Máté Matolcsi: A comparison of the Delsarte bound and the volume packing bound for convex bodies

Given a convex body K in R^d, it is a natural question how densely one can pack translated copies of K in the space. The most famous example, of course, is the density of sphere packings. The Delsarte linear programming bound applies to this situation, and we will show that it always gives a strictly better bound than the trivial volume packing bound, whenever K is not a tile. (When K is a tile, the packing problem is trivial, and both bounds give the optimal estimate.)

Based on joint work with M. Kolountzkis and N. Lev.