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Green, Ben

  1. The primes contain arbitrarily long arithmetic progressions
    2004/04/08 by Ben Green, Terence Tao, Green, Ben +1 · 16 citations
    Mathematics · #Analytic Number Theory Research #Dynamical Systems (math.DS) #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Number Theory (math.NT)
  2. On a conjecture of Marton
    2023/11/09 by W. T. Gowers, Gowers, W. T., Ben Green +5 · 2 voices · 19 citations
    #math.NT #math.CO
  3. The quantitative behaviour of polynomial orbits on nilmanifolds
    2007/09/22 by Green, Ben, Tao, Terence · 8 citations
    #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)
  4. A Szemeredi-type regularity lemma in abelian groups, with applications
    2003/10/30 by Ben Green, Green, Ben · 7 citations
    Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT
  5. The structure of approximate groups
    2011/10/22 by Emmanuel Breuillard, Ben Green, Breuillard, Emmanuel +3 · 8 citations
    Mathematics · Computer Science · #Geometric and Algebraic Topology #Topological and Geometric Data Analysis #Finite Group Theory Research
  6. An inverse theorem for the Gowers Us+1[N]-norm (announcement)
    2010/06/01 by Ben Green, Terence Tao, Green, Ben +3 · 9 citations
    Mathematics · #Analytic Number Theory Research #Dynamical Systems (math.DS) #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Number Theory (math.NT)
  7. Roth's theorem in the primes
    2003/02/25 by Ben Green, Green, Ben · 7 citations
    Mathematics · #11B25 #11P55 #42B15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT) #math.CA #math.NT #msc:11B25 #msc:11P55 #msc:42B15
  8. Freiman's Theorem in an arbitrary abelian group
    2005/05/10 by Ben Green, Imre Z. Ruzsa, Green, Ben +1 · 6 citations
    Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory #Number Theory (math.NT)
  9. Expansion in finite simple groups of Lie type
    2013/09/08 by Emmanuel Breuillard, Breuillard, Emmanuel, Ben Green +5 · 6 citations
    Mathematics · #20G40 #20N99 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Limits and Structures in Graph Theory
  10. Restriction theory of the Selberg sieve, with applications
    2004/05/30 by Ben Green, Terence Tao, Green, Ben +1 · 5 citations
    Mathematics · #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Number Theory (math.NT) #math.CA #math.NT
  11. Primes of the form p2 + nq2
    2024/10/05 by Ben Green, Mehtaab Sawhney, Green, Ben +1 · 5 voices · 1 citation
    #math.NT #math.CO
  12. An inverse theorem for the Gowers U3 norm
    2005/03/01 by Ben Green, Terence Tao, Green, Ben +1 · 5 citations
    Mathematics · #Limits and Structures in Graph Theory #Graph theory and applications #Analytic Number Theory Research
  13. An arithmetic regularity lemma, associated counting lemma, and applications
    2010/02/10 by Ben Green, Terence Tao, Green, Ben +1 · 4 citations
    Computer Science · Mathematics · #Computability, Logic, AI Algorithms #Complexity and Algorithms in Graphs #Limits and Structures in Graph Theory
  14. Linear Equations in Primes
    2006/06/04 by Ben Green, Terence Tao, Green, Ben +1 · 5 citations
    Mathematics · #Analytic Number Theory Research #Dynamical Systems (math.DS) #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Number Theory (math.NT)
  15. Approximate subgroups of linear groups
    2010/05/11 by Emmanuel Breuillard, Breuillard, Emmanuel, Ben Green +3 · 4 citations
    Computer Science · Mathematics · #Advanced Graph Theory Research #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Limits and Structures in Graph Theory
  16. Finite field models in additive combinatorics
    2004/09/22 by Ben Green, Green, Ben · 4 citations
    Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory #Number Theory (math.NT) #math.CO #math.NT
  17. New bounds for Szemerédi's theorem, III: A polylogarithmic bound for r4(N)
    2017/05/04 by Ben Green, Green, Ben, Terence Tao +1 · 4 citations
    Mathematics · Engineering · #Limits and Structures in Graph Theory #Analytic Number Theory Research #graph theory and CDMA systems
  18. On the arithmetic Kakeya conjecture of Katz and Tao
    2017/12/06 by Ben Green, Imre Z. Ruzsa, Green, Ben +1 · 3 citations
    Mathematics · #Advanced Topology and Set Theory #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)
  19. Counting sets with small sumset, and the clique number of random Cayley graphs
    2003/04/14 by Ben Green, Green, Ben · 2 citations
    Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #math.CO #math.NT
  20. Sum-free sets in abelian groups
    2003/07/10 by Ben Green, Green, Ben, Imre Z. Ruzsa +1 · 2 citations
    Engineering · Mathematics · #11B75 #20D60 #20K01 #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #graph theory and CDMA systems #math.CO #math.NT #msc:11B75 #msc:20D60 #msc:20K01
  21. Compressions, convex geometry and the Freiman-Bilu theorem
    2005/11/03 by Green, Ben, Tao, Terence · 2 citations
    #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
  22. On Sárközy's theorem for shifted primes
    2022/06/16 by Green, Ben · 4 citations
    #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
  23. Montreal Lecture Notes on Quadratic Fourier Analysis
    2006/04/04 by Ben Green, Green, Ben · 3 citations
    Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory
  24. On sets defining few ordinary lines
    2012/08/23 by Ben Green, Green, Ben, Terence Tao +1 · 2 citations
    Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Limits and Structures in Graph Theory
  25. Counting sets with small sumset and applications
    2013/05/14 by Green, Ben, Morris, Robert · 2 citations
    #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
  26. Marton's Conjecture in abelian groups with bounded torsion
    2024/04/02 by Gowers, W. T., Green, Ben, Manners, Freddie +1 · 6 citations
    #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
  27. Suzuki groups as expanders
    2010/05/05 by Emmanuel Breuillard, Breuillard, Emmanuel, Ben Green +3 · 4 citations
    Mathematics · Computer Science · #Finite Group Theory Research #Geometric and Algebraic Topology #Coding theory and cryptography
  28. A Weighted Prékopa-Leindler inequality and sumsets with quasicubes
    2020/03/09 by Green, Ben, Matolcsi, Dávid, Ruzsa, Imre +2 · 2 citations
    #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
  29. On the Littlewood problem modulo a prime
    2006/01/23 by Ben Green, Green, Ben, Sergeĭ Konyagin +1 · 1 citation
    Mathematics · #Limits and Structures in Graph Theory #Analytic Number Theory Research #Advanced Topology and Set Theory
  30. New bounds for Szemeredi's theorem, II: A new bound for r4(N)
    2006/10/19 by Green, Ben, Tao, Terence · 1 citation
    #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
  31. Freiman's theorem in finite fields via extremal set theory
    2007/03/22 by Green, Ben, Tao, Terence · 1 citation
    #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
  32. Contractions and expansion
    2011/12/15 by Breuillard, Emmanuel, Green, Ben · 1 citation
    #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
  33. Sarkozy's theorem in function fields
    2016/05/24 by Ben Green, Green, Ben · 1 citation
    Mathematics · #Limits and Structures in Graph Theory #Analytic Number Theory Research #Algebraic Geometry and Number Theory
  34. Quadratic Uniformity of the Mobius Function
    2006/06/04 by Green, Ben, Tao, Terence · 1 citation
    #FOS: Mathematics #Number Theory (math.NT)
  35. An inverse theorem for the Gowers Us+1[N]-norm
    2010/09/21 by Ben Green, Green, Ben, Terence Tao +3 · 2 citations
    Engineering · Mathematics · #11B30 #Analytic Number Theory Research #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Limits and Structures in Graph Theory #graph theory and CDMA systems
  36. Strongly dense free subgroups of semisimple algebraic groups
    2010/10/20 by Breuillard, Emmanuel, Green, Ben, Guralnick, Robert +1 · 1 citation
    #20G40 #20N99 #Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR)
  37. On the quantitative distribution of polynomial nilsequences - erratum
    2013/11/24 by Ben Green, Green, Ben, Terence Tao +1 · 1 citation
    Computer Science · Mathematics · #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)
  38. Waring's problem with restricted digits
    2023/09/17 by Green, Ben · 2 citations
    #FOS: Mathematics #Number Theory (math.NT)
  39. New bounds for the Furstenberg-Sárközy theorem
    2024/11/26 by Green, Ben, Sawhney, Mehtaab · 1 citation
    #FOS: Mathematics #Number Theory (math.NT)