Sphere Packings in Four Dimensions

In this talk I'm going discuss reasonable approaches for solutions to problems related to densest sphere packings in 4-dimensional Euclidean space. I consider two long–standing open problems: the uniqueness of maximum kissing arrangements in 4 dimensions and the 24–cell conjecture. Note that a proof of the 24-cell conjecture also proves that $D_4$ is the densest sphere packing in 4 dimensions.