Maryna Viazovska
fl. 1984, Kyiv, Ukrainian SSR
Arithmetic and number theoryAnalysisGeometryFields Medal 2022
Ukrainian mathematician who solved the sphere-packing problem in dimensions 8 and 24 using modular forms and interpolation.
Maryna Viazovska discovered special functions with remarkable Fourier-interpolation properties and used them to prove optimality of the E8 and Leech lattice packings. Her work completed the sharp dimensions left open after the three-dimensional sphere-packing problem and earned the 2022 Fields Medal.
Workplaces: EPFL
Ukraine, Switzerland
Award-winning work
Fields Medal 2022Awarded for solving the sphere-packing problem in dimensions 8 and 24. In 2016 Viazovska proved that the E8 lattice gives the densest packing of congruent spheres in eight dimensions, by constructing a magic function — a radial Schwartz function whose Fourier-analytic properties force every packing to be no denser than the E8 arrangement — out of modular forms. With Cohn, Kumar, Miller, and Radchenko the method was rapidly extended to dimension 24 and the Leech lattice. Her work established a powerful bridge between discrete geometry and the theory of modular forms.