Time: 16:30-18:00

Location: Mondi 2b / Central Building

Speaker 1: Nikita P. Kalinin

Title: Factorization Norms and the Lower Triangular All-Ones Matrix

Abstract: Matrix norms provide a useful way to study structured linear operators. In this talk, I will discuss the γ2 norm, a factorization norm with roots in functional analysis and important applications in combinatorial discrepancy and theoretical computer science, including communication complexity and differential privacy. I will focus on a particularly simple but surprisingly subtle example: the lower triangular matrix of all ones, also known as the greater-than matrix or the prefix-sum matrix. Besides being a natural test case for the theory, this matrix arises in the private continual summation problem, one of the main motivations for our work, and is connected to practical methods for private machine learning used at Google. I will present results from our recent paper that improve both the lower and upper bounds for the γ2 norm of this matrix, including an improvement over the best previously known upper bound, which dates back about thirty years.

Speaker 2:  Oleksii Kolupaiev

Title: Eigenvalues of iid matrices are hyperuniform

Abstract: We prove that the point process of the eigenvalues of real or complex non-Hermitian matrices X with independent, identically distributed entries is hyperuniform: the variance of the number of eigenvalues in a subdomain Ω of the spectrum is much smaller than the volume of Ω. Our main technical novelty is a very precise computations of the covariance between the resolvents of the Hermitization of X - z1, X - z2, for two distinct complex parameters z1, z2.