# Sebastian Manecke : Inscribable fans, zonotopes, and reflection arrangements

**Time: **
Wed 2021-02-03 10.15 - 11.15

**Lecturer: **
Sebastian Manecke (Goethe-Universität Frankfurt)

**Location: **
Zoom meeting ID: 654 5562 3260

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