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 is small, what can we say about the structures of and ? In the case of th ...

at the interface of

harmonic analysis Harmonic analysis is a branch of mathematics concerned with investigating the connections between a function and its representation in frequency. The frequency representation is found by using the Fourier transform for functions on unbounded do ...

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

Sanders studied mathematics 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 ...

, 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 ...

supervised by

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 ...

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 p ...

ship at

Christ's College, Cambridge Christ's College is a Colleges of the University of Cambridge, constituent college of the University of Cambridge, England. The college includes the Master, the Fellows of the College, and about 450 undergraduate and 250 graduate students. The c ...

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

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

in 2007, the MSRI in 2008, and the

Mittag-Leffler Institute The Mittag-Leffler Institute (Swedish: Institut Mittag-Leffler) is a mathematical research institute in Sweden. Located in Djursholm, a suburb of Stockholm, it invites scholars to participate in half-year programs in specialized mathematical su ...

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 The University of Oxford is a collegiate university, collegiate research university in Oxford, England. There is evidence of teaching as early as 1096, making it the oldest university in the English-speaking world and the List of oldest un ...

, 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 a Colleges of the University of Oxford, constituent college 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 ...

. 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 Mo ...

on three-term

arithmetic progression An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that ...

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 a prize awarded each year by the Faculty of Mathematics at St John's College to a UK-based mathematician for distinguished research in mathematical sciences. The prize is named after the mathematician John Couch Adams and wa ...

(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. He is best known for submitt ...

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

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

". 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 curren ...

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. Whitehe ...

of the

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

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 In additive combinatorics, a discipline within mathematics, Freiman's theorem is a central result which indicates the approximate structure of sets whose sumset is small. It roughly states that if , A+A, /, A, is small, then A can be contained in ...

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 ...

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 Fellows of the Royal Society