Geometric Structures seminar: Raman Sanyal

Miruna - Stefana Sorea mirunastefana.sorea at
Tue Nov 24 09:38:15 CET 2020

Dear All,

this is a reminder of the next seminar from the series "Geometric


Title: Normally inscribable polytopes, routed trajectories, and
reflection arrangements

Time: November 24, 2020, 4:00 pm (Rome Time) 

Venue: from remote only, on zoom at this link
Passcode: geometry

Steiner posed the question if any 3-dimensional polytope had a
realization with vertices on a sphere. Steinitz constructed the first
counter examples and Rivin gave a complete complete answer to Steiner's
question. In dimensions 4 and up, the Universality Theorem renders the
question for inscribable combinatorial types hopeless. In this talk, I
will address the following refined question: Given a polytope P, is
there a continuous deformation of P into an inscribed polytope that
keeps corresponding faces parallel? 
This question has strong ties to deformations of Delaunay subdivisions
and ideal hyperbolic polyhedra and its study reveals a rich interplay of
algebra, geometry, and combinatorics. In the first part of the talk, I
will discuss relations to routed trajectories of particles in a ball and
reflection groupoids and show that that the question is polynomial time
In the second part of the talk, we will focus on class of zonotopes,
that is, polytopes representing hyperplane arrangements. It turns out
that inscribable zonotopes are rare and intimately related to reflection
groups and Gr\"unbaum's quest for simplicial arrangements. This is based
on joint work with Sebastian Manecke. 

More information can be found here: 

Everyone is welcome! 

Miruna-Stefana Sorea 
_Miruna-Stefana Sorea_
_Postdoctoral Researcher_
_Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste,


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