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Introduction to Ehrhart theory

Student-Run Applied & Math Seminar

Speaker: Fu Liu, UC Davis
Location: 2112 MSB
Start time: Wed, Nov 12 2008, 12:10PM

Given a convex polytope P, for any positive integer m, we denote by i(P,m) the number of lattice points inside mP = { mx : x is in P }, the mth dilation of P. Eugene Ehrhart discovered in 1960s that i(P, m) is a polynomial function of degree dim(P) if P is an integral polytope. Thus, we call i(P, m) the Ehrhart polynomial of P (if P is integral). I will discuss the motivation for considering this problem, survey some related results, and then discuss some of my own results.