Papers and preprints — Terence Tao

2026Gilbreath's conjecture: a Cramér random model and a deterministic analysis with Zachary Chase, Zach Hunter Preprint, to be submittedarXiv discussion visualization post array explorer decay-constants visualizer dependency diagram

2026Polynomial towers and inverse Gowers theory for bounded-exponent groups with Asgar Jamneshan, Or Shalom SubmittedarXiv discussion

2026Products of consecutive integers with unusual anatomy Submitted, Acta Arith. (special issue in honor of Heath-Brown)arXiv discussion

2026Primitive sets and von Mangoldt chains: Erdős Problem #1196 and beyond with Boris Alexeev, Kevin Barreto, Yanyang Li, Jared Duker Lichtman, Liam Price, Jibran Iqbal Shah, Quanyu Tang To appeararXiv discussion the zeta process dependency diagram

2026Local Bernstein theory, and lower bounds for Lebesgue constants Submitted, Constructive AnalysisarXiv discussion

2026Mathematical methods and human thought in the age of AI with Tanya Klowden Submitted, Blackwell Companion to Philosophy of MathematicsarXiv discussion

2025New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach with Timothy Trudgian, Andrew Yang To appear, Math. Comp.arXiv discussion

2025Decomposing a factorial into large factors with Boris Alexeev, Evan Conway, Matthieu Rosenfeld, Andrew V. Sutherland, Markus Uhr, Kevin Ventullo To appear, Math. Comp.arXiv code repository discussion

2025Some variants of the periodic tiling conjecture Submitted, Comm. Amer. Math. Soc.arXiv discussion

2025On the number of exceptional intervals to the prime number theorem in short intervals with Ayla Gafni To appear, Essential Number TheoryarXiv discussion

2025Rough numbers between consecutive primes with Ayla Gafni Submitted, Proc Lond. Math. Soc.arXiv discussion

2025Growth rates of sequences governed by the squarefree properties of its translates with Wouter van Doorn To appear, Acta Arith.arXiv discussion

2025Quantitative correlations and some problems on prime factors of consecutive integers with Joni Teräväinen Submitted, GAFAarXiv discussion

2025New Nikodym set constructions over finite fields To appear, Pacific J. Math.arXiv discussion

2025Sum-difference exponents for boundedly many slopes, and rational complexity Submitted, Discrete AnalysisarXiv discussion

2025The maximal length of the Erdős–Herzog–Piranian lemniscate in high degree To appear, Journal d'Analyse MathematiquearXiv discussion

2025Mathematical exploration and discovery at scale with Bogdan Georgiev, Javier Gómez-Serrano, Adam Zsolt Wagner To appear, Proc. Natl. Acad. Sci. USAarXiv code repository discussion

2025The Equational Theories Project: Advancing Collaborative Mathematical Research at Scale with Matthew Bolan, Joachim Breitner, Jose Brox, Nicholas Carlini, Mario Carneiro, Floris van Doorn, Martin Dvorak, Andrés Goens, Aaron Hill, Harald Husum, Hernán Ibarra Mejia, Zoltan Kocsis, Bruno Le Floch, Amir Livne Bar-on, Lorenzo Luccioli, Douglas McNeil, Alex Meiburg, Pietro Monticone, Pace P. Nielsen, Emmanuel Osalotioman Osazuwa, Giovanni Paolini, Marco Petracci, Bernhard Reinke, David Renshaw, Marcus Rossel, Cody Roux, Jérémy Scanvic, Shreyas Srinivas, Anand Rao Tadipatri, Vlad Tsyrklevich, Fernando Vaquerizo-Villar, Daniel Weber, Fan Zheng SubmittedarXiv code repository discussion

2024Marton's conjecture for abelian groups of finite torsion with Timothy Gowers, Ben Green, Freddie Manners SubmittedarXiv code repository discussion

2024On product representations of squares Submitted, Acta Math. HungaricaarXiv discussion

2024Dense sets of natural numbers with unusually large least common multiples To appear, IntegersarXiv discussion

2024Planar point sets with forbidden 4-point patterns and few distinct distances To appear, Combin. Disc. Geom.arXiv discussion

2024Higher uniformity of arithmetic functions in short intervals II. Almost all intervals with Kaisa Matomäki, Maksym Radziwiłł, Xuansheng Shao, Joni Teräväinen Invent. math. (2026)arXiv discussion

2024On several irrationality problems for Ahmes series with Vjekoslav Kovač Submitted, Acta Math. HungaricaarXiv discussion

2024On the distribution of eigenvalues of GUE and its minors at fixed index Submitted, Random Matrix Theory and ApplicationsarXiv discussion

2023Would it be possible to create a tool to automatically diagram papers?short story Blog postblog

2023Infinite partial sumsets in the primes with Tamar Ziegler J. d'Analyse Jerusalem Volume 151, pages 375–389, (2023) 10.1007/s11854-023-0323-yarXiv discussion

2023A 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 with Asgar Jamneshan, Or Shalom Submitted, Math. AnnalenarXiv discussion

2023The 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 with Asgar Jamneshan, Or Shalom To appear, Annales de la Faculté des Sciences de ToulousearXiv discussion

2023An upper bound on the mean value of the Hooley delta function with Dimitris Koukoulopoulos To appear, Proc LMSarXiv discussion

2023Sumsets and entropy revisited with Ben Green, Freddie Manners Random Structures and Algorithms (2023). doi:10.1002/rsa.21252arXiv discussion

2023The convergence of an alternating series of Erdős, assuming the Hardy--Littlewood prime tuples conjecture To appear, Comm. AMSarXiv discussion

2023A lower bound on the mean value of the Hooley delta function with Kevin Ford, Dimitris Koukoulopoulos Proc LMS 127, December 2023, 1865–1885 http://dx.doi.org/10.1112/plms.12572arXiv discussion

2023Monotone non-decreasing sequences of the Euler totient function La Matematica (2024). doi:10.1007/s44007-024-00115-zarXiv discussion

2023Undecidability of translational monotilings with Rachel Greenfeld To appear, J. Eur. Math. Soc.arXiv discussion

2023On a conjecture of Marton with Timothy Gowers, Ben Green, Freddie Manners Submitted, Annals Math.arXiv code repository discussion

2023Adjoint Brascamp-Lieb inequalities with Jon Bennett Submitted, Proc. Lond. Math. Soc.arXiv discussion

2023A Maclaurin type inequality To appear, Proc. Amer. Math. Soc.arXiv code repository discussion

2023Sums of GUE matrices and concentration of hives from correlation decay of eigengaps with Hariharan Narayanan, Scott Sheffield Probab. Theory Relat. Fields 190 (2024), 1121–1165.arXiv discussion

2022A Bayesian probability worksheetshort story Blog postblog

2022Measurable tilings by abelian group actions with Jan Grebík, Rachel Greenfeld, Václav Rozhoň IMRN, rnad048, https://doi.org/10.1093/imrn/rnad048arXiv discussion

2022Higher uniformity of arithmetic functions in short intervals I. All intervals with Kaisa Matomäki, Xuansheng Shao, Joni Teräväinen Forum of Mathematics, Pi. 2023;11:e29. doi:10.1017/fmp.2023.28arXiv discussion

2022A counterexample to the periodic tiling conjecture with Rachel Greenfeld submitted, Annals Math.arXiv arXiv discussion dependency diagram

2022Perfectly packing a square by squares of nearly harmonic sidelength Comp. Disc. Geom.(2023). https://doi.org/10.1007/s00454-023-00523-yarXiv discussion

2021Nines of safety: a proposed unit of measurement of riskshort story Blog postblog

2021Singmaster's conjecture in the interior of Pascal's triangle with Kaisa Matomäki, Maksym Radziwiłł, Xuansheng Shao, Joni Teräväinen The Quarterly Journal of Mathematics, haac006, https://doi.org/10.1093/qmath/haac006arXiv discussion

2021Quantitative bounds for Gowers uniformity of the Möbius and von Mangoldt functions with Joni Teräväinen J. Eur. Math. Soc. 27 (2025), no. 4, 1321–1384.arXiv discussion

2021Undecidable translational tilings with only two tiles, or one nonabelian tile with Rachel Greenfeld to appear, Disc. Comp. Geom.arXiv discussion

2021The Hardy--Littlewood--Chowla conjecture in the presence of a Siegel zero with Joni Teräväinen J. Lond. Math. Soc. https://doi.org/10.1112/jlms.12663arXiv discussion

2021The structure of arbitrary Conze-Lesigne systems with Asgar Jamneshan, Or Shalom submitted, Comm. AMSarXiv discussion

2021The inverse theorem for the U3 Gowers uniformity norm on arbitrary finite abelian groups: Fourier-analytic and ergodic approaches with Asgar Jamneshan Discrete Analysis https://doi.org/10.19086/da.84268arXiv discussion

2021The effective potential of an $M$-matrix with Marcel Filoche, Svetlana Mayboroda J. Math. Phys. 62, 041902 (2021)arXiv

2021Elias M. Stein (2013-2018) with Lillian Pierce et al. Not. Amer. Math. Soc. 68 (2021), 546–563journal

2021Optimal sine and sawtooth inequalities with Louis Esser, Burt Totaro, Chengxi Wang J. Fourier Anal. Appl. (2022) 28:14arXiv discussion

2020Szemeredi's proof of Szemeredi's theorem Acta Math. Hungar. 161 (2020), no. 2, 443–487.journal pdf discussion

2020Higher uniformity of bounded multiplicative functions in short intervals on average with Kaisa Matomäki, Maksym Radziwiłł, Joni Teräväinen, Tamar Ziegler Annals Math Pages 739–857 from Volume 197 (2023), Issue 2arXiv discussion

2020Zarankiewicz's problem for semilinear hypergraphs with Abdul Basit, Artem Chernikov, Sergei Starchenko, Chiu-Minh Tran Forum of Mathematics, Sigma , Volume 9 , 2021 , e59arXiv discussion

2020An uncountable Mackey-Zimmer theorem with Asgar Jamneshan Studia Math. 266 (2022), no. 3, 241–289.journal arXiv discussion

2020The structure of translational tilings in Z^d with Rachel Greenfeld Discrete Analysis 2021:16, 28 pp.arXiv discussion

2020Additive energy of regular measures in one and higher dimensions, and the fractional uncertainty principle with Laura Cladek Ars Inven. Anal. 2021, Paper No. 1, 38 pp.journal arXiv discussion

2020Pointwise ergodic theorems for non-conventional bilinear polynomial averages with Ben Krause, Mariusz Mirek Annals Math. Pages 997–1109 from Volume 195 (2022), Issue 3arXiv discussion

2020The Ionescu-Wainger multiplier theorem and the adeles Mathematika 67 (2021), no. 3, 647–677.journal arXiv discussion

2020Homogenization of iterated singular integrals with applications to random quasiconformal maps with Kari Astala, Steffen Rohde, Eero Saksman Revista Iberoamericana VOL. 38, NO. 7PP. 2285–2336journal arXiv

2020Fractional free convolution powers. With an appendix by David Jekel with Dimitri Shlyakhtenko To appear, Indiana U. Math. J.arXiv discussion

2020Foundational aspects of uncountable measure theory: Gelfand duality, Riesz representation, canonical models, and canonical disintegration with Asgar Jamneshan Fundamenta Mathematicae 261 (2023), 1–98arXiv discussion

2020Sendov's conjecture for sufficiently high degree polynomials Acta Mathematica, Vol. 229, No. 2 (2022), pp. 347–392arXiv discussion

2020Louis Nirenbergobituarylink

2020John Conwayobituarylink

2020Vaughan Jonesobituarylink

2019Least singular value, circular law, and Lindeberg exchange Random matrices, 461–498,IAS/Park City Math. Ser., 26, Amer. Math. Soc., Providence, RI, 2019.journal pdf

2019Value patterns of multiplicative functions and related sequences with Joni Teräväinen Forum Math Sigma Volume 7 (2019), e33arXiv discussion

2019Effective approximation of heat flow evolution of the Riemann xi function, and a new upper bound for the de Bruijn-Newman constant with D.H.J. Polymath Research in the Mathematical Sciences (2019) 6: 31. https://doi.org/10.1007/s40687-019-0193-1arXiv code repository discussion

2019Large prime gaps and probabilistic models with William Banks, Kevin Ford Inventiones Volume 233, pages 1471–1518, (2023)arXiv discussion

2019Almost all orbits of the Collatz map attain almost bounded values Forum Math. Pi 10 (2022), Paper No. e12, 56 pp.journal arXiv discussion

2019An uncountable Moore-Schmidt theorem with Asgar Jamneshan Ergodic Theory and Dynamical Systems Volume 43 , Issue 7 , July 2023 , pp. 2376 - 2403 https://doi.org/10.1017/etds.2022.36arXiv discussion

2019Sharp bounds for multilinear curved Kakeya, restriction and oscillatory integral estimates away from the endpoint Mathematika 66 (2020), 517–576arXiv discussion

2019A Close Call: How a Near Failure Propelled Me to Succeed Living Proof: Stories of Resilience Along the Mathematical Journey, American Math. Society, Math. Assoc. America, 2019. A. Henderson, E. Lawrence, M. Pons, D. Taylor eds., 96–99.link

2019Eigenvectors from Eigenvalues: a survey of a basic identity in linear algebra. with Peter Denton, Stephen Parke, Xining Zhang Bull. Amer. Math. Soc. (N.S.) 59 (2022), no. 1, 31–58.journal arXiv discussion discussion

2019On the universality of the incompressible Euler equation on compact manifolds, II. Non-rigidity of Euler flows Pure Appl. Funct. Anal. 5 (2020), no. 6, 1425–1443.journal arXiv discussion

2019Searching for singularities in the Navier–Stokes equations Nature Reviews Physics 1,418–419(2019)journal discussion

2019Quantitative bounds for critically bounded solutions to the Navier-Stokes equations Nine mathematical challenges—an elucidation, 149–193, Proc. Sympos. Pure Math., 104, Amer. Math. Soc., Providence, RI, [2021], ©2021.journal arXiv discussion

2018QED version 2.0: an interactive text in first-order logicshort story Blog postcode repository blog interactive tool

2018The de Bruijn-Newman constant is nonnegative with Brad Rodgers Forum of Math. Pi, Volume 8 (2020), e6arXiv discussion slides

2018Long gaps in sieved sets with Kevin Ford, Sergei Konyagin, James Maynard, Carl Pomerance J. Eur. Math. Soc. (JEMS) 23 (2021), no. 2, 667–700.journal arXiv discussion

2018The structure of correlations of multiplicative functions at almost all scales, with applications to the Chowla and Elliott conjectures with Joni Teräväinen Algebra & Number Theory 13-9 (2019), 2103–2150. DOI 10.2140/ant.2019.13.2103arXiv discussion

2018Fourier uniformity of bounded multiplicative functions in short intervals on average with Kaisa Matomäki, Maksym Radziwiłł Inventiones, 220 (2020), no. 1, 1–58arXiv discussion

2018Commutators close to the identity J. Op. Thy. 82:2(2019), 369–382arXiv discussion

2018Embedding the Heisenberg group into a bounded dimensional Euclidean space with optimal distortion Rev. Mat. Iberoam. 37 (2021), no. 1, 1–44.journal arXiv discussion

2018Elias Steinobituarylink

2018Jean Bourgainobituarylink

2017New bounds for Szemeredi's Theorem, III: A polylog bound for r_4(N) with Ben Green Mathematika Volume 63, Issue 3 2017 , pp. 944–1040journal arXiv discussion

2017Some remarks on the lonely runner conjecture Contrib. Discrete Math. 13 (2018), no. 2, 1–31.journal arXiv discussion

2017A bound on partitioning clusters with Daniel Kane Electron. J. Combin. 24 (2017), no. 2, Paper 2.31, 13 pp.arXiv discussion

2017Correlations of the von Mangoldt and higher divisor functions I. Long shift ranges with Kaisa Matomäki, Maksym Radziwiłł Proc. Lond. Math. Soc. (3) 118 (2019), no. 2, 284–350.arXiv discussion

2017The structure of logarithmically averaged correlations of multiplicative functions, with applications to the Chowla and Elliott conjectures with Joni Teräväinen Duke Math. J. 168 (2019), no. 11, 1977–2027journal arXiv discussion

2017Odd order cases of the logarithmically averaged Chowla conjecture with Joni Teräväinen J. Théor. Nombres Bordeaux 30 (2018), no. 3, 997–1015.journal arXiv discussion

2017An inverse theorem for an inequality of Kneser Proc. Steklov Inst. Math. 303 (2018), no. 1, 193–219journal arXiv discussion

2017Correlations of the von Mangoldt and higher divisor functions II. Divisor correlations in short ranges with Kaisa Matomäki, Maksym Radziwiłł Math. Ann. 374 (2019), no. 1–2, 793–840.journal arXiv discussion

2017On the sign patterns of entrywise positivity preservers in fixed dimension with Apoorva Khare Amer. J. Math. 143 (2021), 1863–1929.Extended abstract: FPSAC 2018, Volume 80B of Seminaire Lotharingien de Combinatoire (2018)arXiv discussion

2017On the universality of potential well dynamics Dynamics of PDE 14 (2017), 219–238.arXiv discussion

2017On the universality of the incompressible Euler equation on compact manifolds Disc. Cont. Dynam. Sys. 38 (2018), 1553–1565arXiv discussion

2017Maryam Mirzakhaniobituarylink

2016Visualising random variablesshort story Blog postblog interactive tool

2016Sum-avoiding subsets in groups with Van Vu Discrete Analysis 2016:15, 31 pp.Survey: J. Comb. 8n3, 2017, 541–552arXiv arXiv discussion

2016Concatenation theorems for anti-Gowers-uniform functions and Host-Kra characteristic factors with Tamar Ziegler Discrete Anal. 2016, Paper No. 13, 60 pp.arXiv discussion

2016Polynomial patterns in the primes with Tamar Ziegler Forum Math. Pi 6 (2018), e1, 60 pp.arXiv discussion

2016Equivalence of the logarithmically averaged Chowla and Sarnak conjectures Number theory—Diophantine problems, uniform distribution and applications, 391–421, Springer, Cham, 2017.arXiv discussion

2016An integration approach to the Toeplitz square peg problem Forum Math. Sigma 5(2017), e30arXiv discussion

2016Finite time blowup for a supercritical defocusing nonlinear wave system Anal. PDE 9 (2016), no. 8, 1999–2030.arXiv discussion

2016Finite time blowup for a high dimensional nonlinear wave systems with bounded smooth nonlinearity Comm. Partial Differential Equations 41 (2016), no. 8, 1204–1229.arXiv discussion

2016Finite time blowup for Lagrangian modifications of the three-dimensional Euler equation Ann. PDE 2 (2016), no. 2, Art. 9, 79 pp.arXiv discussion

2016Finite time blowup for a supercritical defocusing nonlinear Schrödinger system Analysis & PDE 11-2 (2018), 383–438. DOI 10.2140/apde.2018.11.383arXiv discussion

2015An averaged form of Chowla’s conjecture with Kaisa Matomäki, Maksym Radziwiłł Algebra & Number Theory 9-9 (2015), 2167–2196. DOI 10.2140/ant.2015.9.2167arXiv discussion

2015Random matrices: tail bounds for gaps between eigenvalues with Van Vu, Hoi Nguyen Probab. Theory Related Fields 167 (2017), no. 3–4, 777–816.arXiv discussion

2015Inverse theorems for sets and measures of polynomial growth Q. J. Math. 68 (2017), no. 1, 13–57arXiv discussion

2015Sign patterns for the Liouville and Mobius functions with Kaisa Matomäki, Maksym Radziwiłł Forum Math. Sigma 4 (2016), e14, 44 pp.arXiv discussion

2015The logarithmically averaged Chowla and Elliott conjectures for two-point correlations Forum Math. Pi 4 (2016), e8, 36 pp.arXiv discussion

2015The Erdos discrepancy problem Discrete Analysis 2016:1, 26 pp.arXiv discussion

2015Chains of large gaps between primes with Kevin Ford, James Maynard SubmittedarXiv discussion

2015Failure of the $L^1$ pointwise and maximal ergodic theorems for the free group Forum Math. Sigma 3 (2015), e27, 19 pp.arXiv discussion

2015Cancellation in the multilinear Hilbert transform Collectanea Mathematica 67 (2016), 1–16arXiv discussion

2015Klaus Rothobituarylink

2014New equidistribution results of Zhang type with D.H.J. Polymath Algebra & Number Theory 8-9 (2014), 2067–2199arXiv discussion

2014Variants of the Selberg sieve, and bounded intervals containing many primes with D.H.J. Polymath Research in the Mathematical Sciences 1:12 (2014)arXiv reference material & source files discussion

2014Large gaps between consecutive prime numbers with Kevin Ford, Ben Green, Sergei Konyagin Annals Math. 183 (2016), 935–974.arXiv discussion

2014Narrow progressions in the primes with Tamar Ziegler Analytic number theory, 357–379, Springer, Cham, 2015.arXiv discussion

2014The “bounded gaps between primes” Polymath project - a retrospective with D.H.J. Polymath Newsletter of the European Mathematical Society, Dec 2014. Issue 94, 13–23arXiv discussion

2014The Elliott-Halberstam conjecture implies the Vinogradov least quadratic nonresidue conjecture Algebra & Number Theory 9-4 (2015), 1005–1034. DOI 10.2140/ant.2015.9.1005arXiv discussion

2014Random matrices have simple spectrum with Van Vu Combinatorica 37 (2017), no. 3, 539–553arXiv discussion

2014Long gaps in the primes with Kevin Ford, Ben Green, Sergei Konyagin, James Maynard J. Amer. Math. Soc. 31 (2018), no. 1, 65–105arXiv discussion

2014Finite time blowup for an averaged three-dimensional Navier-Stokes equation J. Amer. Math. Soc. 29 (2016), no. 3, 601–674.arXiv discussion slides

2013Expansion in simple groups of Lie type with Emmanuel Breuillard, Ben Green, Bob Guralnick J. Europ. Math. Soc. 17 (2015), 1367–1434journal arXiv discussion

2013Multiple recurrence and convergence results associated to F_p^omega-actions with Vitaly Bergelson, Tamar Ziegler J. Anal. Math. 127 (2015), 329–378.arXiv discussion

2013A multi-dimensional Szemerédi theorem for the primes via a correspondence principle with Tamar Ziegler Israel J. Math., Feb 2015arXiv discussion

2013Local universality of zeroes of random polynomials with Van Vu International Mathematics Research Notices 2014;doi: 10.1093/imrn/rnu084arXiv discussion

2013Algebraic combinatorial geometry: the polynomial method in arithmetic combinatorics, incidence combinatorics, and number theory EMS surveys in the mathematical sciences 1 (2014), 1–46journal arXiv discussion

2013Concentration compactness for critical wave maps, by Joachim Krieger and Wilhelm Schlag Bull. Amer. Math. Soc. 50 (2013), 655–662journal pdf

2012Gamifying algebrashort story Blog postblog interactive tool

2012New version of algebra gameshort story Blog postblog interactive tool

2012Random matrices: Sharp concentration of eigenvalues with Van Vu Random matrices: Theory and Applications 2 (2013), 1350007journal arXiv discussion

2012Every odd number greater than 1 is the sum of at most five primes Mathematics of Computation 83 (2014), 997–1038journal arXiv discussion

2012Random matrices: The Universality phenomenon for Wigner ensembles with Van Vu In: Modern Aspects of Random Matrix Theory, Proceedings of Symposia in Applied Mathematics 72 (2013), V. Vu Editor, 121–172.arXiv discussion

2012The asymptotic distribution of a single eigenvalue gap of a Wigner matrix Probability Theory and Related Fields 157 (2013), 81–106journal arXiv discussion

2012E pluribus unum: from complexity, universality Daedalus 141 (3) (Summer 2012)journal

2012New bounds for Szemeredi's theorem, Ia: Progressions of length 4 in finite field geometries revisited with Ben Green Submitted, Proc. Lond. Math. Soc.arXiv discussion

2012Random matrices: Universality of local spectral statistics of non-Hermitian matrices with Van Vu Annals of Prob. 43 (2015), 782–874arXiv discussion

2012On sets defining few ordinary lines with Ben Green Disc. Comp. Geom. 50 (2013), 409–468journal arXiv discussion

2012Expanding polynomials over finite fields of large characteristic, and a regularity lemma for definable sets Contrib. Discrete Math. 10 (2015), no. 1, 22–98arXiv discussion

2012Multiple recurrence in quasirandom groups with Vitaly Bergelson Geom. Func. Anal. 24 (2014), 1–48journal arXiv discussion

2012Mixing for progressions in nonabelian groups Forum of Mathematics, Sigma 1 (2013), e2journal arXiv discussion

2012Nonlinear Fourier Analysis with Christoph Thiele To be submittedarXiv pdf

2012Bill Thurstonobituarylink

2012Garth Gaudryobituarylink

2012Lars Hörmanderobituarylink

2011Random matrices: Localization of the eigenvalues and the necessity of four moments with Van Vu Acta Mathematica Vietnamica 36 (2011), 431–449journal discussion

2011The inverse conjecture for the Gowers norm over finite fields in low characteristic with Tamar Ziegler Annals of Combinatorics 16 (2012), 121–188journal arXiv discussion

2011A note on approximate subgroups of GL_n(C) and uniformly nonamenable groups with Emmanuel Breuillard, Ben Green Submitted,arXiv discussion

2011The Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices with Van Vu Electronic Journal of Probability 16 (2011), 2104–2121journal arXiv discussion

2011Random matrices: Universal properties of Eigenvectors with Van Vu Random matrices: Theory and Applications 1 (2012), 1150001journal arXiv discussion

2011An incidence theorem in higher dimensions with Jozsef Solymosi Disc. Comp. Geom. 48 (2012), 255–280journal arXiv discussion

2011Noncommutative sets of small doubling European Journal of Combinatorics 34 (2013), 1459–1465journal arXiv discussion

2011Counting the number of solutions to the Erdös-Straus equation on unit fractions with Christian Elsholtz J. Aust. Math. Soc. 94 (2013), 50–105journal arXiv discussion

2011The structure of approximate groups with Emmanuel Breuillard, Ben Green Publ. Math. Inst. Hautes Études Sci. 116 (2012), 115–221journal arXiv discussion

2011A central limit theorem for the determinant of a Wigner matrix with Van Vu Adv. Math. 231 (2012), 74–101journal arXiv discussion

2011Random matrices: The Four Moment Theorem for Wigner matrices with Van Vu Random matrix theory, interacting particle systems, and integrable systems, 509–528, Math. Sci. Res. Inst. Publ., 65, Cambridge Univ. Press, New York, 2014.arXiv discussion

2011A nilpotent Freiman dimension lemma with Emmanuel Breuillard, Ben Green European Journal of Combinatorics 34 (2013), 1287–1292journal arXiv discussion

2011Effective limiting absorption principles, and applications with Igor Rodnianski Comm. Math. Phys. 333 (2015), 1–95journal arXiv discussion

2011Localisation and compactness properties of the Navier-Stokes global regularity problem Analysis & PDE 6 (2013), 25–107journal arXiv discussion

2010Linear approximate groups with Emmanuel Breuillard, Ben Green Electronic research announcements 17 (2010), 57–67journal arXiv discussion

2010An arithmetic regularity lemma, an associated counting lemma, and applications with Ben Green An Irregular Mind: Szemeredi is 70, Bolyai Society Mathematical Studies, 261–334arXiv discussion

2010Yet another proof of Szemeredi's theorem with Ben Green An Irregular Mind: Szemeredi is 70, Bolyai Society Mathematical Studies, 335–342arXiv discussion

2010The Littlewood-Offord problem in high dimensions and a conjecture of Frankl and Füredi with Van Vu Combinatorica, 32 (2012), 363–372journal arXiv discussion

2010Suzuki groups as expanders with Emmanuel Breuillard, Ben Green Groups, Geometry, and Dynamics 5 (2011), no. 2, 281–-299.journal arXiv discussion

2010Approximate subgroups of linear groups with Emmanuel Breuillard, Ben Green GAFA 21 (2011), 774–819journal arXiv discussion

2010Strongly dense free subgroups of semisimple algebraic groups with Emmanuel Breuillard, Ben Green, Bob Guralnick Israel J. Math. 192 (2012), 347–379journal arXiv discussion

2010An inverse theorem for the Gowers U^s+1[N] norm with Ben Green, Tamar Ziegler Annals of Math. 176 (2012), no. 2, 1231–1372.journal arXiv arXiv discussion discussion

2010Deterministic methods to find primes with Ernie Croot, Harald Helfgott Mathematics of Computation 81 (2012), 1233–1246journal arXiv discussion

2010Large values of the Gowers-Host-Kra seminorms with Tanja Eisner J. d’Analyse Mathematique 117 (2012), 133–186journal arXiv discussion

2010Outliers in the spectrum of iid matrices with bounded rank permutations Probability theory and related fields155 (2013), 231–263journal arXiv discussion

2010Scale-oblivious metric fragmentation and the nonlinear Dvoretzky theorem with Assaf Naor Israel J. Math. 192 (2012), 489–504journal arXiv discussion

2010Asymptotic decay for a one-dimensional nonlinear wave equation with Hans Lindblad Analysis & PDE 5 (2012), 411–422.journal arXiv discussion

2009An inverse theorem for the uniformity seminorms associated with the action of F^omega with Vitaly Bergelson, Tamar Ziegler Geom. Funct. Anal. 19 (2010), no. 6, 1539–1596.arXiv discussion

2009A sharp inverse Littlewood-Offord theorem with Van Vu Random Structures and Algorithms37 (2010), 525–539journal arXiv discussion

2009Random matrices: the distribution of smallest singular values with Van Vu GAFA, 20 (2010), 260–297journal arXiv discussion

2009Random matrices: universality of local eigenvalue statistics with Van Vu Acta Math 206 (2011), 127–204journal arXiv discussion

2009An equivalence between inverse sumset theorems and inverse conjectures for the U^3 norm with Ben Green Math. Proc. Camb. Phil. Soc. 149 (2010), 1–19journal arXiv discussion

2009Freiman’s theorem for solvable groups Contributions to Discrete Mathematics 5 (2010), no. 2, 137–184,journal arXiv discussion

2009Sumset and inverse sumset theorems for Shannon entropy Combinatorics, Probability, and Computing 19 (2010), 603–639journal arXiv discussion

2009Bulk universality for Wigner hermitian matrices with subexponential decay with Laszlo Erdos, Benjamin Schlein, Van Vu, Horng-Tzer Yau, Jose Ramírez Math. Res. Lett. 17 (2010), 793–794journal arXiv discussion

2009Random matrices: universality of local eigenvalue statistics up to the edge with Van Vu Communications in Mathematical Physics, 298 (2010), 549–572journal arXiv discussion

2009A remark on partial sums involving the Mobius function Bull. Aust. Math. Soc. 81 (2010), 343–349journal arXiv discussion

2009A new proof of the density Hales-Jewett theorem with D.H.J. Polymath Annals of Math. 175 (2012), 1283–1327.arXiv discussion

2009A finitary version of Gromov's polynomial growth theorem with Yehuda Shalom GAFA 20 (2010), no. 6, 1502–1547.journal arXiv discussion

2009An inverse theorem for the Gowers U^4 norm with Ben Green, Tamar Ziegler Glasgow Mathematical Journal 53(2011), no. 1, 1–50journal arXiv arXiv

2009Random covariance matrices: Universality of local statistics of eigenvalues with Van Vu Annals of Probability 40 (2012), 1283–1315.arXiv discussion

2009Nonconventional ergodic averages and multiple recurrence for von Neumann dynamical systems with Tim Austin, Tanja Eisner Pacific Journal of Mathematics 250-1 (2011), 1–60. DOI 10.2140/pjm.2011.250.1journal arXiv discussion

2009Random Martingales and localization of maximal inequalities with Assaf Naor J. Funct. Anal. 259 (2010), 731–779journal arXiv discussion

2009The Kakeya set and maximal conjectures for algebraic varieties over finite fields with Jordan Ellenberg, Richard Oberlin Mathematika 56 (2010) 1–25journal arXiv arXiv

2009A variation norm Carleson theorem with Richard Oberlin, Andreas Seeger, Christoph Thiele, Jim Wright J. Europ. Math. Soc. 14 (2012), 421–464.journal arXiv discussion

2009The high exponent limit p to infty for the one-dimensional nonlinear wave equation Anal. PDE 2 (2009), no. 2, 235–259.arXiv discussion

2009An inverse theorem for the bilinear L^2 Strichartz estimate for the wave equation Unpublished preprintarXiv discussion

2009Global regularity of wave maps VI. Abstract theory of minimal-energy blowup solutions(“Project Heatwave”, part 4 of 5.) Unpublished preprintarXiv discussion

2009Global regularity of wave maps VII. Control of delocalised or dispersed solutions(“Project Heatwave”, part 5 of 5.) Unpublished preprintarXiv discussion

2009Global regularity for a logarithmically supercritical hyperdissipative Navier-Stokes equation Analysis & PDE 2 (2009), 361–366journal arXiv discussion

2009Operator splitting for the KdV equation with Helge Holden, Kenneth Karlsen, Nils Risebro Math. Comp. 80 (2011) 821–846.journal arXiv discussion

2009Global well-posedness for the Maxwell-Klein-Gordon equation below the energy norm with Mark Keel, Tristan Roy Discrete Cont. Dynam. Systems 30 (2011), 573–621journal arXiv discussion slides

2009The power of matrix completion: near-optimal convex relaxation with Emmanuel Candes To appear, IEEE Inf. Theoryjournal arXiv discussion

2009Israel Gelfandobituarylink

2008The Möbius function is asymptotically orthogonal to nilsequences with Ben Green Annals of Math., 175 (2012), 541–566journal arXiv discussion

2008On the testability and repair of hereditary hypergraph properties with Tim Austin Random Structures and Algorithms 36 (2010), 373–463journal arXiv discussion

2008A remark on primality testing and decimal expansions J. Aust. Math. Soc. 91 (2011), 405–413journal arXiv discussion

2008On the permanent of random Bernoulli matrices with Van Vu Adv. Math. 220 (2009), 657—669.journal arXiv pdf discussion

2008Smooth analysis of the condition number and the least singular value with Van Vu Mathematics of Computation, 79 (2010), 2333–2352journal arXiv discussion

2008The sum-product phenomenon in arbitrary rings Contrib. Discrete Math. 4 (2009), no. 2, 59–82.arXiv discussion

2008Random matrices: Universality of ESDs and the circular law with Van Vu, Manjunath Krishnapur Annals of Probability 38 (2010), no. 5, 2023–2065.arXiv discussion

2008From the Littlewood-Offord problem to the circular law: universality of the spectral distribution of random matrices with Van Vu Bull. Amer. Math. Soc. 46 (2009), 377–396journal arXiv discussion

2008The inverse conjecture for the Gowers norm over finite fields via the correspondence principle with Tamar Ziegler Analysis & PDE 3 (2010), 1–20journal arXiv discussion

2008Classification of almost quarter-pinched manifolds with Peter Petersen Proc. Amer. Math. Soc. 137 (2009), 2437—2440.journal arXiv discussion

2008Why are solitons stable? Bull. Amer. Math. Soc. 46 (2009), 1–33.journal arXiv discussion

2008A global compact attractor for high-dimensional defocusing non-linear Schrödinger equations with potential Dynamics of PDE 5 (2008), 101—116.journal arXiv discussion

2008Global regularity of wave maps III. Large energy from R^1+2 to hyperbolic spaces.("Project Heatwave", part 1 of 5.) Unpublished preprintarXiv discussion

2008Global regularity of wave maps IV. Absence of stationary or self-similar solutions in the energy class("Project Heatwave", part 2 of 5.) Unpublished preprintarXiv discussion

2008Global existence and uniqueness results for weak solutions of the focusing mass-critical non-linear Schrödinger equation Anal. PDE 2 (2009), no. 1, 61–81.arXiv discussion

2008Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrodinger equation with Jim Colliander, Mark Keel, Gigliola Staffilani, Hideo Takaoka Inventiones Math.181 (2010), 39–113journal arXiv discussion

2008Global regularity of wave maps V. Large data local well-posedness in the energy class("Project Heatwave", part 3 of 5.) Unpublished preprintarXiv discussion

2008Reflections on compressed sensing with Emmanuel Candes IEEE Information Theory Society Newsletter, Dec 2008 58 (4), 20–23journal

2008Oded Schrammobituarylink

2007John-type theorems for generalized arithmetic progressions and iterated sumsets with Van Vu Adv. in Math. 219 (2008), 428—449.journal arXiv

2007A note on the Freiman and Balog-Szemeredi-Gowers theorems in finite fields with Ben Green J. Aust. Math. Soc. 86 (2009), 61–74.journal arXiv

2007The condition number of a randomly perturbed matrix with Van Vu Proceedings of the thirty-ninth annual ACM symposium on Theory of computing (STOC) 2007, 248–255arXiv discussion slides

2007Freiman's theorem in finite fields via extremal set theory with Ben Green Combin. Probab. Comput. 18 (2009), no. 3, 335–355arXiv discussion

2007Norm convergence of multiple ergodic averages for commuting transformations Ergodic Theory and Dynamical Systems 28 (2008), 657–688journal arXiv discussion

2007Structure and randomness in combinatorics Proceedings of the 48th annual symposium on Foundations of Computer Science (FOCS) 2007, 3–18arXiv discussion discussion slides

2007Random Matrices: The circular Law with Van Vu Communications in Contemporary Mathematics, 10 (2008), 261–307journal arXiv discussion

2007The quantitative behaviour of polynomial orbits on nilmanifolds with Ben Green Annals of Math. Volume 175 (2012), Issue 2, 465–540.journal arXiv arXiv discussion

2007The distribution of polynomials over finite fields, with applications to the Gowers norms with Ben Green Contrib. Discrete Math. 4 (2009), no. 2, 1–36.arXiv discussion discussion

2007A quantitative version of the Besicovitch projection theorem via multiscale analysis Proc. Lond. Math. Soc. 98 (2009), 559–584.journal arXiv discussion

2007What is good mathematics? Mathematical Perspectives, Bull. Amer. Math. Soc. 44 (2007), 623–634.journal arXiv

2007Multi-linear multipliers associated to simplexes of arbitrary length with Camil Muscalu, Christoph Thiele Submitted, Analysis & PDEjournal arXiv discussion

2007The Walsh model for $M_2^*$ Carleson with Ciprian Demeter, Michael Lacey, Christoph Thiele Revista Mat. Iber. 24 (2008), 721–744journal arXiv discussion

2007Resonant decompositions and the I-method for cubic nonlinear Schrodinger on R^2 with Jim Colliander, Mark Keel, Gigliola Staffilani, Hideo Takaoka Disc. Cont. Dynam. Systems A 21 (2008), 665–686journal arXiv discussion

2007The cubic nonlinear Schrödinger equation in two dimensions with radial data with Rowan Killip, Monica Visan J. Eur. Math. Soc. (JEMS) 11 (2009), no. 6, 1203–1258.arXiv discussion

2007A quantitative formulation of the global regularity problem for the periodic Navier-Stokes equation Dynamics of PDE 4 (2007), 293–302.journal arXiv discussion

2007Paul Cohenobituarylink

2007Atle Selbergobituarylink

2006New bounds for Szemeredi's Theorem, II: A new bound for r_4(N) with Ben Green 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.arXiv

2006Quadratic uniformity of the Möbius function with Ben Green Annales de l’Institut Fourier 58 (2009), 1863—1935.journal arXiv

2006Linear equations in primes with Ben Green Annals of Math. 171 (2010), 1753–1850journal arXiv

2006Product set estimates in noncommutative groups Combinatorica 28 (2008), 547–594journal arXiv

2006A correspondence principle between (hyper)graph theory and probability theory, and the (hyper)graph removal lemma J. d’Analyse Mathematique 103 (2007), 1–45.journal arXiv slides

2006The ergodic and combinatorial approaches to Szemerédi's theorem Centre de Recerches Mathématiques, CRM Proceedings and Lecture Notes Vol. 43 (2007), 145–193arXiv

2006The primes contain arbitrarily long polynomial progressions with Tamar Ziegler Acta Math. 201 (2008), 213—305.Errata: Acta Math. 210, (2013), Page 403–404journal arXiv

2006Perelman’s proof of the Poincare conjecture – a nonlinear PDE perspective UnpublishedarXiv arXiv

2006Breaking duality in the return times theorem with Ciprian Demeter, Michael Lacey, Christoph Thiele Duke Math. J. 143 (2008), 281–355journal arXiv

2006Spacetime bounds for the energy-critical nonlinear wave equation in three spatial dimensions Dynamics of PDE 3 (2006), 93–110journal arXiv

2006Scattering for the quartic generalised Korteweg-de Vries equation J. Diff. Eq. 232 (2007), 623—651journal arXiv

2006Global regularity for a logarithmically supercritical defocusing nonlinear wave equation for spherically symmetric data J. Hyperbolic Diff. Eq. 4 (2007), 259–266journal arXiv

2006Two remarks on the generalised Korteweg-de Vries equation Discrete Cont. Dynam. Systems 18 (2007), 1–14journal arXiv

2006A pseudoconformal compactification of the nonlinear Schrodinger equation and applications New York J. Math. 15 (2009), 265–282.arXiv

2006Global behaviour of nonlinear dispersive and wave equations Current Developments in Mathematics 2006, International Press. 255–340.arXiv

2006Minimal-mass blowup solutions of the mass-critical NLS with Monica Visan, Xiaoyi Zhang Forum Mathematicum 20 (2008), 881–919journal arXiv

2006Global well-posedness and scattering for the mass-critical nonlinear Schrödinger equation for radial data in high dimensions with Monica Visan, Xiaoyi Zhang Duke Math J. 140 (2007), 165–202journal arXiv

2006A counterexample to an endpoint bilinear Strichartz inequality Electron. J. Diff. Eq. 2006 (2006) 151, 1—6.journal arXiv

2006A (concentration-)compact attractor for high-dimensional non-linear Schrödinger equations Dynamics of PDE 4 (2007), 1–53journal arXiv

2006A priori bounds and weak solutions for the nonlinear Schrödinger equation in Sobolev spaces of negative order with Michael Christ, Jim Colliander J. Funct. Anal 254 (2007), 368–395journal arXiv

2006Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information with Emmanuel Candes, Justin Romberg IEEE Inf. Theory 52 (2006) Vol 2., 489–509journal

2005New bounds for Szemeredi's Theorem, I: Progressions of length 4 in finite field geometries with Ben Green Proc. Lond. Math. Soc. 98 (2009), 365–392arXiv

2005On the singularity probability of random Bernoulli matrices with Van Vu J. Amer. Math. Soc. 20 (2007), 603–628journal arXiv

2005The Gaussian primes contain arbitrarily shaped constellations J. d’Analyse Mathematique 99 (2006), 109–176journal arXiv

2005An inverse theorem for the Gowers $U^3(G)$ norm with Ben Green Proc. Edin. Math. Soc. 51 (2008), 73–153journal arXiv

2005A variant of the hypergraph removal lemma J. Combin. Thy. A 113 (2006), 1257–1280journal arXiv

2005Szemeredi's regularity lemma revisited Contrib. Discrete Math. 1 (2006), 8–28journal arXiv

2005Random symmetric matrices are almost surely non-singular with Van Vu, Kevin Costello Duke Math. J. 135 (2006), 395–413journal arXiv

2005Obstructions 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]journal arXiv

2005Compressions, convex geometry, and the Freiman-Bilu theorem with Ben Green Quarterly J. Math. 57 (2006), 495–504journal arXiv

2005Inverse Littlewood-Offord theorems and the condition number of random discrete matrices with Van Vu Annals of Math. 169 (2009), 595–632journal arXiv

2005The dichotomy between structure and randomness, arithmetic progressions, and the primes 2006 ICM proceedings, Vol. I., 581–608arXiv slides

2005The Brascamp--Lieb Inequalities: Finiteness, Structure and Extremals with Tony Carbery, Michael Christ, Jon Bennett GAFA 17 (2008), 1343–1415journal arXiv

2005Finiteness bounds for Holder-Brascamp-Lieb multilinear inequalities with Tony Carbery, Michael Christ, Jon Bennett Math. Res. Letters, 17 (2010), 647–666journal arXiv

2005On the Multilinear Restriction and Kakeya conjectures with Tony Carbery, Jon Bennett Acta Math. 196 (2006) 261—302journal arXiv

2005Maximal multilinear operators with Ciprian Demeter, Christoph Thiele Trans. Amer. Math. Soc., 360 (2008), 4989–5042journal arXiv

2005Stability of energy-critical nonlinear Schrödinger equations in high dimensions with Monica Visan Electron. J. Diff. Eq. Vol. 2005 (2005), No. 118, 1–28.journal arXiv

2005Sharp well-posedness and ill-posedness results for a quadratic non-linear Schrödinger equation with Ioan Bejenaru J. Funct. Anal. Vol. 233 (2006), 228–259journal arXiv

2005Velocity averaging, kinetic formulations, and regularizing effects in quasilinear PDE. with Eitan Tadmor CPAM 61 (2007), 1–34journal arXiv

2005The nonlinear Schrödinger equation with combined power-type nonlinearities with Monica Visan, Xiaoyi Zhang Comm. PDE 32 (2007), 1281–1343.journal arXiv

2005Decoding by Linear Programming with Emmanuel Candes IEEE Inf. Theory 51 (2005), 4203–4215journal arXiv

2005Stable Signal Recovery from Incomplete and Inaccurate Measurements with Emmanuel Candes, Justin Romberg Comm. Pure Appl. Math. 59 (2006), 1207–1223journal arXiv

2005Error Correction via Linear Programming with Emmanuel Candes, Mark Rudelson, Roman Vershynin Proc. 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS05), IEEE, 2005. pp. 295–308pdf

2005The Dantzig selector: statistical estimation when $p$ is much larger than $n$ with Emmanuel Candes Annals of Statistics 35 (2007), 2313–2351arXiv discussion

2004The primes contain arbitrarily long arithmetic progressions with Ben Green Annals of Math. 167 (2008), 481–547journal arXiv slides slides slides

2004Restriction theory of the Selberg Sieve, with applications with Ben Green Journal de Théorie des Nombres de Bordeaux 18 (2006), 137—172journal arXiv

2004A quantitative ergodic theory proof of Szemerédi's theorem Electron. J. Combin. 13 (2006). 1 No. 99, 1–49.journal arXiv

2004On random pm 1 matrices: Singularity and Determinant with Van Vu 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.]journal arXiv

2004Arithmetic progressions and the primes Collectanea Mathematica (2006), Vol. Extra., 37–88.[Proceedings, 7th International Conference on Harmonic Analysis and Partial Differential Equations]journal arXiv

2004The Bi-Carleson operator with Camil Muscalu, Christoph Thiele GAFA 16 (2006), 230—277journal arXiv

2004Multi-parameter paraproducts with Camil Muscalu, Jill Pipher, Christoph Thiele Revista Mat. Iber. 22 (2006), 963–976journal arXiv

2004Symplectic nonsqueezing of the KdV flow with Jim Colliander, Mark Keel, Gigliola Staffilani, Hideo Takaoka Acta Math. 195 (2005), 197–252journal arXiv

2004Global well-posedness and scattering in the energy space for the critical nonlinear Schrodinger equation in R^3("Project Gopher") with Jim Colliander, Mark Keel, Gigliola Staffilani, Hideo Takaoka Annals of Math. 167 (2007), 767–865[A survey article is in Contemp. Math. 439, "Recent Developments in Nonlinear Partial Differential Equations: The second symposium on Analysis and PDEs June 7–10 2004, Purdue University, West Lafayette Indiana", D. Danielli, Ed., pp. 69–80. American Mathematial Society, Providence RI 2007]journal arXiv

2004Long-time decay estimates for Schrodinger equations on manifolds with Igor Rodnianski Mathematical aspects of nonlinear dispersive equations, 223–253, Ann. of Math. Stud. 163, Princeton University Press, Princeton NJ 2007arXiv

2004Global well-posedness and scattering for the higher-dimensional energy-critical non-linear Schrodinger equation for radial data New York Journal of Mathematics 11 (2005), 57–80journal arXiv

2004Sharp Strichartz estimates on non-trapping asymptotically conic manifolds with Andrew Hassell, Jared Wunsch Amer. J. Math. 128 (2006), 963—1024.journal arXiv

2004Geometric renormalization of large energy wave maps Journees “Equations aux derives partielles”, Forges les Eaux, 7–11 June 2004, XI 1–32arXiv

2004Near Optimal Signal Recovery From Random Projections: Universal Encoding Strategies? with Emmanuel Candes IEEE Inf. Theory 52 (2006), 5406–5425journal arXiv

2003A sum-product estimate for finite fields, and applications with Jean Bourgain, Nets Katz GAFA 14 (2004), 27–57journal arXiv

2003Fuglede's conjecture is false in 5 and higher dimensions Math. Res. Letters 11 (2004), 251–258journal arXiv

2003An uncertainty principle for cyclic groups of prime order Math. Res. Letters 12 (2005), 121–127journal arXiv

2003A positive proof of the Littlewood-Richardson rule using the octahedron recurrence with Allen Knutson, Chris Woodward Electron. J. Combin. 11 (2004), Research Paper 61, 18 pp. (electronic);journal arXiv

2003Some recent progress on the Restriction conjecture Fourier analysis and convexity, 217–243, Appl. Numer. Harmon. Anal., Birkhäuser Boston, Boston,MA, 2004.journal arXiv

2003Recent progress on the Restriction conjecture to appear, Park City proceedingsarXiv

2003Bi-parameter paraproducts with Camil Muscalu, Jill Pipher, Christoph Thiele Acta Math. 193 (2004), 269–296journal arXiv

2003On multilinear oscillatory integrals, nonsingular and singular with Michael Christ, Xiaochun Li, Christoph Thiele Duke Math. J. 130 (2005), 321—351.journal arXiv

2003Global existence and scattering for rough solutions of a nonlinear Schrodinger equation in R^3 with Jim Colliander, Mark Keel, Gigliola Staffilani, Hideo Takaoka CPAM 57 (2004), 987–1014journal arXiv

2003Global regularity for the Maxwell-Klein-Gordon equation in high dimensions with Igor Rodnianski Comm. Math. Phys. 251 (2004), 377–426journal arXiv

2003Ill-posedness for nonlinear Schrodinger and wave equations with Michael Christ, Jim Colliander Unpublished preprintarXiv

2003A Strichartz inequality for the Schrodinger equation on non-trapping asymptotically conic manifolds with Andrew Hassell, Jared Wunsch Comm. PDE 30 (2004), 157–205journal arXiv

2003Global well-posedness of the Benjamin-Ono equation in H^1(R) J. Hyperbolic Diff. Eq. 1 (2004) 27–49journal arXiv

2003Instability of the periodic nonlinear Schrodinger equation with Michael Christ, Jim Colliander Unpublished preprintarXiv

2003On the asymptotic behavior of large radial data for a focusing non-linear Schrödinger equation Dynamics of PDE 1 (2004), 1–48journal arXiv

2002Endpoint mapping properties of spherical maximal operators with Andreas Seeger, Jim Wright J. Institut Math. Jussieu 2 (2003) 1, 109–144arXiv

2002Pointwise convergence of lacunary spherical means with Andreas Seeger, Jim Wright Mt. Holyoke Proceedings (2001), Contemporary Mathematics (2003), 341–352arXiv

2002Singular maximal functions and Radon transforms near L^1 with Andreas Seeger, Jim Wright Amer. J. Math. 126 (2004), 607–647.journal arXiv

2002Weak-type (1,1) bounds for Fourier integral operators J. Aust. Math. Soc. 75 (2003), 1–21.journal arXiv

2002On the Maximal Bochner-Riesz conjecture in the plane, for p<2 Trans. Amer. Math. Soc. 354 (2002), 1947–1959journal

2002Kakeya and restriction phenomena for finite fields with Gerd Mockenhaupt Duke Math. J. 121 (2004), 35–74journal arXiv pdf

2002Bochner-Riesz summability for analytic functions on the m-complex unit sphere and for cylindrically symmetric functions on R^n-1 times R with Adam Sikora Comm. Anal. Geom. 12 (2004), 43–57journal arXiv

2002A new bound for finite field Besicovitch sets in four dimensions Pacific J. Math 222 (2005), 337–363journal arXiv

2002A sharp bilinear restriction estimate for paraboloids GAFA 13 (2003), 1359–1384journal arXiv

2002Relative efficiencies of kernel and local likelihood density estimators with Peter Hall J. R. Stat. Soc. Ser. B Stat. Methodol. 64 (2002), 537–547journal

2002A discrete model for the bi-carleson operator with Camil Muscalu, Christoph Thiele Geom. Func. Anal. 12 (2002), 1324–1364journal arXiv

2002A Carleson-type theorem for a Cantor group model of the Scattering Transform with Camil Muscalu, Christoph Thiele Nonlinearity 19 (2003), 219–246journal arXiv

2002L^p bounds for a maximal dyadic sum operator with Loukas Grafakos, Erin Terwilleger Math. Z. 246 (2004), 321–337journal arXiv

2002Almost conservation laws and global rough solutions to a nonlinear Schrodinger equation with Jim Colliander, Mark Keel, Gigliola Staffilani, Hideo Takaoka Math. Res. Letters 9 (2002), 659–682.journal arXiv slides

2002Polynomial upper bounds for the orbital instability of the 1D cubic NLS below the energy norm with Jim Colliander, Mark Keel, Gigliola Staffilani, Hideo Takaoka Discrete Cont. Dynam. Systems 9 (2003), 31–54journal arXiv

2002Polynomial growth and orbital instability bounds for $L^2$-subcritical NLS below the energy norm with Jim Colliander, Mark Keel, Gigliola Staffilani, Hideo Takaoka Comm. Pure Appl. Anal. 2 (2003), 33–50journal arXiv

2002A singularity removal theorem for Yang-Mills fields in higher dimensions with Gang Tian J. Amer. Math. Soc. 17 (2004), 557–593.journal arXiv

2002Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocussing equations with Michael Christ, Jim Colliander Amer. J. Math. 125 (2003), 1235–1293journal arXiv

2002Upper and lower bounds for Dirichlet eigenfunctions with Andrew Hassell Math. Res. Letters 9 (2002), 289–305journal arXiv pdf

2002Local and global well-posedness for nonlinear dispersive equations Proc. Centre Math. Appl. Austral. Nat. Univ. 40 (2002), 19–48pdf

2002Existence globale et diffusion pour l'équation de Schrödinger nonlinéaire répulsive cubique sur R^3 en dessous l'espace d'énergie with Jim Colliander, Mark Keel, Gigliola Staffilani, Hideo Takaoka Journées "Équations aux Dérivées Partielles" (Forges-les-Eaux, 2002), Exp. No. X, 14 pp., Univ. Nantes, Nantes,2002journal pdf

2001L^p improving estimates for averages along curves with Jim Wright J. Amer. Math. Soc. 16 (2003), 605–638journal arXiv

2001The Fuglede spectral conjecture holds for convex bodies in the plane with Alex Iosevich, Nets Katz Math. Res. Letters 10 (2003), 559–570journal arXiv

2001Carleson measures, trees, extrapolation, and T(b) theorems with Pascal Auscher, Steve Hofman, Camil Muscalu, Christoph Thiele Publications Matematiques Barcelona 46 (2002), 257–325journal arXiv

2001The honeycomb model of GL_n(C) tensor products II. Facets of the Littlewood-Richardson cone with Allen Knutson, Chris Woodward J. Amer. Math. Soc. 17 (2004), 19–48.journal arXiv

2001Puzzles and (equivariant) cohomology of Grassmannians with Allen Knutson Duke Math. J. 119 (2003), 221–260journal arXiv pdf

2001Some connections between the Falconer and Furstenburg conjectures with Nets Katz New York J. Math. 7 (2001), 148–187journal arXiv

2001New bounds for Kakeya problems with Nets Katz Journal d'Analyse de Jerusalem, 87 (2002), 231–263arXiv slides

2001Uniform estimates on paraproducts with Camil Muscalu, Christoph Thiele Journal d'Analyse de Jerusalem 87 (2002), 369–384arXiv

2001Uniform estimates for multi-linear operators with modulation symmetry with Camil Muscalu, Christoph Thiele Journal d'Analyse de Jerusalem 88 (2002), 255–309arXiv

2001L^p estimates for the "biest" I. The Walsh model. with Camil Muscalu, Christoph Thiele Math. Annalen 329 (2004), 401–426journal arXiv

2001L^p estimates for the "biest" II. The Fourier model. with Camil Muscalu, Christoph Thiele Math. Annalen 329 (2004), 427–461journal arXiv

2001A counterexample to a multilinear endpoint question of Christ and Kiselev with Camil Muscalu, Christoph Thiele Math. Res. Letters 10 (2003), 237–246journal arXiv

2001Multilinear interpolation between adjoint operators with Loukas Grafakos J. Funct. Anal. 199 (2003), 379–385journal arXiv

2001Global well-posedness result for KdV in Sobolev spaces of negative index with Jim Colliander, Mark Keel, Gigliola Staffilani, Hideo Takaoka EJDE 2001 (2001) No 26, 1–7journal arXiv

2001Sharp global well-posedness results for periodic and non-periodic KdV and modified KdV on R and T with Jim Colliander, Mark Keel, Gigliola Staffilani, Hideo Takaoka J. Amer. Math. Soc. 16 (2003), 705–749.journal arXiv

2001Multi-linear estimates for periodic KdV equations, and applications with Jim Colliander, Mark Keel, Gigliola Staffilani, Hideo Takaoka J. Funct. Anal. 211 (2004), 173–218journal arXiv

2001Global well-posedness for the Schrodinger equations with derivative with Jim Colliander, Mark Keel, Gigliola Staffilani, Hideo Takaoka Siam J. Math. 33 (2001), 649–669journal arXiv

2001A refined global well-posedness for the Schrodinger equations with derivative with Jim Colliander, Mark Keel, Gigliola Staffilani, Hideo Takaoka Siam J. Math. 34 (2002), 64–86.journal arXiv

2001A physical approach to wave equation bilinear estimates with Sergiu Klainerman, Igor Rodnianski J. Anal. Math. 87 (2002), 299—336journal arXiv

2000Almost everywhere convergence of general wavelet shrinkage estimators with Brani Vidakovic ACHA 9 (2000), 72–82journal

2000Endpoint multiplier theorems of Marcinkiewicz type with Jim Wright Revista Mat. Iber. 17 (2001), 521–558journal arXiv

2000Some light on Littlewood-Paley theory with Michael Cowling Math. Annalen 321 (2001) 4, 885–888journal arXiv

2000Honeycombs and sums of Hermitian matrices with Allen Knutson Notices Amer. Math. Soc. 48 (2001) No. 2, 175–186journal arXiv pdf

2000A bilinear approach to cone multipliers I. Restriction estimates with Ana Vargas GAFA 10 (2000), 185–215journal

2000A bilinear approach to cone multipliers II. Applications with Ana Vargas GAFA10 (2000), 216–258journal

2000An improved bound for the Minkowski dimension of Besicovitch sets in medium dimension with Izabella Laba GAFA 11 (2001), 773–806journal arXiv

2000From rotating needles to stability of waves: emerging connections between combinatorics, analysis, and PDE. Notices Amer. Math. Soc. 48 (2001) No 3, 294–303journal arXiv pdf

2000Recent progress on the Kakeya conjecture with Nets Katz Publicacions Matematiques, Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, U. Barcelona 2002, 161–180arXiv

2000Local well-posedness for the Yang-Mills equation below the energy norm JDE 189 (2003), 366–382journal arXiv

2000Multilinear weighted convolution of L^2 functions, and applications to non-linear dispersive equations Amer. J. Math. 123 (2001), 839–908journal arXiv

2000Global regularity of wave maps I. Small critical Sobolev norm in high dimension IMRN 7 (2001), 299–328journal arXiv pdf slides

2000Global regularity of wave maps II. Small energy in two dimensions Comm. Math. Phys. 224 (2001), 443–544journal arXiv slides

1999The weak-type (1,1) of L log L homogeneous convolution operators Indiana U. Math. J. 48 (1999), 1547–1584journal arXiv

1999Convex bodies with a point of curvature do not admit exponential bases with Alex Iosevich, Nets Katz Amer. J. Math. 123 (2001), 115–120journal arXiv

1999Sharp Lorentz space estimates for rough operators with Andreas Seeger Math. Annalen 320 (2001) 2, 381–415journal arXiv

1999A converse extrapolation theorem for translation-invariant operators J. Funct. Anal. 180 (2001), 1–10journal arXiv

1999The Bochner-Riesz conjecture implies the restriction conjecture Duke Math. J. 96 (1999), 363–376journal pdf

1999An improved bound on the Minkowski dimension of Besicovitch sets in R^3 with Nets Katz, Izabella Laba Annals of Math. 152 (2000), 383–446journal arXiv arXiv

1999Endpoint bilinear restriction theorems for the cone, and some sharp null form estimates Math. Z. 238 (2001), 215–268journal arXiv

1999Bounds on arithmetic projections, and applications to the Kakeya conjecture with Nets Katz Math. Res. Letters 6 (1999), 625–630journal arXiv

1999An x-ray transform estimate in R^n with Izabella Laba Revista Mat. Iber. 17 (2001), 375–408journal arXiv

1999Multilinear operators given by singular multipliers with Camil Muscalu, Christoph Thiele J. Amer. Math. Soc. 15 (2002), 469–496journal arXiv

1999Small data blowup for semilinear Klein-Gordon equations with Mark Keel Amer. J. Math. 121 (1999), 629–669journal

1998The honeycomb model of GL_n(C) tensor products I. Proof of the saturation conjecture with Allen Knutson J. Amer. Math. Soc.12 (1999), 1055–1090journal arXiv

1998The weak-type endpoint Bochner-Riesz conjecture and related topics Indiana U. Math. J. 47 (1998), 1097–1124journal

1998A bilinear approach to the restriction and Kakeya conjectures with Ana Vargas, Luis Vega J. Amer. Math. Soc. 11 (1998), 967–1000journal arXiv

1998Endpoint Strichartz Estimates with Mark Keel Amer. J. Math., 120 (1998), 955–980journal

1998Local and global well-posedness of wave maps in R^1+1 for rough data with Mark Keel IMRN 21 (1998), 1117–1156journal arXiv pdf slides

1998Spherically averaged endpoint Strichartz estimates for the two-dimensional Schrödinger equation Comm. PDE 25 (2000), 1471–1485journal arXiv

1998Ill-posedness for one-dimensional wave maps at the critical regularity Amer. J. Math., 122 (2000), 451–463journal arXiv

1997Low regularity semi-linear wave equations Comm. PDE 24 (1999), 599—630journal arXiv

1996On the almost-everywhere convergence of wavelet summation methods ACHA 3 (1996), 384–387journal

1996Harmonic convolution operators on Lipschitz graphs Adv. Appl. Clifford Alg. 6 (1996), 207–218journal

1996Weak-type endpoint bounds for Riesz means Proc. Amer. Math. Soc. 124 (1996), 2797–2805journal

1996On the Structure of Projective Group Representations in Quaternionic Hilbert Space with Andrew Millard J. Math. Phys. 37 (1996), 5848–5857journal

—Szemeredi's theorem with Ben Green Scholarpedia, p. 15573journal discussion

—Gowers' proof of Szemeredi's theorem for progressions of length 4short storylink

—An ergodic transference theoremshort storylink

—A quantitative ergodic theory proof of Szemeredi’s theorem (abridged)short storylink

—A quantitative bound for prime progressions of length kshort storylink

—Fourier analytic proofs of the prime number theoremshort storylink

—Non-commutative sum set estimatesshort storylink

—A remark on Goldston-Yildirim correlation estimatesshort storylink

—Arithmetic Ramsey Theoryshort storylink

—Menger’s theoremshort storylink

—The Roth-Bourgain theoremshort storylink

—Santalo’s inequalityshort storylink

—Quadratic reciprocity via theta functionsshort storylink

—Entropy sumset estimatesshort storylink

—The parity problem in sieve theoryshort storylink

—The crossing number inequalityshort storylink

—Ratner's theoremsshort storylink

—Dvir's proof of the finite field Kakeya conjectureshort storylink

—The van der Corput trick, and equidistribution on nilmanifoldsshort storylink

—Tate's proof of the functional equationshort storylink

—Some notes on non-classical polynomials in finite characteristicshort storylink

—A counterexample to a strong polynomial Freiman-Ruzsa conjectureshort storylink

—Finite subsets of groups with no finite modelsshort storylink

—The Lucas-Lehmer test for Mersenne primesshort storylink

—The divisor boundshort storylink

—The correspondence principle and finitary ergodic theoryshort storylink

—Szemeredi’s regularity lemma via random partitionsshort storylink

—Szemeredi’s regularity lemma via the correspondence principleshort storylink

—Best bounds for cap setsopen questionlink

—Noncommutative Freiman theoremopen questionlink

—Triangle and diamond densities in large dense graphsopen questionlink

—Effective Skolem-Mahler-Lech theoremopen questionlink

—Van Vuopen questionlink link

—Structure and randomness in the prime numbersopen questionlink

—Analysis and applications: the work of Elias Stein with Charles Fefferman, Alex Ionescu, Stephen Wainger Bull. Amer. Math. Soc. https://doi.org/10.1090/bull/1691pdf

—Counterexample to a self-adjoint Hardy-Littlewood inequalityshort storylink

—The weak-type (1,1) of the parabolic maximal functionshort storylink

—Holder's inequality for Lorentz spacesshort storylink

—Dyadic product H^1, and Carleson's counterexampleshort storylink

—Real interpolation of Lorentz spacesshort storylink

—Notes on Hausdorff and Minkowski dimensionshort storylink

—Atomic decomposition of Orlicz spaces, and extrapolationshort storylink

—Spectral pairs and tilingshort storylink

—Summability of functionsshort storylink

—A hasty interpolationshort storylink

—The dyadic pigeonhole principle in harmonic analysisshort storylink

—Going to extremesshort storylink