Geometric Structures seminar: Raman Sanyal

[Miruna - Stefana Sorea]

Dear All,

this is to announce the next seminar from the series "Geometric
Structures".

Speaker: RAMAN SANYAL (GOETHE-UNIVERSITÄT FRANKFURT) [1]

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 
https://sissa-it.zoom.us/j/85675591787?pwd=TUo2VXpmcEhOU1paRzBXUWp2MU1odz09
Passcode: geometry

Abstract: 
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?math-users at lists.sissa.it 
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
decidable.   
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:
https://sites.google.com/view/geometric-structures/. 

Everyone is welcome! 

Miruna-Stefana Sorea 

---
_Miruna-Stefana Sorea_
_ Postdoctoral Researcher_
_ Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste,
Italy_
_ HTTPS://SITES.GOOGLE.COM/VIEW/MIRUNASTEFANASOREA/_ 

  

Links:
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[1] https://www.math.uni-frankfurt.de/~sanyal/