Speaker: Simon Litsyn (Tel-Aviv University)

Title: "Recent Progress in Sphere-Packing Problems"

Abstract:
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In our talk we describe two recent breakthrough results in the theory of
sphere-packings in Euclidean spaces:

- Musin's proof that the kissing number (the maximum number of spheres
which can touch a central sphere without intersection) in 4 dimensions is
indeed 24. We will also show how the approach of this proof can be used to
show that the kissing number in 3 dimensions is 12 (the Newton-Gregory
problem);

- Cohn and Kumar's proof that the Leech lattice is the densest possible
lattice in 24 dimensions. We will also show how a similar proof works in  
8 dimensions for proving optimality of $E_8$.

No prior knowledge is required. We will introduce all the necessary
ingredients: lattices and spherical codes, Delsarte's method (used in both
problems), orthogonal polynomials and association schemes.