Phoenix Cluster

2014-01-01T09:49:06Z

70.112.97.77: Not exactly "recent" activity - what we're seeing is a snapshot of something occurring more than 5 billion years ago; reworded accordingly

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

Sanders studied mathematics at the [[University of Cambridge]], taking his Ph.D. in 2007 under the direction of [[Timothy Gowers]]. He held a Junior Research Fellowship at [[Christ's College, Cambridge|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 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|St Hugh's College]].

Among several striking results, he has improved the well-known theorem of [[Klaus Friedrich Roth]] on three-term arithmetic progressions,<ref>K.F. Roth, ''On certain sets of integers'', Journal of the London Mathematical Society, Volume 28 (1953) 104–109</ref> 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 <math>O\left(\frac{N (\log \log N)^5}{\log N}\right)</math>.<ref>{{arxiv|1011.0104}}, [http://annals.math.princeton.edu/2011/174-1/p20].</ref>

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".<ref>{{cite journal|last=(reprinted from a University of Cambridge announcement)|title=Helfgott and Sanders Awarded Adams Prize|journal=[[Notices of the American Mathematical Society]]|publisher=AMS|volume=58|issue=7|pages=966|url=http://www.ams.org/notices/201107/rtx110700966p.pdf}}</ref> 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."<ref>[http://www.6ecm.pl/en Announcement of the 2012 Prizes of the European Mathematical Society]</ref> In July 2013, he was awarded the [[Whitehead Prize]] of the [[London Mathematical Society]] 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."<ref name=":0">http://www.lms.ac.uk/prizes/lms-prizes-2013</ref>
In September 2013, he was awarded the European Prize in Combinatorics. <ref>https://en.wikipedia.org/wiki/European_Prize_in_Combinatorics</ref>

==Notes==
{{Reflist|LMS Prizes 2013 = http://www.lms.ac.uk/prizes/lms-prizes-2013}}

==External links==
*[http://people.maths.ox.ac.uk/~sanders/ Homepage in Oxford]
*[http://arxiv.org/a/sanders_t_1 Papers on the arXiv]

{{Persondata 
|NAME= Sanders, Tom
|ALTERNATIVE NAMES=
|SHORT DESCRIPTION= British mathematician
|DATE OF BIRTH=
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{{DEFAULTSORT:Sanders, Tom}}
[[Category:21st-century mathematicians]]
[[Category:English mathematicians]]
[[Category:Living people]]

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