The distortion method and its applications
Jonah Klein (University of South Carolina)
| Thu Jul 16, 15:30-15:55 (6 days from now) | |
| Lecture held in Science Center in the CUNY Graduate Center (4th floor). |
Abstract: A covering system is a finite set of arithmetic progressions, with the property that every integer belongs to at least one of them. Covering systems were introduced by Erdös in 1950. In the same article where he introduced them, he asked if there was a uniform upper bound on the smallest modulus of covering systems with distinct moduli. This problem was resolved by Hough in 2015, showing that the smallest modulus is always smaller than $10^{16}$. Expanding upon his work, Balister, Bollobás, Morris, Sahasrabudhe, and Tiba reduced this bound to $616 000$, with a method that they coined the distortion method. The aim of this talk is to give a brief overview of the distortion method and its applications, with a particular focus on showing that it is impossible to construct 10 disjoint distinct covering systems. This is work in progress with Michael Filaseta and Alexandros Kalogirou.
number theory
Audience: researchers in the topic
Combinatorial and additive number theory seminar (CANT 2026)
| Organizer: | Mel Nathanson* |
| *contact for this listing |