In geometry, sphere packing refers to the arrangement of non-overlapping spheres within a containing space. An everyday example would be how oranges may be stacked as closely and thus efficiently as possible. What appears to be a rather ordinary task, has stumped mathematicians for centuries. It was only in 1998 that it had been proven that the best solution for packing spheres in a three-dimensional space was in the shape of a pyramid. In 2022, Maryna Viazovska received the prestigious Fields Medal, often described as the Nobel Prize of Mathematics, for solving the sphere-packing problem in 8 and 24 dimensions. Viazovska, who holds the Chair of Number Theory at École Polytechnique Fédérale de Lausanne, proved that the E8 lattice provides the densest packing of identical spheres in eight dimensions. At Falling Walls, Viazovska discusses how she solved the long-standing problem in a particularly elegant way. She also provides a sense of what it was like to conduct her research in the context of the war in Ukraine.
Falling Walls
Falling Walls Science Summit 2023
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Packing Spheres in 8 and 24 Dimensions: Breaking the Wall of Unsolved Mathematics Problems
Maryna Viazovska did her bachelor studies at the Kyiv National Taras Shevchenko University and completed her MSc at the Technical University Kaiserslautern. She obtained her PhD in 2013 in Bonn. She was a postdoctoral researcher at the Institut des Hautes Etudes Scientifiques and at the Humboldt University of Berlin, and in 2017 was a Minerva Distinguished Visitor at Princeton University. She joined EPFL in 2017 as Tenure-Track Assistant Professor and was promoted Full Professor in 2018. She has received a Fields Medal, a prestigious honor often described as the Nobel Prize of Mathematics, for her work on the sphere-packing problem in dimensions 8 and 24. Previously, the problem had been solved for only three dimensions or fewer.
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