Mathematics Colloquium Speaker: Prof. Ravi Raghunathan Date: Friday, 9 September 2022 Duration: 4.00-5.00 pm Venue: Ramanujan Hall, Mathematics Department, Room 214 Title: Sphere packing, the Uncertainty Principle, $E_8$ and Fourier interpolation on the real line Abstract: The talk will focus on two theorems of M. Viazovska who was awarded the Fields medal in Helsinki earlier this year. The first theorem resolved the problem of sphere packing in eight dimensions, while the closely related second theorem (proved jointly with D. Radchenko) establishes a new "Fourier interpolation" result for even Schwartz functions on the real line. The first half of the talk should be completely accessible to anyone with a first course in linear algebra and multivariable calculus (MA 109, MA 111, MA 106), and thus to most undergraduate students at IIT. The second half will require some familiarity with basic complex analysis (MA 205).