Tom Sanders (mathematician)

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]
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]
Website	people.maths.ox.ac.uk/sanders

Tom Sanders FRS 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."^[12] In September 2013, he was awarded the European Prize in Combinatorics.^[13]

References

1. Anon (2017). "Dr Tom Sanders, Research Fellow". royalsociety.org. London: Royal Society. Archived from the original on 1 March 2017. 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". Archived from the original on 11 November 2016. Retrieved 9 March 2016.

2. Tom Sanders at the Mathematics Genealogy Project
3. 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 9 March 2017.
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. doi:10.1112/jlms/s1-28.1.104. MR 0051853. Zbl 0050.04002.
8. Sanders, Tom (2011). "On Roth's theorem on progressions". Annals of Mathematics. 174 (1): 619–636. arXiv:1011.0104. doi:10.4007/annals.2011.174.1.20. MR 2811612. S2CID 53331882.
9. "Helfgott and Sanders Awarded Adams Prize" (PDF). Notices of the American Mathematical Society. 58 (7): 966. 2011. (Reprinted from a University of Cambridge announcement.)
10. "6th European Congress of Mathematics". 6ecm.pl. Retrieved 9 March 2017.
11. "LMS Prizes 2014". Lms.ac.uk. UK: London Mathematical Society. 9 July 2013. Retrieved 9 March 2017.
12. "Nick Trefethen, Frances Kirwan, Fernando Alday and Tom Sanders awarded LMS prizes for 2013". UK: University of Oxford Mathematical Institute. 29 September 2014. Retrieved 3 June 2020.
13. "Tom Sanders wins the European Prize in Combinatorics". UK: University of Oxford Mathematical Institute. 29 September 2014. Retrieved 3 June 2020.