|Date: Thursday, January 19, 2006
Title: Integer Points and Rational Functions
Abstract: Motivated by the formula for the sum of the geometric series, where a long polynomial sums up to a short rational function, we ask ourselves which sets of integer lattice points admit a short rational generating function. While examples include the sets of integer points in a rational polyhedron, lattice semigroups, and some other intreresting sets, the true extent of this phenomenon is still unknown (though there is a conjecture). The question turns out to have connections to continued fractions, Hilbert functions, and Presberger arithmetic. This is a survey talk.
Speaker: Alexander Barvinok