FIM Lectures
FIM Lectures are single, one-hour lectures given by renowned mathematicians. They are designed as a platform for the speaker to present his or her latest results, and they are usually followed by an apéro that offers room for further in-depth discussions.
Upcoming FIM Lectures
FIM Lecture
Friday, 24 April 2026, 16:15, HG D 7.2
Prof. Béla Bollobás (University of Cambridge)
Covering Systems
Covering systems, that is, finite collections of arithmetic progressions whose union is \(\mathbb{Z}\), were introduced by Paul Erdős in 1934, but published only in 1950. Of the hundreds of questions and conjectures he posed, questions concerning these systems remained his favourite all his life. The problem he liked best, whether for every constant \(C > 0\) there was a distinct covering systems (one with distinct moduli) whose every modulus at least \(C\), was solved only in 2015 by Hough. We shall review some of the main results about covering systems, including several of the results due to Balister, Morris, Sahasrabudhe, Tiba and me, and shall mention some open problems concerning them.
The lecture is followed by an apéro.