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SUMMARY:Raman Sanyal (Goethe University Frankfurt)
DTSTART:20210128T130000Z
DTEND:20210128T140000Z
DTSTAMP:20260423T022717Z
UID:DCGParis/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/DCGParis/2/"
 >Inscribable polytopes\, routed trajectories\, and reflection arrangements
 </a>\nby Raman Sanyal (Goethe University Frankfurt) as part of Discrete an
 d Computational Geometry Seminar in Paris\n\n\nAbstract\nSteiner posed the
  question if any 3-dimensional polytope had a realization\nwith vertices o
 n a sphere. Steinitz constructed the first counter examples and\nRivin gav
 e a complete answer to Steiner's question. In dimensions 4\nand up\, the U
 niversality Theorem indicates that certifying inscribability is\ndifficult
  if not hopeless. In this talk\, I will address the following\nrefined que
 stion: Given a polytope P\, is there a continuous deformation of P\nto an 
 inscribed polytope that keeps corresponding faces parallel? In other\nword
 s\, is there an inscribed polytope P’ that is normally equivalent (or st
 rongly\nisomorphic) to P?\n\nThis question has strong ties to deformations
  of Delaunay subdivisions and\nideal hyperbolic polyhedra and its study re
 veals a rich interplay of algebra\,\ngeometry\, and combinatorics. In the 
 first part of the talk\, I will discuss\nrelations to routed trajectories 
 of particles and reflection groupoids and\nshow that that the question is 
 polynomial time decidable.\n\nIn the second part of the talk\, we will foc
 us on class of zonotopes\, that is\,\npolytopes representing hyperplane ar
 rangements. It turns out that inscribable\nzonotopes are rare and intimate
 ly related to reflection groups and\nGrünbaum's quest for simplicial arra
 ngements.  This is based on joint work\nwith Sebastian Manecke.\n
LOCATION:https://researchseminars.org/talk/DCGParis/2/
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