News & Events
Speaker: Thomas Bloom, Royal Society University Research Fellow, University of Oxford
Date: Apr 18, 2022
Sponsor: School of Mathematics, Shandong University
In 2021 Croot resolved an old conjecture ofErdős and Graham, proving that in any finite colouring of the positive integers there is a (non-trivial) monochromatic solution to
with all ni distinct. A natural generalization, also conjectured by Erdős and Graham, is that in fact any set of positive density contains such a solution. We will discuss the proof of this conjecture, which extends Croot’s method, and uses Fourier analysis coupled with elementary number theoretic and combinatorial arguments. We will also review several still open
conjectures concerning unit fractions.
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