Imre Barany, Hungarian Academy of Sciences and University College London

August 29, 2017 - 4:15pm to 5:15pm

Cupples I, room 199

*Abstract: Given a convex cone $C$ in $R^d$, an integral zonotope $T$ is the sum of segments $[0,v_i]$ ($i=1,\ldots,m$) where each $v_i \in C$ is a vector with integer coordinates. The endpoint of $T$ is $k=\sum_1^m v_i$. Let $F(C,k)$ be the family of all integral zonotopes in $C$ whose endpoint is $k \in C$. We prove that, for large $k$, the zonotopes in $F(C,k)$ have a limit shape, meaning that, after suitable scaling, the overwhelming majority of the zonotopes in $F(C,k)$ are very close to a fixed convex set which is actually a zonoid. We also establish several combinatorial properties of a typical zonotope in $F(C,k)$. This is joint work with Julien Bureaux and Ben Lund.*

*Tea @ 3:45 in room 200*

*Host: Todd Kuffner*