Some simple observations on Ehrhart Polynomials, Vector Partition Function and Minkowski Decomposition

Description

In this talk we will see some basic facts about Ehrhart polynomials after introducing the necessary notions from polyhedral geometry. The Vector Partition Function, which can be thought of as a generalization of Ehrhart polynomials, will be then explored from both a geometric and an analytic perspective. In particular, we will see that the Vector Partition Function is piecewise (quasi-)polynomial. The regions of polynomiality form a complex which we will compute in two different ways, using Partition Analysis and geometry. The geometric way is based on a simple observation about the connection of the polynomiality complex to a certain cone constructed for the computation of the indecomposable Minkowski summands of a polytope. If time permits, returning to the study of Ehrhart polynomials, we will see how to use geometry to interpolate Ehrhart polynomials.

Period	24 Jan 2018
Event type	Guest talk
Location	AustriaShow on map