Speaker: Jonathan Weitsman (Santa Cruz)
Title: Lattice points in convex polytopes, and Euler-MacLaurin formulas, old and new
Abstract: Recent work arising from ideas in algebraic geometry and symplectic geometry has given rise to new ideas in a classical area of mathematics: the problem of counting lattice points in convex polytopes, and the related problem of finding analogs in higher dimensions to the classical Euler-MacLaurin formula. We review the work of Cappell and Shaneson, Kantor-Khovanskii, Guillemin, and Brion-Vergne, and provide an elementary proof of their results. If time permits, we will discuss the analytical issues arising in the Euler-MacLaurin formula.