Back to my preprints page.If you are interested in long arithmetic progressions in the primes, but don.t want to plunge directly into all the details, I can suggest the following surveys (in roughly increasing order of technical level of treatment):
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Title |
With |
Status |
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A sum-product estimate for finite fields, and applications |
GAFA 14 (2004), 27-57 |
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The primes contain arbitrarily long arithmetic progressions |
Annals of Math. 167 (2008), 481-547 |
math.NT/0404188 |
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New bounds for Szemeredi's Theorem, I: Progressions of length 4 in finite field geometries |
Proc. Lond. Math. Soc. 98 (2009), 365-392 |
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Restriction theory of the Selberg Sieve, with applications |
Journal de Théorie des Nombres de Bordeaux 18 (2006), 137.172 |
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A quantitative ergodic theory proof of Szemer\'edi's theorem |
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Electron. J. Combin. 13 (2006). 1 No. 99, 1-49. |
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On random $\pm 1$ matrices: Singularity and Determinant |
Random Structures and Algorithms 28 (2006), 1.23. |
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Arithmetic progressions and the primes |
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Collectanea Mathematica (2006), Vol. Extra., 37-88. |
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On the singularity probability of random Bernoulli matrices |
J. Amer. Math. Soc. 20 (2007), 603-628 |
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The Gaussian primes contain arbitrarily shaped constellations |
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J. d.Analyse Mathematique 99 (2006), 109-176 |
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An inverse theorem for the Gowers $U^3(G)$ norm |
Proc. Edin. Math. Soc. 51 (2008), 73-153 |
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J. Combin. Thy. A 113 (2006), 1257--1280 |
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Szemer\.edi.s regularity lemma revisited |
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Contrib. Discrete Math. 1 (2006), 8-28 |
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Random symmetric matrices are almost surely non-singular |
Kevin Costello |
Duke Math. J. 135 (2006), 395-413 |
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Obstructions to uniformity, and arithmetic patterns in the primes |
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Quarterly J. Pure Appl. Math. 2 (2006), 199-217 [Special issue in honour of John H. Coates, Vol. 1 of 2] |
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Compressions, convex geometry, and the Freiman-Bilu theorem |
Quarterly J. Math. 57 (2006), 495-504 |
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Inverse Littlewood-Offord theorems and the condition number of random discrete matrices |
Annals of Math. 169 (2009), 595-632 |
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New bounds for Szemeredi's Theorem, II: A new bound for r_4(N) |
Analytic number theory: essays in honour of Klaus Roth, W. W. L. Chen, W. T. Gowers, H. Halberstam, W. M. Schmidt, R. C. Vaughan, eds, Cambridge University Press, 2009. 180-204. |
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New bounds for Szemeredi's Theorem, III: A polylog bound for r_4(N) |
In preparation |
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Quadratic uniformity of the M\"obius function |
Annales de l.Institut Fourier 58 (2009), 1863.1935. |
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Linear equations in primes |
To appear, Annals of Math. |
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The dichotomy between structure and randomness, arithmetic progressions, and the primes |
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2006 ICM proceedings, Vol. I., 581--608 |
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Product set estimates in noncommutative groups |
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Combinatorica 28 (2008), 547-594 |
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J. d.Analyse Mathematique 103 (2007), 1--45. |
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The ergodic and combinatorial approaches to Szemer\'edi's theorem |
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Centre de Recerches Math\'ematiques, CRM Proceedings and Lecture Notes Vol. 43 (2007), 145--193 |
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The primes contain arbitrarily long polynomial progressions |
Acta Math. 201 (2008), 213.305. |
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John-type theorems for generalized arithmetic progressions and iterated sumsets |
Adv. in Math. 219 (2008), 428.449. |
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A note on the Freiman and Balog-Szemeredi-Gowers theorems in finite fields |
J. Aust. Math. Soc. 86 (2009), 61-74. |
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On the condition number of a randomly perturbed matrix |
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing (STOC) 2007, 248-255 |
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Freiman's theorem in finite fields via extremal set theory |
To appear, Combinatorics, Probability, and Computing |
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Szemerédi's theorem |
Scholarpedia, p. 15573 |
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Norm convergence of multiple ergodic averages for commuting transformations |
Ergodic Theory and Dynamical Systems 28 (2008), 657-688 |
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Structure and randomness in combinatorics |
Proceedings of the 48th annual symposium on Foundations of Computer Science (FOCS) 2007, 3-18 |
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Random Matrices: The circular Law |
Communications in Contemporary Mathematics, 10 (2008), 261--307 |
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The quantitative behaviour of polynomial orbits on nilmanifolds |
Submitted, Annals of Math. |
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The M\"obius function is asymptotically orthogonal to nilsequences |
Submitted, Annals of Math. |
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The distribution of polynomials over finite fields, with applications to the Gowers norms |
Submitted, Contributions to Discrete Mathematics |
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On the testability and repair of hereditary hypergraph properties |
To appear, Random Structures and Algorithms |
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A remark on primality testing and decimal expansions |
To appear, J. Aust. Math. Soc. |
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On the permanent of random Bernoulli matrices |
Adv. Math. 220 (2009), 657.669. |
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Smooth analysis of the condition number and the least singular value |
To appear, Mathematics of Computation |
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The sum-product phenomenon in arbitrary rings |
To appear, Contributions to Discrete Mathematics |
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Random matrices: Universality of ESDs and the circular law |
Manjunath Krishnapur(appendix) |
To appear, Annals of Probability |
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From the Littlewood-Offord problem to the circular law: universality of the spectral distribution of random matrices |
Bull. Amer. Math. Soc. 46 (2009), 377-396 |
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The inverse conjecture for the Gowers norm over finite fields via the correspondence principle |
To appear, Analysis & PDE |
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An inverse theorem for the uniformity seminorms associated with the action of $F^\omega$ |
To appear, GAFA |
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A sharp inverse Littlewood-Offord theorem |
To appear, Random Structures and Algorithms |
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Random matrices: the distribution of smallest singular values |
To appear, GAFA |
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Random matrices: universality of local eigenvalue statistics |
To appear, Acta Math. |
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An equivalence between inverse sumset theorems and inverse conjectures for the U^3 norm |
To appear, Math. Proc. Camb. Phil. Soc. |
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Freiman.s theorem for solvable groups |
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Submitted, Contributions to Discrete Mathematics |
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Sumset and inverse sumset theorems for Shannon entropy |
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Submitted, Combinatorics, Probability, and Computing |
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Bulk universality for Wigner hermitian matrices with subexponential decay |
László Erd.s |
To appear, Math. Res. Lett. |
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Random matrices: universality of local eigenvalue statistics up to the edge |
To appear, Communications in Mathematical Physics |
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A remark on partial sums involving the Mobius function |
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To appear, Bull. Aust. Math. Soc. |
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A new proof of the density Hales-Jewett theorem |
D.H.J. Polymath | Submitted | arXiv:0910.3926 discussion |
| A finitary version of Gromov's polynomial growth theorem | Yehuda Shalom | Submitted, GAFA | arXiv:0910.4148 discussion |
| An inverse theorem for the Gowers U^4 norm | Ben Green Tamar Ziegler |
Submitted, Glasgow Mathematical Journal | arXiv:0911.5681 discussion |