EVENT DETAILS AND ABSTRACT

Title: New upper bounds on sphere packings and spherical codes
Speaker: Naser Talebizadeh Sardari
Speaker Info: MPIM & IAS
Brief Description:
Special Note:
Abstract:

We discuss an optimal upper bound on the sphere packing density of almost all integral lattices with co-volume 1 and a new method and upper bound on the density of the spherical codes in high dimensions. Our new method is inspired by the Selberg upper bound sieve in analytic number theory. One of the main novelties of our work is that we work with extremal functions rather than extremal polynomials. As a special case, we recover Levenshtein's extremal polynomials of both odd and even degrees with a different method. Our bounds on spherical codes are joint work with Masoud Zargar.