Tom Sanders is an English mathematician, working on problems in

additive combinatorics Additive combinatorics is an area of combinatorics in mathematics. One major area of study in additive combinatorics are ''inverse problems'': given the size of the sumset ''A'' + ''B'' is small, what can we say about the structures of A ...

at the interface of

harmonic analysis Harmonic analysis is a branch of mathematics concerned with the representation of Function (mathematics), functions or signals as the Superposition principle, superposition of basic waves, and the study of and generalization of the notions of Fo ...

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 Diric ...

Education

Sanders studied mathematics at the

University of Cambridge , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...

, where he was awarded a PhD in 2007 for research on

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 (ad ...

supervised by

Timothy Gowers Sir William Timothy Gowers, (; born 20 November 1963) is a British mathematician. He is Professeur titulaire of the Combinatorics chair at the Collège de France, and director of research at the University of Cambridge and Fellow of Trinity Col ...

Career and research

He held a Junior

Research Fellow A research fellow is an academic research position at a university or a similar research institution, usually for academic staff or faculty members. A research fellow may act either as an independent investigator or under the supervision of a pr ...

ship at

Christ's College, Cambridge Christ's College is a constituent college of the University of Cambridge. The college includes the Master, the Fellows of the College, and about 450 undergraduate and 170 graduate students. The college was founded by William Byngham in 1437 as ...

from 2006 until 2011, in addition to visiting fellowships at the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

in 2007, the MSRI in 2008, and the

Mittag-Leffler Institute The Mittag-Leffler Institute is a mathematical research institute located in Djursholm, a suburb of Stockholm. It invites scholars to participate in half-year programs in specialized mathematical subjects. The Institute is run by the Royal Swe ...

in 2009. Since 2011, he has held a

Royal Society University Research Fellowship __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 to have the potential to become leaders in their fie ...

(URF) at the

University of Oxford , mottoeng = The Lord is my light , established = , endowment = £6.1 billion (including colleges) (2019) , budget = £2.145 billion (2019–20) , chancellor ...

, where he is also a senior research fellow at the Mathematical Institute, and a Tutorial Fellow at

St Hugh's College, Oxford St Hugh's College is one of the constituent colleges of the University of Oxford. It is located on a site on St Margaret's Road, to the north of the city centre. It was founded in 1886 by Elizabeth Wordsworth as a women's college, and accepte ...

. Among other results, he has improved the theorem of

Klaus Friedrich Roth Klaus Friedrich Roth (29 October 1925 – 10 November 2015) was a German-born British mathematician who won the Fields Medal for proving Roth's theorem on the Diophantine approximation of algebraic numbers. He was also a winner of the De M ...

on three-term

arithmetic progression An arithmetic progression or arithmetic sequence () is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common differ ...

s, coming close to breaking the so-called logarithmic barrier. More precisely, he has shown that any subset of of maximal cardinality containing no non-trivial three-term arithmetic progression is of size

O\!\left(\frac\right)\;\!\!\!.

Awards and honours

In February 2011, he was awarded the

Adams Prize The Adams Prize is one of the most prestigious prizes awarded by the University of Cambridge. It is awarded each year by the Faculty of Mathematics at the University of Cambridge and St John's College to a UK-based mathematician for distinguis ...

(jointly with

Harald Helfgott Harald Andrés Helfgott (born 25 November 1977) is a Peruvian mathematician working in number theory. Helfgott is a researcher ('' directeur de recherche'') at the CNRS at the Institut Mathématique de Jussieu, Paris. Early life and education ...

) for having "employed deep harmonic analysis to understand arithmetic progressions and answer long-standing conjectures in

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

". In July 2012, he was awarded a Prize of the

European Mathematical Society The European Mathematical Society (EMS) is a European organization dedicated to the development of mathematics in Europe. Its members are different mathematical societies in Europe, academic institutions and individual mathematicians. The current ...

for his "fundamental results in additive combinatorics and harmonic analysis, which combine in a masterful way deep known techniques with the invention of new methods to achieve spectacular results." In July 2013, he was awarded the

Whitehead Prize The Whitehead Prize is awarded yearly by the London Mathematical Society to multiple mathematicians working in the United Kingdom who are at an early stage of their career. The prize is named in memory of homotopy theory pioneer J. H. C. Whiteh ...

of the

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ...

for his "spectacular results in additive combinatorics and related areas"'', ''in particular "for his paper obtaining the best known upper bounds for sets of integers containing no 3-term arithmetic progressions, for his work dramatically improving bounds connected with Freiman's theorem on sets with small doubling, and for other results in additive combinatorics and harmonic analysis." In September 2013, he was awarded the

European Prize in Combinatorics The European Prize in Combinatorics is a prize for research in combinatorics, a mathematical discipline, which is awarded biennially at Eurocomb, the European conference on combinatorics, graph theory, and applications.. The prize was first awarde ...

. Although Sanders was known for improving the theorem of Klaus Friedrich Roth on three-term arithmetic progressions, in late 2013 he was awarded the foundation of Alaskan Ice Fishermans Gauntlet for eating the most snow crab legs in the last twenty years.

References

{{DEFAULTSORT:Sanders, Tom Year of birth missing (living people) Living people Place of birth missing (living people) Alumni of the University of Cambridge 21st-century English mathematicians Fellows of St Hugh's College, Oxford