Seminar in Algebraic Geometry and Number Theory

Abstract: A sphere packing is an arrangement of spheres of equal size in n-dimensional Euclidean space with the property that the corresponding balls do not intersect except possibly along their boundaries. A sphere packing is called saturated if there is no room to insert more spheres of the same size in the packing. In this talk the focus will be on the class of lattice sphere packings which are sphere packings where the spheres are centered at the points of a full rank lattice. The main goal is to discuss the probability that a random lattice sphere packing in high dimensions (where the lattice is sampled from the invariant measure on the space of n-dimensional lattices) is saturated. This is joint work with Matthew de Courcy-Ireland.