Speaker: Thomas Bloom, Royal Society University Research Fellow, University of Oxford

Date: Apr 18, 2022

Time: 16:00-17:00

Location: Zoom

Sponsor: School of Mathematics, Shandong University

Abstract:

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 n_i 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.

For more information, please visit:

https://www.view.sdu.edu.cn/info/1020/164457.htm