Ukrainian scientist Maryna Viazovska has been awarded the Salem Prize 2016, a prestigious distinction in mathematics.
Viazovska has solved two high-dimensional versions of the “sphere packing” problem. In dimensions 8 and 24, she proved that two highly symmetrical arrangements pack spheres together in the densest possible way.
The famous astronomer Johannes Kepler was first to outline the problem in 1611 because of the need to find the best ways to transport cannonballs on a ship. Though a solution to this problem of packing spheres in 2 dimensions seemed obvious, it was proven only in 1940.
Only two cases of the most effective packing of spheres were proven – for dimensions 2 and 3. Viazovska proved that the densest packing of spheres in an 8-dimensional space is determined by the crystal lattice E8, in a 24-dimensional space – by the Leech lattice. This grid was built by the British mathematician Leech in connection with so-called Golay code (code error correction), which is used to transfer spacecraft “Voyager” pictures of Jupiter and Saturn.
The problem of the most effective ways of packing in 2-3 dimension space is also important for further application in crystallography, chemistry, and nanotechnology. Its practical application related to 8 or 24 dimensions is not that obvious, but unexpected results in the future are possible. The discovery is highly important for mathematics itself.
Viazovska is a researcher at the Berlin Mathematical School and the Humboldt University of Berlin. In 2010, she defended a PhD thesis at the Institute of Mathematics of the National Academy of Science titled “Inequalities for polynomial and rational functions and quadrature formulas on the field.” In 2013 she got a PhD in natural sciences at the University of Bonn with a thesis “Modular functions and special cycles.”
