# Mathematics Colloquia and Seminars

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### Volumes and Ehrhart polynomials of polytopes

**Colloquium**

Speaker: | Fu Liu, University of California, Davis |

Location: | 1147 MSB |

Start time: | Tue, Apr 3 2007, 4:10PM |

We discuss the relationship between the volume and the Ehrhart polynomial of an integral polytope. After a brief introduction to background results in the theory of Ehrhart polynomials, we define a family of polytopes which can be considered as a generalization of cyclic polytopes. The coefficients of the Ehrhart polynomial of these polytopes are given by volumes of iterated projections of the polytopes. Next, in joint work with Jesus De Leora and Ruriko Yoshida, we give a formula for the volume of the Birkhoff polytope obtained by a calculation of its Ehrhart polynomial.

Tea will start at 3:30 in MSB 1147. Dinner will follow the Colloquium.