# Ben Green

British mathematician

## Ben Green 's AcademicInfluence.com Rankings

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Mathematics

## Why Is Ben Green Influential?

(Suggest an Edit or Addition)According to Wikipedia, Ben Joseph Green FRS is a British mathematician, specialising in combinatorics and number theory. He is the Waynflete Professor of Pure Mathematics at the University of Oxford. Early life and education Ben Green was born on 27 February 1977 in Bristol, England. He studied at local schools in Bristol, Bishop Road Primary School and Fairfield Grammar School, competing in the International Mathematical Olympiad in 1994 and 1995. He entered Trinity College, Cambridge in 1995 and completed his BA in mathematics in 1998, winning the Senior Wrangler title. He stayed on for Part III and earned his doctorate under the supervision of Timothy Gowers, with a thesis entitled Topics in arithmetic combinatorics . During his PhD he spent a year as a visiting student at Princeton University. He was a research Fellow at Trinity College, Cambridge between 2001 and 2005, before becoming a Professor of Mathematics at the University of Bristol from January 2005 to September 2006 and then the first Herchel Smith Professor of Pure Mathematics at the University of Cambridge from September 2006 to August 2013. He became the Waynflete Professor of Pure Mathematics at the University of Oxford on 1 August 2013. He was also a Research Fellow of the Clay Mathematics Institute and held various positions at institutes such as Princeton University, University of British Columbia, and Massachusetts Institute of Technology.

## Ben Green 's Published Works

### Published Works

- The primes contain arbitrarily long arithmetic progressions (2004) (881)
- Linear equations in primes (2006) (399)
- AN INVERSE THEOREM FOR THE GOWERS $U^3(G)$ NORM (2008) (245)
- An inverse theorem for the Gowers U^{s+1}[N]-norm (announcement) (2010) (242)
- The Mobius function is strongly orthogonal to nilsequences (2008) (240)
- A Szemerédi-type regularity lemma in abelian groups, with applications (2003) (239)
- Approximate Subgroups of Linear Groups (2010) (217)
- The quantitative behaviour of polynomial orbits on nilmanifolds (2007) (213)
- The structure of approximate groups (2011) (197)
- AN INVERSE THEOREM FOR THE GOWERS U4-NORM (2005) (194)
- Freiman's theorem in an arbitrary abelian group (2005) (176)
- Roth's theorem in the primes (2003) (175)
- The distribution of polynomials over finite fields, with applications to the Gowers norms (2007) (141)
- Finite field models in additive combinatories (2004) (141)
- Expansion in finite simple groups of Lie type (2013) (135)
- Sum-free sets in abelian groups (2003) (130)
- On Sets Defining Few Ordinary Lines (2012) (116)
- An Arithmetic Regularity Lemma, An Associated Counting Lemma, and Applications (2010) (96)
- QUADRATIC UNIFORMITY OF THE MOBIUS FUNCTION (2006) (80)
- Restriction theory of the Selberg sieve, with applications (2004) (76)
- Long gaps between primes (2014) (69)
- Sets with Small Sumset and Rectification (2004) (64)
- On (Not) Computing the Möbius Function Using Bounded Depth Circuits (2011) (58)
- Large gaps between consecutive prime numbers (2014) (57)
- Structure Theory of Set Addition (2002) (55)
- Counting Sets With Small Sumset, And The Clique Number Of Random Cayley Graphs (2003) (54)
- On arithmetic structures in dense sets of integers (2002) (54)
- Freiman's Theorem in Finite Fields via Extremal Set Theory (2007) (51)
- APPROXIMATE GROUPS, II: THE SOLVABLE LINEAR CASE (2009) (51)
- Montréal notes on quadratic Fourier analysis (2007) (46)
- The number of squares and $B_h[g]$ sets (2001) (45)
- On the Littlewood Problem Modulo a Prime (2006) (42)
- COMPRESSIONS, CONVEX GEOMETRY AND THE FREIMAN–BILU THEOREM (2005) (42)
- Approximate groups. I The torsion-free nilpotent case (2009) (42)
- Suzuki groups as expanders (2010) (40)
- Strongly dense free subgroups of semisimple algebraic groups (2010) (40)
- New bounds for Szemerédi's theorem, I: progressions of length 4 in finite field geometries (2005) (39)
- Counting sumsets and sum-free sets modulo a prime (2004) (39)
- New bounds for Szemeredi's theorem, II: A new bound for r_4(N) (2006) (38)
- Arithmetic progressions in sumsets (2002) (37)
- Approximate groups and their applications: work of Bourgain, Gamburd, Helfgott and Sarnak (2009) (37)
- A quantitative version of the idempotent theorem in harmonic analysis (2006) (36)
- The Cameron–Erdős Conjecture (2003) (36)
- An equivalence between inverse sumset theorems and inverse conjectures for the U3 norm (2009) (34)
- Approximate groups, III: the unitary case (2010) (33)
- Sets of integers with no large sum-free subset (2013) (32)
- Boolean Functions with small Spectral Norm (2006) (31)
- Spectral Structure of Sets of Integers (2004) (29)
- Some Constructions in the Inverse Spectral Theory of Cyclic Groups (2003) (28)
- A NOTE ON THE FREIMAN AND BALOG–SZEMERÉDI–GOWERS THEOREMS IN FINITE FIELDS (2007) (27)
- A nilpotent Freiman dimension lemma (2011) (26)
- Montreal Lecture Notes on Quadratic Fourier Analysis (2006) (25)
- Linear Approximate Groups (2010) (24)
- Counting sets with small sumset and applications (2013) (24)
- New bounds for Szemeredi's theorem, Ia: Progressions of length 4 in finite field geometries revisited (2012) (23)
- Monochromatic sums and products (2015) (23)
- Long arithmetic progressions of primes (2005) (23)
- Generalising the Hardy-Littlewood Method for Primes (2006) (22)
- Invariable generation of the symmetric group (2015) (22)
- Permutations fixing a k-set (2015) (22)
- Yet Another Proof Of Szemerédi's Theorem (2010) (21)
- Small Doubling in Groups (2013) (20)
- Szemerédi's Theorem (2007) (19)
- Sarkozy's theorem in function fields (2016) (15)
- Inverse questions for the large sieve (2013) (14)
- Monochromatic Solutions to $x+y=z^{2}$ (2016) (13)
- On the maximal number of 3‐term arithmetic progressions in subsets of ℤ/pℤ (2007) (13)
- What is... an approximate group (2012) (13)
- New bounds for Szemer\'edi's theorem, III: A polylogarithmic bound for $r_4(N)$ (2017) (12)
- A note on approximate subgroups of GL_n(C) and uniformly nonamenable groups (2011) (11)
- On valued function fields III. Reductions of algebraic curves. (1992) (11)
- Sum-product phenomena in F_p: a brief introduction (2009) (11)
- Three topics in additive prime number theory (2007) (11)
- Nonzero coefficients of half-integral weight modular forms mod $$\ell $$ℓ (2017) (11)
- On valued function fields II. Regular functions and elements with the uniqueness property. (1990) (10)
- On a variant of the large sieve (2008) (9)
- A note on multiplicative functions on progressions to large moduli (2016) (9)
- On the quantitative distribution of polynomial nilsequences — erratum (2013) (8)
- On the Local Skolem Property. (1995) (8)
- NOTES ON THE POLYNOMIAL FREIMAN-RUZSA CONJECTURE (2013) (7)
- On the arithmetic Kakeya conjecture of Katz and Tao (2017) (6)
- On the Hardy–Littlewood majorant problem (2003) (6)
- On the width of transitive sets: Bounds on matrix coefficients of finite groups (2018) (5)
- The polynomial Freiman-Ruzsa conjecture (2014) (4)
- Lower bounds for corner-free sets (2021) (4)
- On S\'ark\"ozy's theorem for shifted primes (2022) (4)
- Fourier uniformity on subspaces (2015) (3)
- A Weighted Prékopa-Leindler inequality and sumsets with quasicubes (2020) (3)
- Equal sums in random sets and the concentration of divisors (2019) (3)
- On the Chromatic Number of Random Cayley Graphs (2013) (3)
- On Sets Defining Few Ordinary Lines (2013) (3)
- Bounded gaps between primes (2014) (2)
- The Mobius and Nilsequences Conjecture (2008) (2)
- Multiple correlation sequences not approximable by nilsequences (2020) (2)
- Contractions and expansion (2011) (2)
- Extremal problems for GCDs (2020) (1)
- On a conjecture of Gowers and Long (2019) (1)
- Strongly dense free subgroups of semisimple algebraic groups (2012) (1)
- An Example Concerning Set Addition in $$\mathbb{F}_2^n$$F2n (2018) (0)
- Emmanuel Breuillard and Hee Oh, Thin groups and superstrong approximation (Cambridge University Press, 2014), 376 pp., 978-1-107-03685-7 (hardback), £65. (2016) (0)
- Ju l 2 00 3 Roth ’ s Theorem in the Primes (2008) (0)
- Coffee Coffee Coffee Coffee Coffee 1100-1200 (2012) (0)
- The structure of approximate groups (2012) (0)
- Simply-laced isomonodromy systems . On the functions counting walks with small steps in the quarter plane . The structure of approximate groups . On stably free modules over affine algebras . Perfectoid spaces (2012) (0)
- Arithmetic Progressions in Sumsets and Van der Waerden Numbers (2013) (0)
- Additive combinatorics and its applications organized (2019) (0)
- On the arithmetic Kakeya conjecture of Katz and Tao (2018) (0)
- The Cameron – Erdős Conjecture Ben Green (2008) (0)
- N T ] 2 3 A ug 2 02 1 QUADRATIC FORMS IN 8 PRIME VARIABLES (2021) (0)
- Quadratic forms in 8 prime variables (2021) (0)
- N T ] 2 1 M ar 2 00 4 Sets with small sumset and rectification (2004) (0)
- 2 5 Fe b 20 03 Roth ’ s Theorem in the Primes (2008) (0)
- A ug 2 01 6 INVARIABLE GENERATION OF THE SYMMETRIC GROUP (2016) (0)
- Set addition in boxes and the Freiman-Bilu theorem (2005) (0)
- 2 2 Se p 20 07 QUADRATIC UNIFORMITY OF THE MÖBIUS FUNCTION (2005) (0)
- N T ] 1 0 Ja n 20 06 Generalising the Hardy-Littlewood method for primes (2007) (0)
- The Dirac-Motzkin Problem on Ordinary Lines and the Orchard Problem (Invited Talk) (2015) (0)
- An example concerning set addition in F_2^n (2017) (0)
- Galois representations attached to algebraic automorphic representations (2016) (0)
- New lower bounds for van der Waerden numbers (2021) (0)
- Counting sets with small sumset and applications (2015) (0)

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