Boaz Klartag, speaking at the Institute for Advanced Study's Member's Seminar, presents a new result in the geometry of numbers: for every dimension n there exists an origin-symmetric ellipsoid of volume on the order of n squared that contains no nonzero points of the integer lattice Z^n. That construction translates directly into a lattice sphere packing in R^n with density at least on the order of n squared over 2^n, improving on earlier constructions that only reached densities around n over 2^n up to logarithmic factors. Klartag walks through the core mechanism, a stochastically evolving ellipsoid that grows until it collects roughly n squared lattice points on its boundary while keeping its interior free of lattice points apart from the origin. The talk is aimed at a research audience already comfortable with lattice packings and convex geometry, building the argument step by step from the stochastic process to the density bound. It runs 71 minutes and covers one complete proof rather than a survey of the field.