turkmath.org

Sphere packing is an extremely old problem, yet both widely applied in various domains and very challenging and active mathematically. From inexpected applications to industry to minimizing quadratic forms, from piling up oranges to the mysterious Einstein hat that tiles the plane in an a-periodic way, from very naive questions to the most modern maths (culminating with the groundbreaking achievement of Maryna Viazovska in 2018 to determine the optimal sphere packing in dimensions 8 and 24), I will present some of the developments and ideas behind these questions. These feature in particular beautifully rich mathematical objects: modular forms, which are at the heart of the "modular magic" used by Viazovska, allowing to make the proof of the sphere packing surprisingly accessible.