Dear all, happy 2020! I would like to announce the following seminar by G. Poly (U. Rennes 1). Best, Dario Trevisan #### time and place: Monday 13th January 2020, 14:00, sala Riunoni (dip. Matematica, università degli studi di Pisa, Pisa). speaker: Guillaume Poly (U. Rennes 1) title: Around Salem-Zygmund Central Limit Theorem and application to roots of random trigonometric polynomials abstract: We shall revisit the Salem-Zygmund Central limit Theorem and get several generalizations: a speed of convergence via Stein's method, a functional counterpart and extension to total variation topology. As an application we prove the almost-sure convergence of the empirical measure of the number of real roots of a random trigonometric polynomial under-mild conditions on the coefficients. This is a joint work with Jurgen Angst.