Geometry Seminar

Date: April 24, 2014

Time: 2:15PM - 3:15PM

Location: Blocker 627 - No

Speaker: Shamgar Gurevich, U. Wisconson

Title: Weil representations and explicit Mordell--Weil lattices

Abstract: The Weil representation is a central object in mathematics. It explains the zero point energy of crystals in quantum mechanics, it can be used to prove the Quadratic Reciprocity Law, and to derive the theory of spherical harmonics. In this talk, the Weil representation will be applied to sphere packing. I will an show explicit construction of the Weil representation of the conformal symplectic group GSp(2N,p) acting on a vector space over Q -the rationals. In case p=1 mod 4, this can be used to give an explicit construction for the Weil representation of the symplectic group Sp(2N,p) acting on a vector space over Q(Gauss) - the field of rationals numbers extended by a Gauss sum. If time permits, I will apply this to explicit constructions of the Mordell-Weil lattices which give very good sphere packings.