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# Ben Lund, Limit shape of lattice Zonotopes

## Tuesday, May 25, 2021 @ 4:30 PM - 5:30 PM KST

Room B232, IBS (기초과학연구원)

### Speaker

Ben Lund
IBS Discrete Mathematics Group
http://www.ben-lund.com

A convex lattice polytope is the convex hull of a set of integral points. Vershik conjectured the existence of a limit shape for random convex lattice polygons, and three proofs of this conjecture were given in the 1990s by Bárány, by Vershik, and by Sinai. To state this old result more precisely, there is a convex curve $L \subset [0,1]^2$ such that the following holds. Let $P$ be a convex lattice polygon chosen uniformly at random from the set of convex lattice polygons with vertices in $[0,N]^2$. Then, for $N$ sufficiently large, $(1/N)P$ will be arbitrarily close (in Hausdorff distance) to $L$ with high probability. It is an open question whether there exists a limit shape for three dimensional polyhedra.

I will discuss this problem and some relatives, as well as joint work with Bárány and Bureaux on the existence of a limit shape for lattice zonotopes in all dimensions.

## Details

Date:
Tuesday, May 25, 2021
Time:
4:30 PM - 5:30 PM KST
Event Category:
Event Tags:

Room B232
IBS (기초과학연구원)

## Organizer

Sang-il Oum (엄상일)
View Organizer Website
기초과학연구원 수리및계산과학연구단 이산수학그룹
대전 유성구 엑스포로 55 (우) 34126
IBS Discrete Mathematics Group (DIMAG)
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
E-mail: dimag@ibs.re.kr, Fax: +82-42-878-9209