Old and new ideas in sphere packing, Maryna Viazovska,
8/10/2023, Kyiv - Numbers in the Universe school and conference.
Lecture 4. Upper bounds for the sphere packing constant.
In the last lecture we will speak about upper bounds for the sphere packing constant. The exact value of the sphere packing constant is known only in dimensions 1,2,3,8 and 24. We will briefly speak about the methods used to prove each of these results. We will mostly focus on dimensions 8 and 24 and the Cohn-Elkies linear programming bound which has lead to the sharp result in these two dimensions.