The densest packing of equal spheres in the two-dimensional Euclidean space corresponds to the well-known hexagonal lattice (or honeycomb). However, already in dimension three the proof of the result on the densest sphere packing is rather difficult. Nevertheless, in 2016 Maryna Viazovska elegantly, but relatively easy (by means of modular forms), proved that the packing corresponding to the Korkine–Zolotareff lattice is the densest in ${\mathbb R}^8$. In this course we provide the details of Viazovska's proof.

Financial support. The course is supported by the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, Agreement no. 075-15-2019-1614).

Lecturer
Rezvyakova Irina Sergeevna

Organizations
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center