Three-point bounds for sphere packing

The sphere packing problems asks for the densest packing of Euclidean space by congruent balls that do not intersect in their interiors. The Cohn-Elkies linear programming bound can be used to obtain upper bounds on the optimal density and has been used by Viazovska and others to show the E_8 root lattice and Leech lattice configurations in dimensions 8 and 24 are optimal. In other dimensions (except for dimensions 1 and 2) the linear programming bound is not expected to be sharp and currently only small improvements on this bound are known. In this talk I will discuss new three-point bounds for sphere packing and lattice sphere packing that we use to obtain larger improvements.

Joint work with Henry Cohn and Andrew Salmon

Join Zoom Meeting
https://maths-cam-ac-uk.zoom.us/j/98523135167?pwd=U01ldkI1Vnk5OHpYeEo3UXJJUE1ZZz09

Meeting ID: 985 2313 5167
Passcode: 3aHUXI5F

• Speaker: David de Laat (Delft)
• Wednesday 20 October 2021, 14:00–15:00
• Venue: Virtual (Zoom details under abstract).
• Series: CCIMI Seminars; organiser: Hamza Fawzi.