inscribed polytope with normal fan F. Linear
hyperplane arrangements can be realized as normal fans via zonotopes.
It turns out that inscribed zonotopes are rare and in this talk I
will focus on the question of classifying the corresponding
arrangements. This relates to localizatons and restrictions of
reflection arrangements and Grünbaum's quest for the classification of
simplicial arrangements. The talk is based on joint work with Raman
Sanyal.

https://kth-se.zoom.us/j/65455623260

Zoom meeting ID: 654 5562 3260