Title | With | Status | Download |
A sum-product estimate for finite fields, and applications | GAFA 14 (2004), 27-57 | ||
The primes contain arbitrarily long arithmetic progressions | Annals of Math. 167 (2008), 481-547 | ||
New bounds for Szemeredi's Theorem, I: Progressions of length 4 in finite field geometries | Proc. Lond. Math. Soc. 98 (2009), 365-392 | ||
Restriction theory of the Selberg Sieve, with applications | Journal de Théorie des Nombres de Bordeaux 18 (2006), 137—172 | ||
A quantitative ergodic theory proof of Szemer\'edi's theorem |
| Electron. J. Combin. 13 (2006). 1 No. 99, 1-49. | |
On random $\pm 1$ matrices: Singularity and Determinant | Random Structures and Algorithms 28 (2006), 1—23. [An extended abstracted is also in: STOC’05: Proceedings of the 37thannual ACM symposium on the theory of computing, 431—440, New York 2005.] | ||
Arithmetic progressions and the primes |
| Collectanea Mathematica (2006), Vol. Extra., 37-88. [Proceedings, 7th International Conference on Harmonic Analysis and Partial Differential Equations] | |
On the singularity probability of random Bernoulli matrices | J. Amer. Math. Soc. 20 (2007), 603-628 | ||
The Gaussian primes contain arbitrarily shaped constellations |
| J. d’Analyse Mathematique 99 (2006), 109-176 | |
An inverse theorem for the Gowers $U^3(G)$ norm | Proc. Edin. Math. Soc. 51 (2008), 73-153 | ||
| J. Combin. Thy. A 113 (2006), 1257--1280 | ||
Szemeredi's regularity lemma revisited |
| Contrib. Discrete Math. 1 (2006), 8-28 | |
Random symmetric matrices are almost surely non-singular | Kevin Costello | Duke Math. J. 135 (2006), 395-413 | |
Obstructions to uniformity, and arithmetic patterns in the primes |
| Quarterly J. Pure Appl. Math. 2 (2006), 199-217 [Special issue in honour of John H. Coates, Vol. 1 of 2] | |
Compressions, convex geometry, and the Freiman-Bilu theorem | Quarterly J. Math. 57 (2006), 495-504 | ||
Inverse Littlewood-Offord theorems and the condition number of random discrete matrices | Annals of Math. 169 (2009), 595-632 | ||
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. | ||
New bounds for Szemeredi's Theorem, III: A polylog bound for r_4(N) | Mathematika Volume 63, Issue 3 2017 , pp. 944-1040 | ||
Quadratic uniformity of the M\"obius function | Annales de l’Institut Fourier 58 (2009), 1863—1935. | ||
Linear equations in primes | Annals of Math. 171 (2010), 1753-1850 | ||
The dichotomy between structure and randomness, arithmetic progressions, and the primes |
| 2006 ICM proceedings, Vol. I., 581--608 | |
Product set estimates in noncommutative groups |
| Combinatorica 28 (2008), 547-594 | |
| J. d’Analyse Mathematique 103 (2007), 1--45. | ||
The ergodic and combinatorial approaches to Szemer\'edi's theorem |
| Centre de Recerches Math\'ematiques, CRM Proceedings and Lecture Notes Vol. 43 (2007), 145--193 | |
The primes contain arbitrarily long polynomial progressions | Acta Math. 201 (2008), 213—305. Errata: Acta Math. 210, (2013), Page 403-404 | ||
John-type theorems for generalized arithmetic progressions and iterated sumsets | Adv. in Math. 219 (2008), 428—449. | ||
A note on the Freiman and Balog-Szemeredi-Gowers theorems in finite fields | J. Aust. Math. Soc. 86 (2009), 61-74. | ||
The condition number of a randomly perturbed matrix | Proceedings of the thirty-ninth annual ACM symposium on Theory of computing (STOC) 2007, 248-255 | ||
Freiman's theorem in finite fields via extremal set theory | Combin. Probab. Comput. 18 (2009), no. 3, 335--355 | ||
Szemeredi's theorem | Scholarpedia, p. 15573 | ||
Norm convergence of multiple ergodic averages for commuting transformations | Ergodic Theory and Dynamical Systems 28 (2008), 657-688 | ||
Structure and randomness in combinatorics | Proceedings of the 48th annual symposium on Foundations of Computer Science (FOCS) 2007, 3-18 | ||
Random Matrices: The circular Law | Communications in Contemporary Mathematics, 10 (2008), 261--307 | ||
The quantitative behaviour of polynomial orbits on nilmanifolds | Annals of Math. Volume 175 (2012), Issue 2, 465-540. | ||
The M\"obius function is asymptotically orthogonal to nilsequences | Annals of Math., 175 (2012), 541--566 | ||
The distribution of polynomials over finite fields, with applications to the Gowers norms | Contrib. Discrete Math. 4 (2009), no. 2, 1--36. | ||
On the testability and repair of hereditary hypergraph properties | Random Structures and Algorithms 36 (2010), 373-463 | ||
A remark on primality testing and decimal expansions | 91 (2011), 405-413 | ||
On the permanent of random Bernoulli matrices | Adv. Math. 220 (2009), 657—669. | ||
Smooth analysis of the condition number and the least singular value | Mathematics of Computation, 79 (2010), 2333-2352 | ||
The sum-product phenomenon in arbitrary rings | Contrib. Discrete Math. 4 (2009), no. 2, 59--82. | ||
Random matrices: Universality of ESDs and the circular law | Manjunath Krishnapur(appendix) | Annals of Probability 38 (2010), no. 5, 2023--2065. | |
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 | ||
The inverse conjecture for the Gowers norm over finite fields via the correspondence principle | Analysis & PDE 3 (2010), 1-20 | ||
An inverse theorem for the uniformity seminorms associated with the action of $F^\omega$ | Geom. Funct. Anal. 19 (2010), no. 6, 1539--1596. | ||
A sharp inverse Littlewood-Offord theorem | |||
Random matrices: the distribution of smallest singular values | GAFA, 20 (2010), 260-297 | ||
Random matrices: universality of local eigenvalue statistics | Acta Math 206 (2011), 127-204 | ||
An equivalence between inverse sumset theorems and inverse conjectures for the U^3 norm | Math. Proc. Camb. Phil. Soc. 149 (2010), 1-19 | ||
Freiman’s theorem for solvable groups |
| Contributions to Discrete Mathematics 5 (2010), no. 2, 137–184, | |
Sumset and inverse sumset theorems for Shannon entropy |
| Combinatorics, Probability, and Computing 19 (2010), 603-639 | |
Bulk universality for Wigner hermitian matrices with subexponential decay | Jose Ramírez | Math. Res. Lett. 17 (2010), 793-794 | |
Random matrices: universality of local eigenvalue statistics up to the edge | Communications in Mathematical Physics, 298 (2010), 549-572 | ||
A remark on partial sums involving the Mobius function |
| Bull. Aust. Math. Soc. 81 (2010), 343-349 | |
A new proof of the density Hales-Jewett theorem | Annals of Math. 175 (2012), 1283-1327. | ||
A finitary version of Gromov's polynomial growth theorem | Yehuda Shalom | GAFA 20 (2010), no. 6, 1502–1547. | |
An inverse theorem for the Gowers U^4 norm | |||
Random covariance matrices: Universality of local statistics of eigenvalues | Annals of Probability 40 (2012), 1283--1315. | ||
Nonconventional ergodic averages and multiple recurrence for von Neumann dynamical systems | Pacific Journal of Mathematics 250-1 (2011), 1--60. DOI 10.2140/pjm.2011.250.1 | ||
Linear approximate groups | Electronic research announcements 17 (2010), 57-67 | ||
An arithmetic regularity lemma, an associated counting lemma, and applications | An Irregular Mind: Szemeredi is 70, Bolyai Society Mathematical Studies, 261-334 | ||
Yet another proof of Szemeredi's theorem | An Irregular Mind: Szemeredi is 70, Bolyai Society Mathematical Studies, 335-342 | ||
The Littlewood-Offord problem in high dimensions and a conjecture of Frankl and F\"uredi | Combinatorica, 32 (2012), 363-372 | ||
Suzuki groups as expanders | Groups, Geometry, and Dynamics 5 (2011), no. 2, 281–-299. | ||
Approximate subgroups of linear groups | |||
Strongly dense free subgroups of semisimple algebraic groups | |||
Expansion in simple groups of Lie type | J. Europ. Math. Soc. 17 (2015), 1367-1434 | ||
An inverse theorem for the Gowers U^{s+1}[N] norm | Annals of Math. 176 (2012), no. 2, 1231–1372. (Announcement: Submitted, Electronic Research Announcements) | ||
Random matrices: Localization of the eigenvalues and the necessity of four moments | Acta Mathematica Vietnamica 36 (2011), 431--449 | arXiv:1005.2901 | |
Deterministic methods to find primes | Ernie Croot Harald Helfgott | Mathematics of Computation 81 (2012), 1233-1246 | |
Large values of the Gowers-Host-Kra seminorms | |||
Outliers in the spectrum of iid matrices with bounded rank permutations | Probability theory and related fields 155 (2013), 231-263 | ||
The inverse conjecture for the Gowers norm over finite fields in low characteristic | |||
A note on approximate subgroups of GL_n(C) and uniformly nonamenable groups | Submitted, | ||
The Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices | Electronic Journal of Probability 16 (2011), 2104-2121 | ||
Random matrices: Universal properties of Eigenvectors | |||
An incidence theorem in higher dimensions | |||
Noncommutative sets of small doubling | |||
Counting the number of solutions to the Erdös-Straus equation on unit fractions | |||
The structure of approximate groups | |||
A central limit theorem for the determinant of a Wigner matrix | Adv. Math. 231 (2012), 74-101 | ||
Random matrices: The Four Moment Theorem for Wigner matrices | Random matrix theory, interacting particle systems, and integrable systems, 509–528, Math. Sci. Res. Inst. Publ., 65, Cambridge Univ. Press, New York, 2014. | ||
A nilpotent Freiman dimension lemma | European Journal of Combinatorics 34 (2013), 1287-1292 | ||
Random matrices: Sharp concentration of eigenvalues | Random matrices: Theory and Applications 2 (2013), 1350007 | ||
Every odd number greater than 1 is the sum of at most five primes | Mathematics of Computation 83 (2014), 997-1038 | ||
Random matrices: The Universality phenomenon for Wigner ensembles | In: Modern Aspects of Random Matrix Theory, Proceedings of Symposia in Applied Mathematics 72 (2013), V. Vu Editor, 121--172. | ||
The asymptotic distribution of a single eigenvalue gap of a Wigner matrix | Probability Theory and Related Fields 157 (2013), 81-106 | ||
E pluribus unum: from complexity, universality | Daedalus 141 (3) (Summer 2012) | Web version | |
New bounds for Szemeredi's theorem, Ia: Progressions of length 4 in finite field geometries revisited | Ben Green | Submitted, Proc. Lond. Math. Soc. | arXiv:1205.1330 |
Random matrices: Universality of local spectral statistics of non-Hermitian matrices | Van Vu | Annals of Prob. 43 (2015), 782-874 | arXiv:1206:1893 |
On sets defining few ordinary lines | Ben Green | Disc. Comp. Geom. 50 (2013), 409-468 | arXiv:1208.4714 |
Expanding polynomials over finite fields of large characteristic, and a regularity lemma for definable sets | Contrib. Discrete Math. 10 (2015), no. 1, 22–98 | arXiv:1211.2894 | |
Multiple recurrence in quasirandom groups | Vitaly Bergelson | Geom. Func. Anal. 24 (2014), 1-48 | arXiv:1211.6372 |
Mixing for progressions in nonabelian groups | Forum of Mathematics, Sigma 1 (2013), e2 | arXiv:1212.2586discussion | |
Multiple recurrence and convergence results associated to $\F_{p}^{\omega}$-actions | J. Anal. Math. 127 (2015), 329–378. | arXiv:1305.4717 | |
A multi-dimensional Szemer\'edi theorem for the primes via a correspondence principle | Israel J. Math., Feb 2015 | arXiv:1306.2886 | |
Local universality of zeroes of random polynomials | International Mathematics Research Notices 2014;doi: 10.1093/imrn/rnu084 | arXiv:1307.4357 | |
Algebraic combinatorial geometry: the polynomial method in arithmetic combinatorics, incidence combinatorics, and number theory | EMS surveys in the mathematical sciences 1 (2014), 1--46 | arXiv:1310.6482 | |
New equidistribution results of Zhang type | Algebra & Number Theory 8-9 (2014), 2067--2199 | arXiv:1402.0811 | |
Variants of the Selberg sieve, and bounded intervals containing many primes | Research in the Mathematical Sciences 1:12 (2014) | arXiv:1407.4897Best Paper Award | |
Large gaps between consecutive prime numbers | Sergei Konyagin | Annals Math. 183 (2016), 935--974. | arXiv:1408.4505 |
Narrow progressions in the primes | Analytic number theory, 357–379, Springer, Cham, 2015. | arXiv:1409.1327 | |
The “bounded gaps between primes” Polymath project - a retrospective | Newsletter of the European Mathematical Society, Dec 2014. Issue 94, 13--23 | arXiv:1409.8361 | |
The Elliott-Halberstam conjecture implies the Vinogradov least quadratic nonresidue conjecture | Algebra & Number Theory 9-4 (2015), 1005--1034. DOI 10.2140/ant.2015.9.1005 | arXiv:1410.7073 | |
Random matrices have simple spectrum | Combinatorica 37 (2017), no. 3, 539–553 | arXiv:1412.1438 | |
Long gaps in the primes | J. Amer. Math. Soc. 31 (2018), no. 1, 65–105 | arXiv:1412.5029 | |
An averaged form of Chowla’s conjecture | Algebra & Number Theory 9-9 (2015), 2167--2196. DOI 10.2140/ant.2015.9.2167 | arXiv:1503.05121 and erratum | |
Random matrices: tail bounds for gaps between eigenvalues | Hoi Nguyen | Probab. Theory Related Fields 167 (2017), no. 3-4, 777–816. | arXiv:1504.00396 |
Inverse theorems for sets and measures of polynomial growth | Q. J. Math. 68 (2017), no. 1, 13–57 | arXiv:1507:01276 | |
Sign patterns for the Liouville and Mobius functions | Forum Math. Sigma 4 (2016), e14, 44 pp. | arXiv:1509.01545 | |
The logarithmically averaged Chowla and Elliott conjectures for two-point correlations | Forum Math. Pi 4 (2016), e8, 36 pp. | arXiv:1509.05422 | |
The Erdos discrepancy problem | Discrete Analysis 2016:1, 26 pp. | arXiv:1509.05363 | |
Chains of large gaps between primes | Submitted | arXiv:1511.04468 | |
Sum-avoiding subsets in groups | Discrete Analysis 2016:15, 31 pp.Survey: J. Comb. 8n3, 2017, 541--552 | arXiv:1603.03068 | |
Concatenation theorems for anti-Gowers-uniform functions and Host-Kra characteristic factors | Discrete Anal. 2016, Paper No. 13, 60 pp. | arXiv:1603.07815 | |
Polynomial patterns in the primes | Forum Math. Pi 6 (2018), e1, 60 pp. | arXiv:1603.07817 | |
Equivalence of the logarithmically averaged Chowla and Sarnak conjectures | Number theory—Diophantine problems, uniform distribution and applications, 391–421, Springer, Cham, 2017. | arXiv:1605.04628 | |
An integration approach to the Toeplitz square peg problem | Forum Math. Sigma 5(2017), e30 | arXiv:1611.07441 | |
Some remarks on the lonely runner conjecture | Contrib. Discrete Math. 13 (2018), no. 2, 1–31. | arXiv:1701.02048 | |
A bound on partitioning clusters | Daniel Kane | Electron. J. Combin. 24 (2017), no. 2, Paper 2.31, 13 pp. | arXiv:1702.00912 |
Correlations of the von Mangoldt and higher divisor functions I. Long shift ranges | Proc. Lond. Math. Soc. (3) 118 (2019), no. 2, 284–350. | arXiv:1707.01315 | |
The structure of logarithmically averaged correlations of multiplicative functions, with applications to the Chowla and Elliott conjectures | Joni Teräväinen | Duke Math. J. 168 (2019), no. 11, 1977–2027 | arXiv:1708;02610 |
Odd order cases of the logarithmically averaged Chowla conjecture | Joni Teräväinen | J. Théor. Nombres Bordeaux 30 (2018), no. 3, 997–1015. | arXiv:1710.02112 |
An inverse theorem for an inequality of Kneser | Proc. Steklov Inst. Math. 303 (2018), no. 1, 193–219 | arXiv:1711.04337 | |
Correlations of the von Mangoldt and higher divisor functions II.Divisor correlations in short ranges | Math. Ann. 374 (2019), no. 1-2, 793–840. | arXiv:1712.08840 | |
The de Bruijn-Newman constant is nonnegative | Forum of Math. Pi, Volume 8 (2020), e6 | arXiv:1801.03908 | |
Long gaps in sieved sets | Kevin Ford Sergei Konyagin James Maynard Carl Pomerance | J. Eur. Math. Soc. (JEMS) 23 (2021), no. 2, 667–700. | arXiv:1802.07604 |
The structure of correlations of multiplicative functions at almost all scales, with applications to the Chowla and Elliott conjectures | Joni Teräväinen | Algebra & Number Theory 13-9 (2019), 2103--2150. DOI 10.2140/ant.2019.13.2103 | arXiv:1809.02518 |
Fourier uniformity of bounded multiplicative functions in short intervals on average | Inventiones, 220 (2020), no. 1, 1–58 | arXiv:1812.01224 | |
Least singular value, circular law, and Lindeberg exchange | Random matrices, 461–498,IAS/Park City Math. Ser., 26, Amer. Math. Soc., Providence, RI, 2019. | ||
Value patterns of multiplicative functions and related sequences | Joni Teräväinen | Forum Math Sigma Volume 7 (2019), e33 | arXiv:1904.05096 |
Effective approximation of heat flow evolution of the Riemann $\xi$ function, and a new upper bound for the de Bruijn-Newman constant | D.H.J. Polymath | Research in the Mathematical Sciences (2019) 6: 31. https://doi.org/10.1007/s40687-019-0193-1 | arXiv:1904.12438 |
Large prime gaps and probabilistic models | William Banks, Kevin Ford | Inventiones Volume 233, pages 1471–1518, (2023) | arXiv:1908.08613 |
Almost all orbits of the Collatz map attain almost bounded values | Forum Math. Pi 10 (2022), Paper No. e12, 56 pp. | arXiv:1909.03562 | |
Szemeredi's proof of Szemeredi's theorem | Acta Math. Hungar. 161 (2020), no. 2, 443–487. | discussion | |
Higher uniformity of bounded multiplicative functions in short intervals on average | Kaisa Matomaki, Maksym Radziwill, Joni Teravainen, Tamar Ziegler | Annals Math Pages 739-857 from Volume 197 (2023), Issue 2 | arXiv:2007.15644discussionAndersson award |
Zarankiewicz's problem for semilinear hypergraphs | Abdul Basit, Artem Chernikov, Sergei Starchenko, Chiu-Minh Tran | Forum of Mathematics, Sigma , Volume 9 , 2021 , e59 | arXiv:2009.02922 |
An uncountable Moore-Schmidt theorem | Asgar Jamneshan | Ergodic Theory and Dynamical Systems Volume 43 , Issue 7 , July 2023 , pp. 2376 - 2403 https://doi.org/10.1017/etds.2022.36 | arXiv:1911.12033discussion |
An uncountable Mackey-Zimmer theorem | Asgar Jamneshan | Studia Math. 266 (2022), no. 3, 241–289. | arXiv:2010.00574 |
The structure of translational tilings in Z^d | Rachel Greenfeld | Discrete Analysis 2021:16, 28 pp. | arXiv:2010.03254 |
Additive energy of regular measures in one and higher dimensions, and the fractional uncertainty principle | Laura Cladek | Ars Inven. Anal. 2021, Paper No. 1, 38 pp. | arXiv:2012.02747 |
Singmaster's conjecture in the interior of Pascal's triangle | Kaisa Matomaki, Maksym Radziwill, Xuansheng Shao, Joni Teravainen | The Quarterly Journal of Mathematics, haac006, https://doi.org/10.1093/qmath/haac006 | arXiv:2106.03335 |
Quantitative bounds forGowers uniformity of the M\"obius and von Mangoldt functions | Joni Teravainen | to appear, J. Europ. Math. Soc. | arXiv:2107.02158 |
Undecidable translational tilings with only two tiles, or one nonabelian tile | Rachel Greenfeld | to appear, Disc. Comp. Geom. | arXiv:2108.07902 |
The Hardy--Littlewood--Chowla conjecture in the presence of a Siegel zero | Joni Teravainen | J. Lond. Math. Soc. https://doi.org/10.1112/jlms.12663 | arXiv:2109.06291 |
The structure of arbitrary Conze-Lesigne systems | Asgar Jamneshan, Or Shalom | submitted, Comm. AMS | arXiv:2112.02056 |
The inverse theorem for the U3 Gowers uniformity norm on arbitrary finite abelian groups: Fourier-analytic and ergodic approaches | Asgar Jamneshan | Discrete Analysis https://doi.org/10.19086/da.84268 | arXiv:2112.13759 |
Measurable tilings by abelian group actions | Jan Grebík, Rachel Greenfeld, Václav Rozhoň | IMRN, rnad048, https://doi.org/10.1093/imrn/rnad048 | arXiv:2203.01511 |
Higher uniformity of arithmetic functions in short intervals I. All intervals | Kaisa Matomaki, Xuansheng Shao, Joni Teravainen | Forum of Mathematics, Pi. 2023;11:e29. doi:10.1017/fmp.2023.28 | arXiv:2204.03754 |
A counterexample to the periodic tiling conjecture | Rachel Greenfeld | submitted, Annals Math. | arXiv:2211.15847(announcement) |
Infinite partial sumsets in the primes | Tamar Ziegler | J. d'Analyse Jerusalem Volume 151, pages 375–389, (2023) 10.1007/s11854-023-0323-y | arXiv:2301.10303 |
A Host--Kra Fω2-system of order 5 that is not Abramov of order 5, and non-measurability of the inverse theorem for the U6(Fn2) norm | Asgar Jamneshan, Or Shalom | submitted,JEMS | arXiv:2303.04853 |
The structure of totally disconnected Host--Kra--Ziegler factors, and the inverse theorem for the Uk Gowers uniformity norms on finite abelian groups of bounded torsion | Asgar Jamneshan, Or Shalom | submitted | arXiv:2303.04860 |
An upper bound on the mean value of the Hooley delta function | Dimitris Koukouloupolous | To appear, Proc LMS | arXiv:2306.08615 |
Sumsets and entropy revisited | Ben Green Freddie Manners | Submitted, Random Structures and Algorithms | arXiv:2306.13403 |
The convergence of an alternating series of Erd\H{o}s, assuming the Hardy--Littlewood prime tuples conjecture | To appear, Comm. AMS | arXiv:2308.07205 | |
A lower bound on the mean value of the Hooley delta function | Kevin Ford Dimitris Koukouloupolous | Proc LMS 127, December 2023, 1865-1885http://dx.doi.org/10.1112/plms.12572 | arXiv:2308.11987 |
Monotone non-decreasing sequences of the Euler totient function | submitted, La Matematica | arXiv:2309.02325 | |
Undecidability of translational monotilings | Rachel Greenfeld | submitted, JEMS | arXiv:2309.09504 |
On a conjecture of Marton | Timothy Gowers Ben Green Freddie Manners | Submitted, Annals Math. | arXiv.2311.05762 |
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