Special HARVARD / MIT -- Joint COMBINATORICS SEMINAR
Wednesday, October 24, 2018 at 4:15pm to 5:15pm
Science Center Hall E - One Oxford Street - Harvard University - Cambridge, MA
SPEAKER: Bernd Sturmfels (MPI Leipzig and UC Berkeley)
TITLE: Moment Varieties of Measures on Polytopes
The uniform probability measure on a convex polytope induces piecewise polynomial densities on the projections of that polytope. For a fixed combinatorial type, the moments of these measures are rational functions in the vertex coordinates. We study projective varieties that are parametrized by such rational functions, with focus on the ideals defining these moment varieties. Special cases include Hankel determinantal ideals for polytopal splines, and relations among multisymmetric functions given by cumulants of a simplex. In general, our moment varieties are quite complicated, and they offer nice challenges, also for combinatorialists. This is joint work with Kathlen Kohn and Boris Shapiro.