# Chris O'Neill : An Introduction to Ehrhart Theory and Lattice Point Enumeration

A polytope is a subset of R^d which is the convex hull of a finite set of vertices. Given a polytope P, we can consider integer dilations of P, and ask how many integer points are contained in each dilation, as a function of the dilation factor. A theorem by Eugene Ehrhart tells us that, under the right conditions, this counting function is a polynomial, with some very interesting and unexpected properties. To demonstrate the usefulness of these results, we will give alternative proofs to some well known results from far outside the realm of geometry, including some basic facts about the chromatic polynomial of a graph. This talk will contain a little geometry, a little analysis, a little algebra, and a little combinatorics, and will be accessible to anyone who enjoys at least one of these topics.

**Category**: Graduate/Faculty Seminar**Duration**: 01:34:51**Date**: February 11, 2011 at 4:25 PM**Views**: 123-
**Tags:**seminar, Graduate/faculty Seminar

## 0 Comments