3:45PM: Moment Varieties of Measures on PolytopesBernd SturmfelsThe uniform probability measure on a convex polytope induces piecewise polynomial densities on the projections of that polytope. For a fixed combinatorial type of simplicial polytopes, the moments of these measures are rational functions in the vertex coordinates. We study projective varieties that are parametrized by finite collections of such rational functions. Our focus lies on determining the prime ideals of these moment varieties. Special cases include Hankel determinantal ideals for polytopal splines on line segments, and the relations among multisymmetric functions given by the cumulants of a simplex. In general, our moment varieties are more complicated, and they offer nice challenges for both numerical and symbolic computing in algebraic geometry. This is joint work with Kathlen Kohn and Boris Shapiro.

3:45PM: Moment Varieties of Measures on PolytopesBernd SturmfelsThe uniform probability measure on a convex polytope induces piecewise polynomial densities on the projections of that polytope. For a fixed combinatorial type of simplicial polytopes, the moments of these measures are rational functions in the vertex coordinates. We study projective varieties that are parametrized by finite collections of such rational functions. Our focus lies on determining the prime ideals of these moment varieties. Special cases include Hankel determinantal ideals for polytopal splines on line segments, and the relations among multisymmetric functions given by the cumulants of a simplex. In general, our moment varieties are more complicated, and they offer nice challenges for both numerical and symbolic computing in algebraic geometry. This is joint work with Kathlen Kohn and Boris Shapiro.

5:00PM: TensorMultinomial Sums of Ideals and ApplicationsRobert WalkerGiven a polynomial ring $C$ over a field and proper ideals $I$ and $J$ whose generating sets involve disjoint variables, we determine how to embed the associated primes of each power of $I+J$ into a collection of primes described in terms of the associated primes of select powers of $I$ and of $J$. We discuss applications to constructing primary decompositions for powers of $I+J$, and to attacking the persistence problem for associated primes of powers of an ideal. This is joint work with Irena Swanson found on arXiv:1806.03545.
