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SUMMARY:Sebastian Manecke (University of Frankfurt)
DTSTART:20210211T150000Z
DTEND:20210211T160000Z
DTSTAMP:20260422T065500Z
UID:CJCS/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CJCS/4/">Ins
 cribable fans\, zonotopes\, and reflection arrangements</a>\nby Sebastian 
 Manecke (University of Frankfurt) as part of Copenhagen-Jerusalem Combinat
 orics Seminar\n\n\nAbstract\nSteiner posed the question if any 3-dimension
 al polytope had a\nrealization with vertices on a sphere. Steinitz constru
 cted the first\ncounter example and Rivin gave a complete resolution. In\n
 dimensions 4 and up\, universality theorems by Mnev/Richter-Gebert\nrender
  the question for inscribable combinatorial types hopeless.\n\nHowever\, f
 or a given complete fan N\, we can decide in polynomial time\nif there is 
 an inscribed polytope with normal fan N. Linear\nhyperplane arrangements c
 an be realized as normal fans via zonotopes.\nIt turns out that inscribed 
 zonotopes are rare and in this talk I\nwill focus on the question of class
 ifying the corresponding\narrangements. This relates to localizatons and r
 estrictions of\nreflection arrangements and Grünbaum's quest for the clas
 sification of \nsimplicial arrangements. The talk is based on joint work w
 ith Raman\nSanyal.\n
LOCATION:https://researchseminars.org/talk/CJCS/4/
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