Levi L. Conant 2018 LECTURE SERIES
Henry Cohn, Principal Research, Microsoft Research New England.
Adjunct Professor of Mathematics, MIT
Title: A conceptual breakthrough in sphere packing.
Abstract: What is the densest packing of congruent spheres in euclidean space? this problem arises naturally
in geometry, number theory, and information theory, but it is notoriously diﬃcult to solve, and
until recently no sharp bounds were known above three dimensions. In 2016 Maryna Viazovska found a
remarkable solution of the sphere packing problem in eight dimensions, which is much simpler than
the proof in three dimensions but tells us nothing about dimensions four through seven. In this
talk Cohn describes how her breakthrough works and where it comes from, as well as follow-up work
extending it to twenty-four dimensions (joint work with
Kumar, Miller, Radchenko, and Viazovska).