Speaker: Nihar Gargava
Date: February 03, 2026
Affiliation: Paris-Saclay University

Abstract: In the first part, we will talk about random lattices that are modules over the ring of integers of a cyclotomic number field. We will also go over the connections of this topic to the packing of Euclidean spheres in high dimensions. This is joint work with V. Serban, M. Viazovska, I. Viglino In the second part, I will speak about lattices that come from the multiplicative groups of units of an order in a totally real cubic number field. We plot these lattices in the appropriate moduli space of Euclidean lattices in 2 dimensions and ask where the points lie. It was conjectured by David-Shapira that these unit lattices generate a dense set of lattices. I will explain the problem and sketch the proof. This is joint work with N. T. Dang and J. Li