We solve steps of the Lasserre hierarchy for various topological packing graphs. New techniques were necessary to do so and this thesis focuses on the calculation of the zonal Stiefel harmonics. First, we develop an appropriate harmonic analytical framework. To use this, the subspaces of representations of the orthogonal group, which are invariant under a subgroup, have to be determined. Then, the matrix coefficients of these invariants have to be calculated in practice. We give two methods to do so. For the equiangular lines problem with a fixed angle this leads to new bounds. For the kissing number problem in dimension four, a sharp optimal solution is obtained. Via complementary slackness, this leads to the new result that the D4 root system is the unique optimal kissing configuration in dimension four.