Laboratory of combinatorial and geometric structures

The next Big Seminar:

событие October 1, 202019.00

Rob Morris "Erdős covering systems"

Big Seminar Zoom

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.

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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

Recent video lectures:

Recent video lectures:

REC $Rightarrow$ Watch the videos from our conference in April (in process)

Recent big seminar videos

Recent events:

событие December 18 MIPT Cifra 2.35

Lecture by Balázs Patkós "Turán problems with dergee conditions"

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событие November 29 and December 2 MIPT Arctica

Mini-course by István Tomon "Intersection graphs of geometric objects"

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событие November 26-28 MIPT Arctica

Mini-course by Gábor Tardos "Extremal theory of vertex- and edge-ordered graphs"

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All events

Video lectures:

Oleg Musin
Sphere packings in low dimensions (in Russian)
The lecture by Oleg Rustamovich Musin that took place on December 20, 2019 as a part of Mathematical Workshop of the School of Applied Mathematics and Computer Science at MIPT
Gábor Tardos
Extremal theory of vertex- and edge-ordered graphs
Mini-course by Gábor Tardos. Two lectures were part of the "Combinatorics and Geometry Days I" conference on November 26-27, and the last one took place on November 28.
István Tomon
Intersection graphs of geometric objects
The two-lecture course by István Tomon that took place on 29 November and 2 December 2019
István Tomon
Turán number of bipartite graphs with no $K_{t,t}$
At the Сonference “Combinatorics and Geometry Days I” at MIPT, 27 November 2019