# Mathematical Sciences Research Institute

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# Seminar

Tropical Seminar: "Kneser's theorem and inequalities in Ehrhart theory" October 23, 2009
Parent Program: -- MSRI: Simons Auditorium
Speaker(s) Alan Stapledon
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We demonstrate how additive number theory can be used to produce new classes of inequalities in the theory of enumeration of
lattice points in polytopes. More specifically, we use a classical result of Kneser to produce new inequalities between the coefficients of the Ehrhart $h^*$-vector of a lattice polytope. As an application, we deduce all possible `balanced' inequalities between the coefficients of the Ehrhart $h^*$-vector of a lattice polytope containing an interior lattice point, in dimension at most $6$.

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