**UM Math Graduate Students Seminar**

Brittney Ellzey

* University of Miami *

**will present**

**What is Erhart Theory?**

Friday, October 10, 2014, 2:30pm

Ungar Building Room 402

**Abstract: **

Ehrhart theory gives a discrete analogy of volume by counting the number of integer points inside a polytope. The Ehrhart polynomial of a polytope gives the number of integer points inside dilations of the polytope. During this talk, I will introduce some of the basic concepts of Ehrhart theory and Ehrhart polynomials. I will work out a few examples in order for us to get a feel for the material, and I will also mention Pick's theorem, Stanley's nonnegativity theorem, and the Ehrhart-Macdonald reciprocity theorem.

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