G眉nter Ziegler (Freie Universit盲t Berlin): The Realization Space of the 24-Cell.
Abstract:听 If anyone will ever write 鈥淭he BOOK of Examples鈥, then the 24-cell, discovered in the 18th century, will surely be one of its highlights: A self-dual regular polytope of dimension 4 with 24 vertices and 24 octahedra as facets, exceptional and unique in many respects鈥
The 鈥渞ealization space鈥 of a type of polytope is the space of all correct sets of coordinates for this type. There are published proofs that all realization spaces of polytopes are manifolds, while the 鈥渦niversality theorem for polytopes鈥 claims that this is far from the truth, that basically anything can happen, any semi-algebraic set occurs.
However, the examples that were constructed to prove this are very artificial 鈥 most polytopes that occur 鈥渋n nature鈥 (such as the 3-dimensional polytopes, simple polytopes, simplicial polytopes, etc.) have manifolds as realization spaces.
However, the 24-cell鈥
(Joint work in progress with Laith Rastanawi and Rainer Sinn.)
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The event will be followed by the Reception held on Huxley Concourse Level 3.听Registration in advance due to capacity restrictions by filling the听.
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