Thomas Bloom

Thomas did his undergraduate degree in Mathematics and Philosophy at Merton College, Oxford. He then went on to do his PhD in mathematics at the University of Bristol under the supervision of Trevor Wooley. After finishing his PhD, he was a Heilbronn Research Fellow at the University of Bristol. In 2018, he became a postdoctoral research fellow at the University of Cambridge with Timothy Gowers. In 2021, he joined the University of Oxford as a Research Fellow.{{Cite web |title=Thomas Bloom |url=http://thomasbloom.org/aboutme.html |access-date=2022-07-28 |website=thomasbloom.org}} Then, in 2024, he moved to the University of Manchester, where he also took on a Research Fellow position.

In July 2020, Bloom and Sisask{{Cite arXiv|last1=Bloom |first1=Thomas F. |last2=Sisask |first2=Olof |date=2021-09-01 |title=Breaking the logarithmic barrier in Roth's theorem on arithmetic progressions |eprint=2007.03528|class=math.NT }} proved that any set such that $\backslash sum\_\{n\; \backslash in\; A\}\; \backslash frac\{1\}\{n\}$ diverges must contain arithmetic progressions of length 3. This is the first non-trivial case of a conjecture of Erdős postulating that any such set must in fact contain arbitrarily long arithmetic progressions.{{cite web |last1=Spalding |first1=Katie |title=Math Problem 3,500 Years In The Making Finally Gets A Solution |url=https://www.iflscience.com/math-problem-3500-years-in-the-making-finally-gets-a-solution-62925 |website=IFLScience |date=11 March 2022 |access-date=28 July 2022 |language=en}}{{cite web |last1=Klarreich |first1=Erica |title=Landmark Math Proof Clears Hurdle in Top Erdős Conjecture |url=https://www.quantamagazine.org/landmark-math-proof-clears-hurdle-in-top-erdos-conjecture-20200803/ |website=Quanta Magazine |access-date=28 July 2022 |language=en |date=3 August 2020}}

In November 2020, in joint work with James Maynard,{{Cite arXiv|last1=Bloom |first1=Thomas F. |last2=Maynard |first2=James |title=A new upper bound for sets with no square differences |date=24 February 2021|class=math.NT |eprint=2011.13266 }} he improved the best-known bound for square-difference-free sets, showing that a set $A\; \backslash subset\; [N]$ with no square difference has size at most $\backslash frac\{N\}\{(\backslash log\; N)^\{c\backslash log\; \backslash log\backslash log\; N\}\}$ for some $c>0$.

In December 2021, he proved {{Cite arXiv|last=Bloom |first=Thomas F. |date=2021-12-07 |title=On a density conjecture about unit fractions |eprint=2112.03726v2|class=math.NT}} that any set $A\; \backslash subset\; \backslash mathbb\{N\}$ of positive upper density contains a finite $S\; \backslash subset\; A$ such that $\backslash sum\_\{n\; \backslash in\; S\}\; \backslash frac\{1\}\{n\}=1$.{{Cite web |last=Cepelewicz |first=Jordana |date=2022-03-09 |title=Math's 'Oldest Problem Ever' Gets a New Answer |url=https://www.quantamagazine.org/maths-oldest-problem-ever-gets-a-new-answer-20220309/ |access-date=2022-07-28 |website=Quanta Magazine |language=en}} This answered a question of Erdős and Graham.{{cite web | last=Erdos | first=P. | last2=Graham | first2=R. |author-link1=Paul Erdős |author-link2=Ronald Graham| title=Old and new problems and results in combinatorial number theory |publisher=L'Enseignement Mathématique|location=Université de Genève| website=Semantic Scholar | date=1980 | url=https://www.semanticscholar.org/paper/Old-and-new-problems-and-results-in-combinatorial-Erdos-Graham/eb4df07db4226b5fa73fe2e2292044f5a789558b | access-date=23 April 2024}}

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Category:Royal Society University Research Fellows

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Category:Alumni of Merton College, Oxford

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