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Several approaches to Ehrhart theory

Student-Run Applied & Math Seminar

Speaker: Federico Castillo, UC Davis
Location: 2112 MSB
Start time: Wed, May 28 2014, 1:10PM

The basic problem is enumerating the number of integer points in a polytope. People have used different mathematical tools to study this problem: shellability, valuations in the algebra of polyhedra, unimodular triangulations, local cohomology, toric varieties, complex analysis, and more. At first glance these approaches look very different but we'll see that there are a lot common ideas. The talk will focus on a relatively new point of view, a local Euler-Maclaurin formula given by Berline & Vergne in 2007, and some new consequences that can be deduced from it. This is a practice qual talk.