# Tom Sanders (mathematician)

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Tom Sanders
Nationality British
Alma mater University of Cambridge
Known for Arithmetic combinatorics
Awards European Prize in Combinatorics (2013)
Whitehead Prize (2013)
EMS Prize (2012)
Adams Prize (2011)
Royal Society University Research Fellowship[1]
Website people.maths.ox.ac.uk/sanders
Scientific career
Fields Mathematics
Institutions University of Oxford
Thesis Topics in arithmetic combinatorics (2007)
Doctoral advisor Timothy Gowers[2]
Other academic advisors Ben Green[3]

Tom Sanders is an English mathematician, working on problems in additive combinatorics at the interface of harmonic analysis and analytic number theory.[4][5]

## Education

Sanders studied mathematics at the University of Cambridge, where he was awarded a PhD in 2007 for research on arithmetic combinatorics supervised by Timothy Gowers.[2][3]

## Career and research

He held a Junior Research Fellowship at Christ's College, Cambridge from 2006 until 2011, in addition to visiting fellowships at the Institute for Advanced Study in 2007, the MSRI in 2008, and the Mittag-Leffler Institute in 2009. Since 2011, he has held a Royal Society University Research Fellowship (URF)[1] at the University of Oxford, where he is also a Senior Research Fellow at the Mathematical Institute, and a Tutorial Fellow at St Hugh's College, Oxford.[6]

Among other results, he has improved the theorem of Klaus Friedrich Roth on three-term arithmetic progressions,[7] coming close to breaking the so-called logarithmic barrier. More precisely, he has shown that any subset of {1, 2, ..., N} of maximal cardinality containing no non-trivial three-term arithmetic progression is of size ${\displaystyle O\left({\frac {N(\log \log N)^{5}}{\log N}}\right)}$.[8]

### Awards and honours

In February 2011, he was awarded the Adams Prize (jointly with Harald Helfgott) for having "employed deep harmonic analysis to understand arithmetic progressions and answer long-standing conjectures in number theory".[9] In July 2012, he was awarded a Prize of the European Mathematical Society 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."[10] In July 2013, he was awarded the Whitehead Prize of the London Mathematical Society[11] 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."[citation needed] In September 2013, he was awarded the European Prize in Combinatorics.[citation needed]

## References

1. ^ a b Anon (2017). "Dr Tom Sanders, Research Fellow". royalsociety.org. London: Royal Society. Archived from the original on 2017-03-01. One or more of the preceding sentences incorporates text from the royalsociety.org website where:

“All text published under the heading 'Biography' on Fellow profile pages is available under Creative Commons Attribution 4.0 International License.” --Royal Society Terms, conditions and policies at the Wayback Machine (archived 2016-11-11)

2. ^ a b
3. ^ a b Sanders, Tom (2007). Topics in arithmetic combinatorics. cam.ac.uk (PhD thesis). University of Cambridge. OCLC 879379453.
4. ^ "Tom Sanders Homepage in Oxford". people.maths.ox.ac.uk.
5. ^ "Tom Sanders's articles on arXiv". Arxiv.org. Retrieved 2017-03-09.
6. ^ "Tom Sanders, Mathematical Institute". maths.ox.ac.uk.
7. ^ Roth, Klaus Friedrich (1953). "On certain sets of integers". Journal of the London Mathematical Society. 28: 104–109. MR 0051853. Zbl 0050.04002. doi:10.1112/jlms/s1-28.1.104.
8. ^ Sanders, Tom (2011), "On Roth's theorem on progressions", Annals of Mathematics, 174 (1): 619–636, MR 2811612, arXiv:, doi:10.4007/annals.2011.174.1.20
9. ^ (reprinted from a University of Cambridge announcement) (2011). "Helfgott and Sanders Awarded Adams Prize" (PDF). Notices of the American Mathematical Society. 58 (7): 966.
10. ^ "Home | 6th European Congress of Mathematics". 6ecm.pl. Retrieved 2017-03-09.
11. ^ "LMS Prizes 2014 | London Mathematical Society". Lms.ac.uk. 2013-07-09. Retrieved 2017-03-09.