Joint Colloquium: Sinai Robins -- Asymptotics of cone theta functions, Gauss sums over parallelepipeds, and generalized Gram relations for polyhedra

We begin with cone theta functions, which are cousins of theta functions, but are
defined as a natural discretization of the volume of a spherical polytope.  We obtain
precise asymptotics of the cone theta function attached to any simplicial cone, near a
rational "cusp", and use these asymptotics to give new extensions of the Gram-relations
for the solid angles of faces of a simple rational polytope.