Speaker: Nihar Gargava, EPFL
Time: Monday 9th November 4 to 5pm (joining time 3.45 pm IST)
Google Meet Link:
https://meet.google.com/qvo-kduy-yco
Title: Asymptotic Lower Bounds on Sphere Packing Efficiency of Lattices
Abstract: In 1945, Siegel showed that the expected value of the
lattice-sums of a function over all the lattices of unit covolume in an
n-dimensional real vector space is equal to the integral of the function.
In 2012, Venkatesh restricted the lattice-sum function to a collection of
lattices that had a cyclic group of symmetries and proved a similar mean
value theorem. Using this approach, new lower bounds on the most optimal
sphere packing density in n dimensions were established for infinitely
many n. We will discuss this result, and some surrounding literature.
The talk will only assume the knowledge of Haar measure.