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Eigenfunctions Seminar

Title: Recent breakthroughs in sphere packing
Speaker: Abhinav Kumar (Stony Brook University, USA)
Date: 08 November 2019
Time: 3 – 5 pm (with a 15 minute break at 3:45)
Venue: LH-1, Mathematics Department

The sphere packing problem asks for the densest packing by congruent non-overlapping spheres in n dimensions. It is a famously hard problem, though easy to state, and with many connections to different parts of mathematics and physics. In particular, every dimension seems to have its own idiosyncracies, and until recently no proven answers were known beyond dimension 3, with the 3-dimensional solution being a tour de force of computer-aided mathematics.

Then in 2016, a breakthrough was achieved by Viazovska, solving the sphere packing problem in 8 dimensions. This was followed shortly by joint work of Cohn-Kumar-Miller-Radchenko-Viazovska solving the sphere packing problem in 24 dimensions. The solutions involve linear programming bounds and modular forms. I will attempt to describe the main ideas of the proof.

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 18 May 2024