Number Theory and Random Geometry Seminar
Speaker: Nihar Gargava, Institut de Mathématiques d'Orsay, Université Paris-Saclay,
Host: Sudhir R. Ghorpade
Title: Random lattices that are modules over the ring of integers
Day, Date and Time: Wednesday, 4th February 2026 at 4 pm
Venue: Ramanujan Hall, Dept. of Mathematics
Abstract: We investigate the average number of lattice points within a ball where the lattice is chosen at random from the set of unit determinant ideals or modules lattices of some cyclotomic number field. The goal is to consider the space of such lattices as a probabilistic space and then study the distribution of lattice point counts. This is inspired by the connections of this problem to lattice-based cryptography and sphere packings in a high dimensional Euclidean space. Based on joint work with Vlad Serban, Maryna Viazovska, Ilaria Viglino.