Departmental Colloquium
Mathilde Gerbelli-Gauthier
University of Toronto
Sphere-Packing, Fourier Interpolation, and the Segal--Shale--Weil Representation
Abstract: In 2016, Viazovska proved that the $E_8$ lattice provides the optimal
sphere-packing in dimension 8, and soon after,
Cohn--Kumar--Miller--Radchenko--Viazovska proved the analogous result
for the Leech lattice in dimension 24. Viazovska's breakthrough came
through the solution of a Fourier interpolation problem: she constructed
a function $f$ such that $f$, its Fourier transform, and their first
derivatives take on specific values at square roots of natural numbers.
Prior to this, Radchenko and Viazovska had solved a "toy case"—a
Fourier interpolation result for even Schwartz functions on the
real line. In this talk, I will explain how this one-dimensional
version can be understood through the lens of the Segal--Shale--Weil
representation, an infinite-dimensional representation that
originally arose in the context of quantum mechanics.
Friday February 28, 2025 at 3:00 PM in 636 SEO