### Monday September 9, 2002

**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.