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October 1, 202019.00 |
Rob Morris "Erdős covering systems" |
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A covering system of the integers is a finite collection of arithmetic progressions whose union is the set $\mathbb{Z}$. The study of these objects was initiated by Erdős in 1950, and over the following decades he asked a number of beautiful questions about them. Most famously, his so-called "minimum modulus problem" was resolved in 2015 by Hough, who proved that in every covering system with distinct moduli, the minimum modulus is at most $10^{16}$. In this talk I will present a variant of Hough's method, which turns out to be both simpler and more powerful. In particular, I will sketch a short proof of Hough's theorem, and discuss several further applications. I will also discuss a related result, proved using a different method, about the number of minimal covering systems. Joint work with Paul Balister, Béla Bollobás, Julian Sahasrabudhe and Marius Tiba. See more
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Welcome!
We are the Laboratory of Combinatorial and Geometric Structures at the Moscow Institute of Physics and Technology. On this website, you can learn about Lab activities and members, as well as related events and useful materials like past and future workshops, talks, and video lectures. The lab aims to initiate collaboration and exchange between foreign and Russian researchers who work on different theoretical questions in the fields of Combinatorics, Discrete and Computational Geometry, and Theoretical Сomputer Science, and it was formed in December 2019.
Head of the laboratory: Prof. János Pach
Vice-head: Dr. Andrey Kupavskii
Assistant head: Dr. Alexandr Polyanskii