##### Department of Mathematics,

University of California San Diego

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### Colloquium

## Imre Barany

#### University College London and Mathematical Institute of the Hungarian Academy of Sciences

## The minimum area convex lattice $n$-gon

##### Abstract:

Let $A(n)$ be the minimum area of convex lattice $n$-gons. (Here lattice is the usual lattice of integer points in $R^2$.) G. E. Andrews proved in 1963 that $A(n)>cn^3$ for a suitable positive $c$. We show here that $\\lim A(n)/n^3$ exists, and explain what the shape of the minimizing convex lattice $n$-gon is. This is joint work with Norihide Tokushige.

Host: Van Vu

### October 27, 2003

### 3:00 PM

### AP&M 7321

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