Ben Green

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Ben Green, Oberwolfach 2010

Ben Joseph Green (born February 27, 1977 in Bristol , England ) is a British mathematician who made significant contributions to combinatorics and number theory .

Life

Ben Green between 1995 and 2002 at Trinity College of Cambridge University studied mathematics in 1998 was Senior Wrangler in the Tripos examinations and was treated with a thesis on 2003 Topics in Arithmetic Combinatorics at Tim Gowers doctorate. He then spent three months at the Alfréd Rényi Institute in Budapest and then from 2003 to 2004 at the University of British Columbia in Vancouver . In 2005 he received a professorship in mathematics at the University of Bristol , which he held until 2006. From September 2006 to July 2013 he was Professor of Mathematics at Cambridge University . Since then he has been the Waynflete Professor of Pure Mathematics at Oxford University

Services

Ben Green has shown deep combinatorial results that have interesting applications in number theory . His proof of the conjecture by Cameron and Erdős (2004) and his joint work with Terence Tao The primes contain arbitrarily long arithmetic progressions, in which it is shown that there are arbitrarily long arithmetic progressions of prime numbers ( Green-Tao theorem ). The longest (2010) known arithmetic progression of prime numbers is 26.

The conjecture of Cameron and Erdős, which he proved, says that the number of sum-free subsets in {1,…, N} is of order . A subset A is sum-free if there are no x, y, z in A with x + y = z.

Honors

In 2001 Ben Green received the Smith Prize from Cambridge University and in 2004 he was honored with the Clay Research Award . He was awarded the Whitehead Prize of the London Mathematical Society and the Salem Prize in 2005. In 2006 he received the Ostrowski Prize together with Terence Tao . He was awarded the SASTRA Ramanujan Prize in 2007. In 2014 he was awarded the New Year's Eve Medal by the Royal Society .

In 2006 he was invited speaker at the International Congress of Mathematicians in Madrid ( Generalizing the Hardy-Littlewood method for primes ). In 2013 he gave a Gauss lecture . He is a fellow of the American Mathematical Society . He was selected as plenary speaker at the International Congress of Mathematicians 2014 in Seoul (Approximate algebraic structure).

In 2016/17 and 2017/18 he was on the Abel Prize Committee . For 2019 he was awarded the Senior Whitehead Prize of the London Mathematical Society .

Fonts (selection)

  • with Terence Tao : The primes contain arbitrarily long arithmetic progressions. In: Annals of Mathematics . Series 2, Vol. 167, No. 2, 2008, pp. 481-547, JSTOR 40345354 .
  • with Terence Tao: Linear equations in primes. In: Annals of Mathematics. Series 2, Vol. 171, No. 3, 2010, pp. 1753-1850, JSTOR 20752252 .
  • with Terence Tao: The quantitative behavior of polynomial orbits on nilmanifolds. In: Annals of Mathematics. Series 2, Vol. 175, No. 2, 2012, pp. 465-540, JSTOR 23234621 .
  • with Terence Tao: The Möbius function is strongly orthogonal to nilsequences. In: Annals of Mathematics. Series 2, Vol. 175, No. 2, 2012, pp. 541-566, JSTOR 23234622 .
  • with Terence Tao, Tamar Ziegler : An inverse theorem for the Gowers U s + 1 [N] -norm. In: Annals of Mathematics. Series 2, Vol. 176, No. 2, 2012, pp. 1231-1372, JSTOR 23350588 .
  • with Emmanuel Breuillard , Terence Tao: The structure of approximate groups. In: Publications Mathématiques de l'IHÉS . Vol. 116, 2012, pp. 115-221, doi : 10.1007 / s10240-012-0043-9 .

Web links

Individual evidence

  1. ↑ B. Green: The Cameron-Erdős conjecture. In: Bulletin of the London Mathematical Society . Vol. 36, No. 6, 2004, pp. 769-778, doi : 10.1112 / S0024609304003650 .
  2. ^ Annals of Mathematics. Vol. 167, No. 2, 2008, pp. 481-547.
  3. ^ Abel Committee
personal data
SURNAME Green, Ben
ALTERNATIVE NAMES Green, Ben Joseph (full name)
BRIEF DESCRIPTION British mathematician
DATE OF BIRTH February 27, 1977
PLACE OF BIRTH Bristol