Maryna Viazovska

Maryna Viazovska is a Ukrainian mathematician who proved that the E8 lattice gives the densest sphere packing in eight dimensions and, with collaborators, that the Leech lattice does so in twenty-four dimensions.

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Sphere packing: The study of placing nonoverlapping equal spheres in space to maximize the fraction of space they occupy. Her theorems solve the densest-packing problem in two exceptional dimensions.
Cohn–Elkies linear programming bound: A Fourier-analytic upper bound on sphere-packing density derived from suitable auxiliary functions. Viazovska found functions that make this bound exact for the E8 lattice.
Henry Cohn: An American mathematician known for work on discrete geometry, optimization, and sphere packing. He coauthored the proof of optimal packing in twenty-four dimensions with Viazovska and others.
Sphere packing in eight dimensions: The problem of finding the densest arrangement of equal nonoverlapping spheres in eight-dimensional space. Viazovska proved that the E8 lattice achieves the maximum possible density.
Lattice: A discrete set of points generated by integer combinations of basis vectors. Both optimal configurations in her results are highly structured lattices.
Auxiliary function: A function introduced to establish an inequality or bound in a mathematical argument. The proof's specially designed functions certify that no packing can exceed the lattice density.
A. Kumar: A mathematician whose work includes sphere packing and discrete geometry. He coauthored the twenty-four-dimensional optimality proof.
Sphere packing in twenty-four dimensions: The problem of finding the densest arrangement of equal nonoverlapping spheres in twenty-four-dimensional space. The Leech lattice's optimality was proved by Viazovska and her collaborators.
E8 lattice: An exceptional eight-dimensional lattice with strong symmetry and a highly efficient sphere packing. Viazovska proved its sphere packing is optimal in eight dimensions.
Modular form: A complex analytic function with prescribed transformation behavior under a discrete group of fractional linear maps. Modular forms supply the structure behind the auxiliary function in eight dimensions.