Speaker: Maryna Viazovska (EPFL)

Title: Random lattices with symmetries
Abstract: What is the densest lattice sphere packing in the d-dimensional Euclidean space? In this talk, we will investigate this question as the dimension goes to infinity, and we will focus on the lower bounds for the best packing density, or in other words, on the existence results. We will give a historical overview of the lower bounds proved by H. Minkowski, E. Hlawka, C. L. Siegel, C. A. Rogers, and more recently by S. Vance and A. Venkatesh. In the final part of the lecture, we will present recent work done in collaboration with V. Serban and N. Gargava on the moments of the number of lattice points in a bounded set for random lattices constructed from a number field.

Mathematics Hall, room 417 from 4:30 – 5:30pm

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