Title: The Sphere Packing Problem - A Breakthrough
Abstract: I will state the general sphere-packing problem in arbitrary dimensions. In three dimensions, the solution is familiar to fruit-sellers; and is known as Kepler’s Conjecture to Mathematicians. It is ‘considered’ solved sometime in the years 1998-2014. I will tell the story of this unusual solution. In higher dimensions, the problem is profoundly difficult. There was a breakthrough for dimension 8 in 2016 (uploaded on Pi-day) and then a week later for dimension 24. I will give a flavour of the solution and how it came about with the magical coming together of Linear Programming, Fourier Analysis and Analytic Number Theory. Dimension 8 is important to Physicists (The E8 theory: ‘An exceptionally Simple Theory of Everything’), and dimension 24 occurs in Error Correcting Codes.
There is no prerequisite!
The talk is largely in the nature of a mathematical storyline.
Prof. Shobha Madan is a distinguished harmonic analyst, who inspired generations of students at IIT-Kanpur by her example and instruction. After retiring from IIT Kanpur, she has held positions at IISER Mohali and IIT Goa. She had earlier visited SNU during April 2018 as our inaugural speaker under the Face to Face program initiated by the Department of Mathematics and the Mathematics Society.
