Thomas F. Bloom is a mathematician, who is a
Royal Society University Research Fellow
__NOTOC__
The Royal Society University Research Fellowship (URF) is a research fellowship awarded to outstanding early career scientists in the United Kingdom who are judged by the Royal Society
The Royal Society, formally The Royal Society ...
at the
University of Manchester
The University of Manchester is a public university, public research university in Manchester, England. The main campus is south of Manchester city centre, Manchester City Centre on Wilmslow Road, Oxford Road. The University of Manchester is c ...
. He works in
arithmetic combinatorics
In mathematics, arithmetic combinatorics is a field in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis.
Scope
Arithmetic combinatorics is about combinatorial estimates associated with arithmetic operations ...
and
analytic number theory
In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Dir ...
.
Education and career
Thomas did his undergraduate degree in Mathematics and Philosophy at
Merton College, Oxford
Merton College (in full: The House or College of Scholars of Merton in the University of Oxford) is a Colleges of the University of Oxford, constituent college of the University of Oxford in England. Its foundation can be traced back to the 126 ...
. He then went on to do his PhD in mathematics at the
University of Bristol
The University of Bristol is a public university, public research university in Bristol, England. It received its royal charter in 1909, although it can trace its roots to a Merchant Venturers' school founded in 1595 and University College, Br ...
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
The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...
with
Timothy Gowers
Sir William Timothy Gowers, (; born 20 November 1963) is a British mathematician. He is the holder of the Combinatorics chair at the Collège de France, a director of research at the University of Cambridge and a Fellow of Trinity College, Camb ...
. In 2021, he joined the University of Oxford as a Research Fellow. Then, in 2024, he moved to the University of Manchester, where he also took on a Research Fellow position.
Research
In July 2020, Bloom and Sisask proved that any set such that
diverges must contain arithmetic progressions of length 3. This is the first non-trivial case of a
conjecture
In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis or Fermat's conjecture (now a theorem, proven in 1995 by Andrew Wiles), ha ...
of
Erdős
Erdős, Erdos, or Erdoes is a Hungarian surname.
Paul Erdős (1913–1996), Hungarian mathematician
Other people with the surname
* Ágnes Erdős (1950–2021), Hungarian politician
* Brad Erdos (born 1990), Canadian football player
* Éva Erd� ...
postulating that any such set must in fact contain arbitrarily long arithmetic progressions.
In November 2020, in joint work with
James Maynard, he improved the best-known bound for
square-difference-free sets, showing that a set