#25,468

Most Influential Person

British mathematician

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.

- The primes contain arbitrarily long arithmetic progressions (805)
- Linear equations in primes (348)
- A Szemerédi-type regularity lemma in abelian groups, with applications (214)
- An inverse theorem for the Gowers U^{s+1}[N]-norm (183)
- Approximate Subgroups of Linear Groups (181)
- The quantitative behaviour of polynomial orbits on nilmanifolds (180)
- AN INVERSE THEOREM FOR THE GOWERS $U^3(G)$ NORM (170)
- The structure of approximate groups (163)
- Freiman's theorem in an arbitrary abelian group (161)
- Roth's theorem in the primes (155)
- AN INVERSE THEOREM FOR THE GOWERS U4-NORM (155)
- The Mobius function is strongly orthogonal to nilsequences (131)
- Finite field models in additive combinatories (126)
- The distribution of polynomials over finite fields, with applications to the Gowers norms (125)
- Expansion in finite simple groups of Lie type (111)
- Sum-free sets in abelian groups (108)
- An inverse theorem for the Gowers U^{s+1}[N]-norm (announcement) (105)
- On Sets Defining Few Ordinary Lines (99)
- The Mobius function is strongly orthogonal to nilsequences (93)
- An Arithmetic Regularity Lemma, An Associated Counting Lemma, and Applications (85)
- QUADRATIC UNIFORMITY OF THE MOBIUS FUNCTION (77)
- Restriction theory of the Selberg sieve, with applications (63)
- Arithmetic progressions in sumsets (60)
- A Note on Elkin’s Improvement of Behrend’s Construction (59)
- The Cameron–Erdős Conjecture (55)
- Sets with small sumset and rectification (55)
- Long gaps between primes (53)
- On arithmetic structures in dense sets of integers (50)
- APPROXIMATE GROUPS, II: THE SOLVABLE LINEAR CASE (48)
- On (Not) Computing the Möbius Function Using Bounded Depth Circuits (48)
- Freiman's Theorem in Finite Fields via Extremal Set Theory (46)
- Counting Sets With Small Sumset, And The Clique Number Of Random Cayley Graphs (45)
- Large gaps between consecutive prime numbers (44)
- The number of squares and $B_h[g]$ sets (42)
- On the Littlewood Problem Modulo a Prime (41)
- New bounds for Szemeredi's theorem, II: A new bound for r_4(N) (40)
- Montréal notes on quadratic Fourier analysis (40)
- Approximate groups. I The torsion-free nilpotent case (39)
- Structure Theory of Set Addition (36)
- Approximate groups and their applications: work of Bourgain, Gamburd, Helfgott and Sarnak (35)
- Counting sumsets and sum-free sets modulo a prime (35)
- Suzuki groups as expanders (35)
- COMPRESSIONS, CONVEX GEOMETRY AND THE FREIMAN–BILU THEOREM (35)
- New bounds for Szemerédi's theorem, I: progressions of length 4 in finite field geometries (33)
- A quantitative version of the idempotent theorem in harmonic analysis (33)
- Strongly dense free subgroups of semisimple algebraic groups (32)
- Boolean Functions with small Spectral Norm (31)
- An equivalence between inverse sumset theorems and inverse conjectures for the U3 norm (30)
- Approximate groups, III: the unitary case (30)
- Spectral Structure of Sets of Integers (28)
- Sets of integers with no large sum-free subset (27)
- A nilpotent Freiman dimension lemma (25)
- Some Constructions in the Inverse Spectral Theory of Cyclic Groups (25)
- A NOTE ON THE FREIMAN AND BALOG–SZEMERÉDI–GOWERS THEOREMS IN FINITE FIELDS (25)
- Montreal Lecture Notes on Quadratic Fourier Analysis (22)
- Linear Approximate Groups (22)
- Long arithmetic progressions of primes (21)
- Permutations fixing a k-set (20)
- Counting sets with small sumset and applications (20)
- Invariable generation of the symmetric group (19)
- Yet Another Proof Of Szemerédi's Theorem (18)
- New bounds for Szemeredi's theorem, Ia: Progressions of length 4 in finite field geometries revisited (17)
- Generalising the Hardy-Littlewood Method for Primes (16)
- Small Doubling in Groups (15)
- Monochromatic sums and products (15)
- What is... an approximate group (13)
- On the maximal number of 3-term arithmetic progressions in subsets of ℤ/pℤ (13)
- Szemerédi's Theorem (13)
- Approximate algebraic structure (12)
- Three topics in additive prime number theory (11)
- New bounds for Szemer\'edi's theorem, III: A polylogarithmic bound for $r_4(N)$ (11)
- Inverse questions for the large sieve (11)
- Sarkozy's theorem in function fields (11)
- On valued function fields III. Reductions of algebraic curves. (11)
- Nonzero coefficients of half-integral weight modular forms mod $$\ell $$ℓ (11)
- On valued function fields II. Regular functions and elements with the uniqueness property. (10)
- Sum-product phenomena in F_p: a brief introduction (10)
- Monochromatic Solutions to $x+y=z^{2}$ (9)
- A note on approximate subgroups of GL_n(C) and uniformly nonamenable groups (9)
- Generalising the Hardy-Littlewood Method for Primes (7)
- On the quantitative distribution of polynomial nilsequences — erratum (7)
- A note on multiplicative functions on progressions to large moduli (6)
- NOTES ON THE POLYNOMIAL FREIMAN-RUZSA CONJECTURE (6)
- On a variant of the large sieve (6)
- Lecture Notes for the 22nd Mcgill Invitational Workshop on Computational Complexity (6)
- Finite Field Models in Arithmetic Combinatorics (6)
- On the Hardy–Littlewood majorant problem (5)
- On the Chromatic Number of Random Cayley Graphs (5)
- On the width of transitive sets: Bounds on matrix coefficients of finite groups (5)
- The polynomial Freiman-Ruzsa conjecture (4)
- On the Local Skolem Property. (4)
- The twilight kingdom: Structure and meaning inThe Wanderer (3)
- Fourier uniformity on subspaces (3)
- The Mobius and Nilsequences Conjecture (3)
- A Weighted Prékopa-Leindler inequality and sumsets with quasicubes (3)
- Bounded gaps between primes (2)
- The Village Horse Doctor: West of the Pecos (2)
- Lower bounds for corner-free sets (2)
- On the arithmetic Kakeya conjecture of Katz and Tao (2)
- Equal sums in random sets and the concentration of divisors (2)
- Book Review: Additive combinatorics (2)
- 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 (1)
- Contractions and expansion (1)
- 1 Arithmetic progressions in primes I after (1)
- Interaction with local energy grid (1)
- Popular music in mediated and collective memory (1)
- Some Applications of Harmonic Analysis to Arithmetic Combinatorics (1)
- Frontiers of American culture (1)
- Daily living programme (1)
- Debate Apple after Jobs (1)
- On a conjecture of Gowers and Long (1)
- Wild Cow Tales (1)
- Multiple correlation sequences not approximable by nilsequences (1)
- How distributed ledger technology could solve regulatory problems (1)
- Extremal problems for GCDs (1)
- 2 2 Se p 20 07 QUADRATIC UNIFORMITY OF THE MÖBIUS FUNCTION (0)
- Arithmetic Progressions in Sumsets and Van der Waerden Numbers (0)
- 2 5 Fe b 20 03 Roth ’ s Theorem in the Primes (0)
- An example concerning set addition in F_2^n (0)
- N T ] 2 1 M ar 2 00 4 Sets with small sumset and rectification (0)
- Coffee Coffee Coffee Coffee Coffee 1100-1200 (0)
- Galois representations attached to algebraic automorphic representations (0)
- A CASE FOR ETHERNET IN PROGRAMMABLE MOTION CONTROL (0)
- Book Reviews (0)
- Ju l 2 00 3 Roth ’ s Theorem in the Primes (0)
- An Example Concerning Set Addition in $$\mathbb{F}_2^n$$F2n (0)
- III.90 Topological Spaces (0)
- Additive combinatorics and its applications organized (0)
- New lower bounds for van der Waerden numbers (0)
- Quadratic forms in 8 prime variables (0)
- The Dirac-Motzkin Problem on Ordinary Lines and the Orchard Problem (Invited Talk) (0)
- N T ] 1 0 Ja n 20 06 Generalising the Hardy-Littlewood method for primes (0)
- Expert Reports Filed in CCLA v. Waterfront Toronto (0)
- Book Review: Heart Disease in Pregnancy (0)
- ACC 250 UOP Tutorial / Uoptutorial (0)
- III.73 Quadratic Forms (0)
- III.41 Irrational and Transcendental Numbers (0)
- ‘I just wanted to be a part of it’ (0)
- Emmanuel Breuillard and Hee Oh, Thin groups and superstrong approximation (Cambridge University Press, 2014), 376 pp., 978-1-107-03685-7 (hardback), £65. (0)
- III.31 The Gamma Function (0)
- The Cameron – Erdős Conjecture Ben Green (0)
- III.63 Number Fields (0)
- III.58 Modular Arithmetic (0)
- N T ] 2 3 A ug 2 02 1 QUADRATIC FORMS IN 8 PRIME VARIABLES (0)
- III.92 Trigonometric Functions (0)
- Set addition in boxes and the Freiman-Bilu theorem (0)

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