## Linear Analysis Seminar

**Date:** November 10, 2017

**Time:** 4:00PM - 5:00PM

**Location:** BLOC 220

**Speaker:** Florin Boca, University of Illinois at Urbana-Champaign

**Title:** *Farey statistics and the distribution of eigenvalues in large sieve matrices*

**Abstract:** Some parts of the fine distribution of Farey fractions (a.k.a. roots of unity) is captured by their spacing statistics (consecutive gaps and correlations). A large sieve matrix is a N x N matrix A*A, where A is a Vandermonde type matrix defined by roots of unity of order at most Q. The classical large sieve inequality provides an upper bound estimate for the largest eigenvalue of A*A. This talk will discuss some connections between these topics. We will focus on the behavior of these matrices when N ~ cQ^2, with Q --> infty and c>0 constant, establishing asymptotic formulas for their moments and proving the existence of a limiting distribution for their eigenvalues as a function of c. This is joint work with Maksym Radziwill.