Friday, 16:15 - 16:40 h, Room: H 2032

 

Alexander Kasprzyk
Riemannian polytopes

Coauthor: Gabor Hegedus

 

Abstract:
Given a convex lattice polytope P, one can count the number of points in a dilation mP via the Ehrhart polynomial LP. The roots of LP (over C) have recently been the subject of much study, with a particular focus on the distribution of the real parts. In particular, V. Golyshev conjectured, and the authors recently proved, that any smooth polytope of dimension at most five are so-called Riemannian polytopes; this is, the roots of LP all satisfy ℜ (z)=-1/2.
I shall discuss some recent results on Riemannian polytopes, with particular emphasis on reflexive polytopes. In particular, I will discuss the distribution of the roots in the case of a reflexive polytope P, and a characterisation of when P is Reimannian.

 

Talk 3 of the invited session Fri.3.H 2032
"Integer points in polytopes II" [...]
Cluster 11
"Integer & mixed-integer programming" [...]

 

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