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.

Real Algebraic Geometry and Combinatorial Optimization Seminar
Speaker: Luca Wellmeier, UiT - The Arctic University of Norway
Host: Sudhir R. Ghorpade
Title: Hierarchies in Polynomial Optimization
Day, Date and Time: Wednesday, 4th February 2026 at 5.15 pm
Venue: Ramanujan Hall, Dept. of Mathematics
Abstract: In the first part, we explored polynomial optimization through the lens of the sum-of-squares hierarchy. By relaxing the question of non-negativity of a given polynomial by whether it is a sum-of-squares (SOS) or not, we were able to derive a tractable way for solving polynomial optimization problems: a series of semidefinite convex optimization problems that provide increasingly tight, certified bounds on the true solution. A recap can be found at https://lcwllmr.github.io/momsos/. The second talk will focus on the dual viewpoint. As we will see, the conic dual of the SOS cone is closely related to moment sequences of probability measures. We will end up with a second hierarchy of optimization problems that will turn out to be mostly equivalent to the SOS hierarchy. It allows for new insights into the original problem. As an application we will see how to use the moment perspective to extract concrete minimizers on top of just bounds.