EVENT DETAILS AND ABSTRACT

Title: Sphere packing, Fourier interpolation, and Universal Optimality
Speaker: Steven D. Miller
Speaker Info:
Brief Description:
Special Note:
Abstract:

I will discuss recent work on the optimal arrangement of points in 8- and 24-dimensional euclidean space. In addition to the solution to the sphere packing problem in these dimensions from 2016, the "Universal Optimality" conjecture has now been solved as well. This shows that in these dimensions, E8 and the Leech lattice minimize energy for any completely monotonic function of distance-squared. Beyond implying the sphere packing results, it also gives information about long-range interactions. Another application is to find the global minimum of the log-determinant of the laplacian among flat tori in those dimensions. The techniques involve arranging both a function and its Fourier transform vanish at certain points, which leads to a new interpolation formula in harmonic analysis.

(joint with Henry Cohn, Abhinav Kumar, Danylo Radchenko, and Maryna Viazovska)