Tom Sanders (mathematician)

Tom Sanders is an English mathematician who studies additive combinatorics and its connections to harmonic analysis and analytical number theory.

Life

Sanders studied mathematics at Cambridge University , where he received his PhD in 2007 from Timothy Gowers ( Topics in arithmetic combinatorics ). He was then a Junior Research Fellow at Christ's College, Cambridge. In 2007/08 he was at the Institute for Advanced Study and in 2008/09 at the MSRI and the Mittag-Leffler Institute . Since 2011 he has been a Royal Society University Research Fellow at Oxford University , where he is a tutor and fellow at St. Hugh's College.

In 2011 he received the Adams Prize . In 2012 he received the EMS Prize for his fundamental results in additive combinatorics and harmonic analysis . For 2013 he was awarded the Whitehead Prize . In 2014 he was invited speaker at the ICM in Seoul ( Roth's theorem: an application of approximate groups ). In 2013 he received the European Prize in Combinatorics .

plant

He improved Klaus Friedrich Roth's theorem on arithmetic progressions with three terms. Roth had given an upper bound for the size of subsets of natural numbers less than or equal to, which do not contain a nontrivial arithmetic progression of length 3. Roth proved ${\ displaystyle A}$ ${\ displaystyle N}$

{\ displaystyle | A | = O \ left ({\ frac {N} {\ log \ log N}} \ right)}

(using the Landau symbols ), Sanders improved it to include logarithmic terms

{\ displaystyle | A | = O \ left ({\ frac {N {(\ log \ log N)} ^ {5}} {\ log N}} \ right)}

.

Previously, Jean Bourgain , Roger Heath-Brown and Endre Szemerédi (Roth's theorem is also the simplest case of Szemeredi's theorem) had tightened it up.

He also made progress towards improving the bound in Freiman's theorem of additive combinatorial number theory.

Web links

Homepage in Oxford

Individual evidence

↑ Laudation for EMS Prize 2012
↑ Roth: On certain sets of integers. J. London Math. Soc., Vol. 28, 1953, pp. 104-109
↑ On Roth's theorem on progressions. Preprint 2011, Annals of Mathematics, Volume 174, 2011, pp. 619-636.

personal data
SURNAME	Sanders, Tom
BRIEF DESCRIPTION	British mathematician
DATE OF BIRTH	20th century

[1] Laudation for EMS Prize 2012

[2] Roth: On certain sets of integers. J. London Math. Soc., Vol. 28, 1953, pp. 104-109

[3] On Roth's theorem on progressions. Preprint 2011, Annals of Mathematics, Volume 174, 2011, pp. 619-636.