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Erdős covering systems

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OOEW04 - Structure and Randomness - a celebration of the mathematics of Timothy Gowers

Covering Systems (that is, finite collections of arithmetic progressions that cover the integers) were introduced by Paul Erdős over seventy years ago.The initial flow of results by Erdős, Davenport, Selfridge, Graham, and otherswas followed by a lull of activity for several decades. Although in the last twenty years several important results were proved, many old questions have remained open. In the talk I shall survey a number of the early results about covering systems, and then turn to the recent results obtained in several papers on the problems of Erdős and Selfridge; Schinzel; Filaseta, Ford, Konyagin Pomerance and Yu; and others.The results are joint with Balister, Morris, Sahasrabudhe and Tiba.

This talk is part of the Isaac Newton Institute Seminar Series series.

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