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.