Edit Profile Bourgain, Jean Compute Distance To: Compute Author ID: bourgain.jean Published as: Bourgain, J.; Bourgain, Jean Homepage: https://www.math.ias.edu/people/faculty/bourgain External Links: MGP · Math-Net.Ru · Wikidata · dblp · GND · MacTutor Awards: Fields Medal (1994) · Shaw Prize (2010) · Breakthrough Prize in Mathematics (2017) Documents Indexed: 524 Publications since 1976, including 14 Books Biographic References: 13 Publications all top 5 Co-Authors 305 single-authored 18 Milman, Vitali D. 15 Brézis, Haïm 13 Konyagin, Sergeĭ Vladimirovich 12 Gamburd, Alexander 11 Demeter, Ciprian 11 Kontorovich, Alex V. 11 Lindenstrauss, Joram 10 Chang, Mei-Chu 9 Shparlinski, Igor E. 8 Rudnick, Zeév 8 Sarnak, Peter Clive 7 Mironescu, Petru 7 Tzafriri, Lior 6 Garaev, Moubariz Z. 5 Alon, Noga M. 5 Gromov, Mikhael Leonidovich 5 Lindenstrauss, Elon 4 Bombieri, Enrico 4 Bulut, Aynur 4 Connes, Alain 4 Li, Dong 4 Rosenthal, Haskell P. 4 Wang, Wei-Min 3 Berkson, Earl 3 Ford, Kevin B. 3 Goldstein, Michael 3 Guth, Lawrence David 3 Jitomirskaya, Svetlana Ya. 3 Kalai, Gil 3 Mirek, Mariusz 3 Schlag, Wilhelm 3 Stein, Elias Menachem 3 Talagrand, Michel 3 Wróbel, Błażej Jan 2 Ambrosio, Luigi 2 Cochrane, Todd 2 Delbaen, Freddy 2 Dilworth, Stephen J. 2 Dirksen, Sjoerd 2 Dyatlov, Semyon 2 Figalli, Alessio 2 Fuchs, Elena D. 2 Furman, Alex 2 Glibichuk, A. A. 2 Kahane, Jean-Pierre 2 Kashin, Boris Sergeevich 2 Kenig, Carlos Eduardo 2 Klartag, Bo’az 2 Korobkov, Mikhail V. 2 Kristensen, Jan 2 Kutzarova, Denka N. 2 Mozes, Shahar 2 Nelson, Jelani 2 Nguyen, Hoai-Minh 2 Pajor, Alain 2 Paulhus, Jennifer 2 Pinner, Christopher G. 2 Pisier, Gilles 2 Reinov, Oleg I. 2 Schechtman, Gideon 2 Szarek, Stanislaw Jerzy 2 Yehudayoff, Amir 1 Aleksandrov, Aleksei B. 1 Argyros, Spiros A. 1 Asmar, Nakhlé Habib 1 Benyamini, Yoav 1 Bergelson, Vitaly 1 Bethuel, Fabrice 1 Bleher, Pavel M. 1 Blomer, Valentin 1 Boshernitzan, Michael D. 1 Bourgain-Chang, Eric 1 Burq, Nicolas 1 Casazza, Peter George 1 Clozel, Laurent 1 Colliander, James E. 1 Davis, William Jay 1 Diestel, Joseph 1 Dvir, Zeev 1 Figiel, Tadeusz 1 Fremlin, David H. 1 Ghoussoub, Nassif A. 1 Giesecke, M. 1 Gillespie, Thomas Alastair 1 Golse, François 1 Grünbaum, Francisco Alberto 1 Guo, Shaoming 1 Khavin, Viktor Petrovich 1 Johnson, William Buhmann 1 Kachkovskiy, Ilya V. 1 Kahn, Jeff D. 1 Kaloshin, Vadim Yu. 1 Kalton, Nigel John 1 Katz, Nets Hawk 1 Katznelson, Yitzhak 1 Kemp, Dominique 1 Kesten, Harry 1 Klainerman, Sergiu 1 Klein, Abel 1 Kostyukovsky, Sergey ...and 42 more Co-Authors all top 5 Serials 45 Israel Journal of Mathematics 34 Geometric and Functional Analysis. GAFA 33 Journal d’Analyse Mathématique 30 Comptes Rendus. Mathématique. Académie des Sciences, Paris 22 IMRN. International Mathematics Research Notices 18 Bulletin de la Société Matheḿatique de Belgique. Série B 12 Communications in Mathematical Physics 12 Comptes Rendus de l’Académie des Sciences. Série I 11 Studia Mathematica 11 Inventiones Mathematicae 11 Journal of the European Mathematical Society (JEMS) 9 Journal of Functional Analysis 9 Annals of Mathematics. Second Series 8 Proceedings of the American Mathematical Society 7 Journal of the American Mathematical Society 6 Acta Mathematica 6 Annales de l’Institut Fourier 6 Transactions of the American Mathematical Society 5 Acta Arithmetica 5 Duke Mathematical Journal 4 Journal of Statistical Physics 4 American Journal of Mathematics 4 Fundamenta Mathematicae 4 Journal of the London Mathematical Society. Second Series 4 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 3 Illinois Journal of Mathematics 3 Journal für die Reine und Angewandte Mathematik 3 Mathematische Nachrichten 3 Proceedings of the Steklov Institute of Mathematics 2 Communications on Pure and Applied Mathematics 2 Mathematical Notes 2 Russian Mathematical Surveys 2 Arkiv för Matematik 2 Colloquium Mathematicum 2 Compositio Mathematica 2 Publications Mathématiques 2 Integral Equations and Operator Theory 2 Memoirs of the American Mathematical Society 2 Pacific Journal of Mathematics 2 Ergodic Theory and Dynamical Systems 2 Notices of the American Mathematical Society 2 Selecta Mathematica. New Series 2 Discrete and Continuous Dynamical Systems 2 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 2 Annals of Mathematics Studies 2 Modern Birkhäuser Classics 1 Letters in Mathematical Physics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Mathematics of Computation 1 Advances in Mathematics 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Boletim da Sociedade Brasileira de Matemática 1 Bulletin de la Société Mathématique de France 1 Michigan Mathematical Journal 1 Real Analysis Exchange 1 SIAM Journal on Computing 1 Simon Stevin 1 Journal of Operator Theory 1 Chinese Annals of Mathematics. Series B 1 Bulletin of the Iranian Mathematical Society 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Discrete & Computational Geometry 1 Revista Matemática Iberoamericana 1 SIAM Journal on Discrete Mathematics 1 Differential and Integral Equations 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Proceedings of the National Academy of Sciences of the United States of America 1 Computational Complexity 1 Mathematical Research Letters 1 Sbornik: Mathematics 1 Izvestiya: Mathematics 1 The Journal of Fourier Analysis and Applications 1 Annales Henri Poincaré 1 Moscow Mathematical Journal 1 International Journal of Number Theory 1 Colloquium Publications. American Mathematical Society 1 Lecture Notes in Mathematics 1 Journal of Spectral Theory 1 Discrete Analysis all top 5 Fields 145 Number theory (11-XX) 139 Functional analysis (46-XX) 94 Partial differential equations (35-XX) 86 Harmonic analysis on Euclidean spaces (42-XX) 62 Operator theory (47-XX) 41 Dynamical systems and ergodic theory (37-XX) 38 Probability theory and stochastic processes (60-XX) 35 Statistical mechanics, structure of matter (82-XX) 33 Abstract harmonic analysis (43-XX) 26 Measure and integration (28-XX) 26 Convex and discrete geometry (52-XX) 26 Quantum theory (81-XX) 19 Global analysis, analysis on manifolds (58-XX) 18 Functions of a complex variable (30-XX) 15 Combinatorics (05-XX) 12 General topology (54-XX) 11 Topological groups, Lie groups (22-XX) 9 Computer science (68-XX) 8 Group theory and generalizations (20-XX) 8 Difference and functional equations (39-XX) 8 Information and communication theory, circuits (94-XX) 7 History and biography (01-XX) 7 Potential theory (31-XX) 6 Mathematical logic and foundations (03-XX) 6 Algebraic geometry (14-XX) 6 Several complex variables and analytic spaces (32-XX) 6 Approximations and expansions (41-XX) 5 General and overarching topics; collections (00-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Real functions (26-XX) 4 Ordinary differential equations (34-XX) 3 Sequences, series, summability (40-XX) 2 Field theory and polynomials (12-XX) 2 Differential geometry (53-XX) 2 Algebraic topology (55-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Commutative algebra (13-XX) 1 Integral transforms, operational calculus (44-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Numerical analysis (65-XX) 1 Mechanics of particles and systems (70-XX) 1 Fluid mechanics (76-XX) 1 Operations research, mathematical programming (90-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 455 Publications have been cited 10,309 times in 6,233 Documents Cited by ▼ Year ▼ Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations. Zbl 0787.35097Bourgain, J. 432 1993 Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation. Zbl 0787.35098Bourgain, J. 348 1993 Global solutions of nonlinear Schrödinger equations. Zbl 0933.35178Bourgain, Jean 184 1999 Another look at Sobolev spaces. Zbl 1103.46310Bourgain, Jean; Brezis, Haim; Mironescu, Petru 177 2001 A sum-product estimate in finite fields, and applications. Zbl 1145.11306Bourgain, Jean; Katz, N.; Tao, Terence C. 157 2004 Green’s function estimates for lattice Schrödinger operators and applications. Zbl 1137.35001Bourgain, J. 155 2005 Refinements of Strichartz’ inequality and applications to \(2D-NLS\) with critical nonlinearity. Zbl 0917.35126Bourgain, Jean 155 1998 Some remarks on Banach spaces in which martingale difference sequences are unconditional. Zbl 0533.46008Bourgain, J. 155 1983 Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations. Zbl 0928.35161Bourgain, Jean 149 1998 Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case. Zbl 0958.35126Bourgain, Jean 128 1999 Pointwise ergodic theorems for arithmetic sets. With an appendix on return-time sequences, jointly with Harry Furstenberg, Yitzhak Katznelson and Donald S. Ornstein. Zbl 0705.28008Bourgain, Jean 127 1989 Periodic nonlinear Schrödinger equation and invariant measures. Zbl 0822.35126Bourgain, J. 125 1994 New volume ratio properties for convex symmetric bodies in \({\mathbb{R}}^ n\). Zbl 0617.52006Bourgain, J.; Milman, V. D. 122 1987 Construction of quasi-periodic solutions for Hamiltonian perturbations of linear equations and applications to nonlinear PDE. Zbl 0817.35102Bourgain, Jean 113 1994 Ill-posedness of the Navier-Stokes equations in a critical space in 3D. Zbl 1161.35037Bourgain, Jean; Pavlović, Nataša 104 2008 Limiting embedding theorems for \(W^{s,p}\) when \(s\uparrow 1\) and applications. Zbl 1029.46030Bourgain, Jean; Brezis, Haïm; Mironescu, Petru 103 2002 Invariant measures for the 2D-defocusing nonlinear Schrödinger equation. Zbl 0852.35131Bourgain, Jean 102 1996 Averages in the plane over convex curves and maximal operators. Zbl 0626.42012Bourgain, J. 96 1986 On localization in the continuous Anderson-Bernoulli model in higher dimension. Zbl 1084.82005Bourgain, Jean; Kenig, Carlos E. 93 2005 On the Cauchy problem for the Kadomtsev-Petviashvili equation. Zbl 0787.35086Bourgain, J. 91 1993 On Lipschitz embedding of finite metric spaces in Hilbert space. Zbl 0657.46013Bourgain, J. 91 1985 Uniform expansion bounds for Cayley graphs of \(\text{SL}_2(\mathbb F_p)\). Zbl 1216.20042Bourgain, Jean; Gamburd, Alex 90 2008 On the equation \(\text{div }Y=f\) and application to control of phases. Zbl 1075.35006Bourgain, Jean; Brezis, Haïm 90 2003 Periodic Korteweg-de Vries equation with measures as initial data. Zbl 0891.35138Bourgain, Jean 87 1997 Pointwise compact sets of Baire-measurable functions. Zbl 0413.54016Bourgain, Jean; Fremlin, David H.; Talagrand, Michel 87 1978 On nonperturbative localization with quasi-periodic potential. Zbl 1053.39035Bourgain, J.; Goldstein, M. 85 2000 Besicovitch type maximal operators and applications to Fourier analysis. Zbl 0756.42014Bourgain, J. 80 1991 Estimates for the number of sums and products and for exponential sums in fields of prime order. Zbl 1093.11057Bourgain, J.; Glibichuk, A. A.; Konyagin, S. V. 79 2006 Bounds on oscillatory integral operators based on multilinear estimates. Zbl 1237.42010Bourgain, Jean; Guth, Larry 78 2011 On the distribution of polynomials on high dimensional convex sets. Zbl 0773.46013Bourgain, J. 78 1991 More on the sum-product phenomenon in prime fields and its applications. Zbl 1173.11310Bourgain, J. 77 2005 The proof of the \(l^2\) decoupling conjecture. Zbl 1322.42014Bourgain, Jean; Demeter, Ciprian 75 2015 Lifting in Sobolev spaces. Zbl 0967.46026Bourgain, Jean; Brézis, Haïm; Mironescu, Petru 73 2000 Construction of periodic solutions of nonlinear wave equations in higher dimension. Zbl 0834.35083Bourgain, Jean 69 1995 On the maximal ergodic theorem for certain subsets of the integers. Zbl 0642.28010Bourgain, J. 68 1988 Invertibility of “large” submatrices with applications to the geometry of Banach spaces and harmonic analysis. Zbl 0631.46017Bourgain, J.; Tzafriri, L. 68 1987 \(H^{1/2}\) maps with values into the circle: minimal connections, lifting, and the Ginzburg-Landau equation. Zbl 1051.49030Bourgain, Jean; Brezis, Haim; Mironescu, Petru 66 2004 A class of special L//infinity spaces. Zbl 0466.46024Bourgain, J.; Delbaen, F. 65 1980 Proof of the main conjecture in Vinogradov’s mean value theorem for degrees higher than three. Zbl 1408.11083Bourgain, Jean; Demeter, Ciprian; Guth, Larry 63 2016 On high dimensional maximal functions associated to convex bodies. Zbl 0621.42015Bourgain, J. 62 1986 On triples in arithmetic progression. Zbl 0959.11004Bourgain, Jean 60 1999 On dentability and the Bishop-Phelps property. Zbl 0365.46021Bourgain, J. 60 1977 Construction of approximative and almost periodic solutions of perturbed linear Schrödinger and wave equations. Zbl 0872.35007Bourgain, Jean 59 1996 The metrical interpretation of superreflexivity in Banach spaces. Zbl 0643.46013Bourgain, J. 59 1986 Continuity of the Lyapunov exponent for quasiperiodic operators with analytic potential. Zbl 1039.81019Bourgain, J.; Jitomirskaya, S. 58 2002 Affine linear sieve, expanders, and sum-product. Zbl 1239.11103Bourgain, Jean; Gamburd, Alex; Sarnak, Peter 56 2010 New estimates for elliptic equations and Hodge type systems. Zbl 1176.35061Bourgain, Jean; Brezis, Haïm 56 2007 On the spectral gap for finitely-generated subgroups of \(\text{SU}(2)\). Zbl 1135.22010Bourgain, Jean; Gamburd, Alex 52 2008 Approximation of zonoids by zonotopes. Zbl 0682.46008Bourgain, J.; Lindenstrauss, J.; Milman, V. 51 1989 Disjointness of Moebius from horocycle flows. Zbl 1336.37030Bourgain, J.; Sarnak, P.; Ziegler, T. 50 2013 On a variant of sum-product estimates and explicit exponential sum bounds in prime fields. Zbl 1194.11086Bourgain, J.; Garaev, M. Z. 50 2009 Generalization of Selberg’s \(\frac {3}{16} \) theorem and affine sieve. Zbl 1276.11081Bourgain, Jean; Gamburd, Alex; Sarnak, Peter 49 2011 Exponential sums and nonlinear Schrödinger equations. Zbl 0787.35096Bourgain, J. 49 1993 New Banach space properties of the disc algebra and \(H^{\infty}\). Zbl 0574.46039Bourgain, J. 47 1984 Decoupling, exponential sums and the Riemann zeta function. Zbl 1352.11065Bourgain, J. 46 2017 Construction of blowup solutions for the nonlinear Schrödinger equation with critical nonlinearity. Zbl 1043.35137Bourgain, Jean; Wang, W. 46 1997 The influence of variables in product spaces. Zbl 0771.60002Bourgain, Jean; Kahn, Jeff; Kalai, Gil; Katznelson, Yitzhak; Linial, Nathan 46 1992 On wellposedness of the Zakharov system. Zbl 0909.35125Bourgain, Jean; Colliander, J. 45 1996 On the growth in time of higher Sobolev norms of smooth solutions of Hamiltonian PDE. Zbl 0934.35166Bourgain, Jean 45 1996 On the Erdős-Volkmann and Katz-Tao ring conjectures. Zbl 1115.11049Bourgain, J. 44 2003 Limited operators and strict cosingularity. Zbl 0601.47019Bourgain, Jean; Diestel, Joe 43 1984 On Melnikov’s persistency problem. Zbl 0897.58020Bourgain, Jean 42 1997 On the Hausdorff dimension of harmonic measure in higher dimension. Zbl 0616.31004Bourgain, J. 42 1987 Explicit constructions of RIP matrices and related problems. Zbl 1236.94027Bourgain, Jean; Dilworth, Stephen; Ford, Kevin; Konyagin, Sergei; Kutzarova, Denka 41 2011 Mordell’s exponential sum estimate revisited. Zbl 1072.11063Bourgain, J. 41 2005 On the Busemann-Petty problem for perturbations of the ball. Zbl 0752.52001Bourgain, J. 41 1991 Double recurrence and almost sure convergence. Zbl 0685.28008Bourgain, J. 39 1990 Positivity and continuity of the Lyapunov exponent for shifts on \(\mathbb T^d\) with arbitrary frequency vector and real analytic potential. Zbl 1089.81021Bourgain, J. 37 2005 New estimates for the Laplacian, the div-curl, and related Hodge systems. Zbl 1101.35013Bourgain, Jean; Brezis, Haïm 37 2004 On growth of Sobolev norms in linear Schrödinger equations with smooth time dependent potential. Zbl 0938.35026Bourgain, Jean 37 1999 Anderson localization for Schrödinger operators on \(\mathbb Z\) with potentials given by the skew-shift. Zbl 0994.82044Bourgain, Jean; Goldstein, Michael; Schlag, Wilhelm 36 2001 Strong ill-posedness of the incompressible Euler equation in borderline Sobolev spaces. Zbl 1320.35266Bourgain, Jean; Li, Dong 35 2015 Nonlinear Schrödinger equations. Zbl 0952.35127Bourgain, Jean 35 1999 On the structure of the Sobolev space \(H^{1/2}\) with values into the circle. Zbl 0970.35069Bourgain, Jean; Brézis, Haïm; Mironescu, Petru 34 2000 On invariant tori of full dimension for 1D periodic NLS. Zbl 1088.35061Bourgain, J. 33 2005 Growth of Sobolev norms in linear Schrödinger equations with quasi-periodic potential. Zbl 0938.35150Bourgain, Jean 33 1999 On the compactness of the support of solutions of dispersive equations. Zbl 0882.35106Bourgain, Jean 33 1997 Sieving and expanders. Zbl 1217.11081Bourgain, Jean; Gamburd, Alex; Sarnak, Peter 32 2006 Anderson localization for Schrödinger operators on \(\mathbb{Z}^2\)with quasi-periodic potential. Zbl 1022.47023Bourgain, Jean; Goldstein, Michael; Schlag, Wilhelm 32 2002 A Szemerédi type theorem for sets of positive density in \(\mathbb R^k\). Zbl 0609.10043Bourgain, J. 32 1986 Vector-valued singular integrals and the \(H^ 1\)-BMO duality. Zbl 0602.42015Bourgain, Jean 32 1986 On the Schrödinger maximal function in higher dimension. Zbl 1291.35253Bourgain, Jean 31 2013 Roth’s theorem on progressions revisited. Zbl 1155.11011Bourgain, Jean 31 2008 On \(\Lambda\) (p)-subsets of squares. Zbl 0692.43005Bourgain, J. 31 1989 On type of metric spaces. Zbl 0617.46024Bourgain, J.; Milman, V.; Wolfson, H. 31 1986 A construction of \({\mathcal L}_{\infty}\)-spaces and related Banach spaces. Zbl 0586.46011Bourgain, Jean; Pisier, Gilles 31 1983 Moment inequalities for trigonometric polynomials with spectrum in curved hypersurfaces. Zbl 1271.42039Bourgain, J. 30 2013 On the singularity probability of discrete random matrices. Zbl 1186.60003Bourgain, Jean; Vu, Van H.; Wood, Philip Matchett 30 2010 Multilinear exponential sums in prime fields under optimal entropy condition on the sources. Zbl 1162.11043Bourgain, Jean 30 2009 Periodic solutions of nonlinear wave equations. Zbl 0976.35041Bourgain, Jean 30 1999 On the pointwise ergodic theorem on \(L^ p\) for arithmetic sets. Zbl 0642.28011Bourgain, J. 30 1988 Banach spaces with a unique unconditional basis, up to permutation. Zbl 0575.46011Bourgain, J.; Casazza, P. G.; Lindenstrauss, J.; Tzafriri, L. 30 1985 Applications of the theory of semi-embeddings to Banach space theory. Zbl 0541.46020Bourgain, J.; Rosenthal, H. P. 30 1983 Martingales valued in certain subspaces of \(L^1\). Zbl 0445.46015Bourgain, J.; Rosenthal, H. P. 30 1980 On the distribution of free path lengths for the periodic Lorentz gas. Zbl 0910.60082Bourgain, Jean; Golse, François; Wennberg, Bernt 29 1998 On a problem of Kadison and Singer. Zbl 0729.47028Bourgain, J.; Tzafriri, L. 29 1991 Bounded orthogonal systems and the \(\Lambda\) (p)-set problem. Zbl 0674.43004Bourgain, J. 29 1989 The discretized sum-product and projection theorems. Zbl 1234.11012Bourgain, Jean 28 2010 Estimates on exponential sums related to the Diffie-Hellman distributions. Zbl 1102.11041Bourgain, J. 28 2005 Absolutely continuous spectrum for 1D quasiperiodic operators. Zbl 1036.47019Bourgain, J.; Jitomirskaya, S. 28 2002 Anderson localization for two interacting quasiperiodic particles. Zbl 07040581Bourgain, Jean; Kachkovskiy, Ilya 6 2019 Galilean boost and non-uniform continuity for incompressible Euler. Zbl 1431.35114Bourgain, Jean; Li, Dong 2 2019 Dimension-free estimates for discrete Hardy-Littlewood averaging operators over the cubes in \(\mathbb{Z}^d\). Zbl 1431.42033Bourgain, Jean; Mirek, Mariusz; Stein, Elias M.; Wróbel, Błażej 2 2019 Spectral gaps without the pressure condition. Zbl 1392.37065Bourgain, Jean; Dyatlov, Semyon 10 2018 Decoupling for perturbed cones and the mean square of \(|\zeta (\frac{1}{2}+it)|\). Zbl 07013525Bourgain, Jean; Watt, Nigel 6 2018 On a homogenization problem. Zbl 1401.35356Bourgain, J. 5 2018 On dimension-free variational inequalities for averaging operators in \({\mathbb{R}^d}\). Zbl 1402.42023Bourgain, Jean; Mirek, Mariusz; Stein, Elias M.; Wróbel, Błażej 4 2018 Decoupling, exponential sums and the Riemann zeta function. Zbl 1352.11065Bourgain, J. 46 2017 Decouplings for curves and hypersurfaces with nonzero Gaussian curvature. Zbl 1384.42016Bourgain, Jean; Demeter, Ciprian 16 2017 Fourier dimension and spectral gaps for hyperbolic surfaces. Zbl 1421.11071Bourgain, Jean; Dyatlov, Semyon 11 2017 A study guide for the \(l^{2}\) decoupling theorem. Zbl 1370.42021Bourgain, Jean; Demeter, Ciprian 9 2017 On the Vinogradov mean value. Zbl 1371.11138Bourgain, J. 8 2017 Decoupling inequalities and some mean-value theorems. Zbl 1380.42008Bourgain, Jean 6 2017 Nonlinear Roth type theorems in finite fields. Zbl 1420.11024Bourgain, J.; Chang, M.-C. 6 2017 Sidonicity and variants of Kaczmarz’s problem. Zbl 1388.43008Bourgain, Jean; Lewko, Mark 5 2017 Spatial statistics for lattice points on the sphere. I: Individual results. Zbl 07006293Bourgain, Jean; Rudnick, Zeév; Sarnak, Peter 4 2017 Small gaps in the spectrum of the rectangular billiard. Zbl 1405.35120Blomer, Valentin; Bourgain, Jean; Radziwiłł, Maksym; Rudnick, Zeév 4 2017 Sharp bounds for the cubic Parsell-Vinogradov system in two dimensions. Zbl 1386.11093Bourgain, Jean; Demeter, Ciprian; Guo, Shaoming 4 2017 Beyond expansion. II: Low-lying fundamental geodesics. Zbl 1403.11054Bourgain, Jean; Kontorovich, Alex 3 2017 On a problem of Farrell and Vershynin in random matrix theory. Zbl 1366.60008Bourgain, Jean 1 2017 Proof of the main conjecture in Vinogradov’s mean value theorem for degrees higher than three. Zbl 1408.11083Bourgain, Jean; Demeter, Ciprian; Guth, Larry 63 2016 A note on the Schrödinger maximal function. Zbl 1361.35151Bourgain, J. 22 2016 BMO-type norms related to the perimeter of sets. Zbl 1352.46026Ambrosio, Luigi; Bourgain, Jean; Brezis, Haim; Figalli, Alessio 15 2016 Mean value estimates for Weyl sums in two dimensions. Zbl 1408.11082Bourgain, Jean; Demeter, Ciprian 10 2016 Local statistics of lattice points on the sphere. Zbl 1394.11059Bourgain, Jean; Sarnak, Peter; Rudnick, Zeév 9 2016 Markoff triples and strong approximation. Zbl 1378.11043Bourgain, Jean; Gamburd, Alexander; Sarnak, Peter 8 2016 A quantitative Oppenheim theorem for generic diagonal quadratic forms. Zbl 1361.11024Bourgain, Jean 6 2016 Decouplings for surfaces in \(\mathbb{R}^4\). Zbl 1332.53007Bourgain, Jean; Demeter, Ciprian 6 2016 The essential centre of the mod a diagonalization ideal commutant of an \(n\)-tuple of commuting Hermitian operators. Zbl 1375.47011Bourgain, Jean; Voiculescu, Dan-Virgil 5 2016 Affine extractors over large fields with exponential error. Zbl 1419.11132Bourgain, Jean; Dvir, Zeev; Leeman, Ethan 1 2016 On uniformly bounded bases in spaces of holomorphic functions. Zbl 1350.32012Bourgain, Jean 1 2016 On the Fourier-Walsh spectrum of the Moebius function. II. Zbl 1417.11046Bourgain, Jean 1 2016 The proof of the \(l^2\) decoupling conjecture. Zbl 1322.42014Bourgain, Jean; Demeter, Ciprian 75 2015 Strong ill-posedness of the incompressible Euler equation in borderline Sobolev spaces. Zbl 1320.35266Bourgain, Jean; Li, Dong 35 2015 A new function space and applications. Zbl 1339.46028Bourgain, Jean; Brezis, Haim; Mironescu, Petru 21 2015 Strong illposedness of the incompressible Euler equation in integer \(C^m\) spaces. Zbl 06422797Bourgain, Jean; Li, Dong 21 2015 Prescribing the binary digits of primes. II. Zbl 1310.11097Bourgain, Jean 15 2015 A problem on sums of two squares. Zbl 1364.11091Bombieri, Enrico; Bourgain, Jean 13 2015 On the Morse-Sard property and level sets of \(W^{n,1}\) Sobolev functions on \(\mathbb{R}^n\). Zbl 1322.46022Bourgain, Jean; Korobkov, Mikhail V.; Kristensen, Jan 13 2015 On \(L^p\)-resolvent estimates and the density of eigenvalues for compact Riemannian manifolds. Zbl 1396.58025Bourgain, Jean; Shao, Peng; Sogge, Christopher D.; Yao, Xiaohua 10 2015 New bounds for the discrete Fourier restriction to the sphere in 4D and 5D. Zbl 1322.42013Bourgain, Jean; Demeter, Ciprian 8 2015 On Pleijel’s nodal domain theorem. Zbl 1317.35145Bourgain, Jean 8 2015 The affine sieve beyond expansion. I: Thin hypotenuses. Zbl 1347.11068Bourgain, Jean; Kontorovich, Alex 6 2015 Toward a unified theory of sparse dimensionality reduction in Euclidean space. Zbl 1341.46007Bourgain, Jean; Dirksen, Sjoerd; Nelson, Jelani 5 2015 Character sums and deterministic polynomial root finding in finite fields. Zbl 1400.11153Bourgain, Jean; Konyagin, Sergei V.; Shparlinski, Igor E. 5 2015 Nodal intersections and \(L^p\) restriction theorems on the torus. Zbl 1319.58023Bourgain, Jean; Rudnick, Zeév 5 2015 A remark on solutions of the Pell equation. Zbl 1372.11039Bourgain, J. 2 2015 Almost sure global well-posedness for the radial nonlinear Schrödinger equation on the unit ball. II: the 3D case. Zbl 1301.35145Bourgain, Jean; Bulut, Aynur 27 2014 Sumsets of reciprocals in prime fields and multilinear Kloosterman sums. Zbl 1316.11071Bourgain, J.; Garaev, M. Z. 25 2014 On Zaremba’s conjecture. Zbl 1370.11083Bourgain, Jean; Kontorovich, Alex 22 2014 On an endpoint Kato-Ponce inequality. Zbl 1340.42021Bourgain, Jean; Li, Dong 19 2014 Invariant Gibbs measure evolution for the radial nonlinear wave equation on the 3d ball. Zbl 1295.35323Bourgain, Jean; Bulut, Aynur 17 2014 Almost sure global well posedness for the radial nonlinear Schrödinger equation on the unit ball I: the 2D case. Zbl 1307.35272Bourgain, Jean; Bulut, Aynur 16 2014 Quantum recurrence of a subspace and operator-valued Schur functions. Zbl 1296.37014Bourgain, J.; Grünbaum, F. A.; Velázquez, L.; Wilkening, J. 15 2014 On the local-global conjecture for integral Apollonian gaskets. With an appendix by Péter P. Varjú. Zbl 1301.11046Bourgain, Jean; Kontorovich, Alex 13 2014 An improved estimate in the restricted isometry problem. Zbl 1323.46009Bourgain, Jean 11 2014 Multiplicative congruences with variables from short intervals. Zbl 1385.11002Bourgain, Jean; Garaev, Moubariz Z.; Konyagin, Sergei V.; Shparlinski, Igor E. 11 2014 On the Hardy-Littlewood maximal function for the cube. Zbl 1309.42023Bourgain, Jean 11 2014 On toral eigenfunctions and the random wave model. Zbl 1305.60013Bourgain, Jean 8 2014 Kloosterman sums in residue rings. Zbl 1319.11051Bourgain, J.; Garaev, M. Z. 8 2014 Additive patterns in multiplicative subgroups. Zbl 1377.11013Alon, Noga; Bourgain, Jean 7 2014 Perimeter of sets and BMO-type norms. Zbl 1316.46026Ambrosio, Luigi; Bourgain, Jean; Brezis, Haïm; Figalli, Alessio 6 2014 Monotone Boolean functions capture their primes. Zbl 1370.11113Bourgain, Jean 3 2014 An application of group expansion to the Anderson-Bernoulli model. Zbl 1293.82015Bourgain, J. 3 2014 On the control problem for Schrödinger operators on tori. Zbl 1318.35093Bourgain, Jean 2 2014 Some Diophantine applications of the theory of group expansion. Zbl 1370.11082Bourgain, Jean 1 2014 On eigenvalue spacings for the 1-D Anderson model with singular site distribution. Zbl 1319.35125Bourgain, Jean 1 2014 On oscillatory integral operators in higher dimensions. Zbl 1301.42022Bourgain, Jean 1 2014 Disjointness of Moebius from horocycle flows. Zbl 1336.37030Bourgain, J.; Sarnak, P.; Ziegler, T. 50 2013 On the Schrödinger maximal function in higher dimension. Zbl 1291.35253Bourgain, Jean 31 2013 Moment inequalities for trigonometric polynomials with spectrum in curved hypersurfaces. Zbl 1271.42039Bourgain, J. 30 2013 On the correlation of the Moebius function with rank-one systems. Zbl 1358.37017Bourgain, J. 24 2013 On the Morse-Sard property and level sets of Sobolev and BV functions. Zbl 1273.26017Bourgain, Jean; Korobkov, Mikhail V.; Kristensen, Jan 21 2013 Bounds on the density of states for Schrödinger operators. Zbl 1362.35113Bourgain, Jean; Klein, Abel 19 2013 On congruences with products of variables from short intervals and applications. Zbl 1301.11041Bourgain, Jean; Garaev, Moubariz Z.; Konyagin, Sergei V.; Shparlinski, Igor E. 17 2013 Möbius-Walsh correlation bounds and an estimate of Mauduit and Rivat. Zbl 1357.11092Bourgain, J. 17 2013 Expansion in SL\(_2(\mathbb R)\) and monotone expanders. Zbl 1268.05103Bourgain, Jean; Yehudayoff, Amir 11 2013 Control for Schrödinger operators on 2-tori: rough potentials. Zbl 1279.35016Bourgain, Jean; Burq, Nicolas; Zworski, Maciej 10 2013 Prescribing the binary digits of primes. Zbl 1309.11065Bourgain, Jean 8 2013 On the Fourier-Walsh spectrum of the Moebius function. Zbl 1336.11038Bourgain, J. 6 2013 Improved estimates for the discrete Fourier restriction to the higher dimensional sphere. Zbl 1319.42006Bourgain, Jean; Demeter, Ciprian 4 2013 A lower bound for the Lyapounov exponents of the random Schrödinger operator on a strip. Zbl 1432.82016Bourgain, J. 3 2013 On Pleijel’s nodal domain theorem – Retraction notice. Zbl 06437691Bourgain, J. 2 2013 On the Lyapounov exponents of Schrödinger operators associated with the standard map. Zbl 1273.37025Bourgain, J. 2 2013 On the hidden shifted power problem. Zbl 1311.11111Bourgain, Jean; Garaev, Moubariz Z.; Konyagin, Sergei V.; Shparlinski, Igor E. 25 2012 A spectral gap theorem in SU\((d)\). Zbl 1254.43010Bourgain, Jean; Gamburd, Alex 23 2012 Restriction of toral eigenfunctions to hypersurfaces and nodal sets. Zbl 1276.53047Bourgain, Jean; Rudnick, Zeév 17 2012 Expansion in \(\text{SL}_d(\mathbb Z/q\mathbb Z)\), \(q\) arbitrary. Zbl 1247.20052Bourgain, Jean; Varjú, Péter P. 15 2012 Finitely supported measures on \(\mathrm{SL}_2(\mathbb R)\) which are absolutely continuous at infinity. Zbl 1272.60004Bourgain, Jean 10 2012 On the Furstenberg measure and density of states for the Anderson-Bernoulli model at small disorder. Zbl 1275.82006Bourgain, J. 8 2012 Gibbs measure evolution in radial nonlinear wave and Schrödinger equations on the ball. Zbl 1251.35141Bourgain, Jean; Bulut, Aynur 7 2012 Integral Apollonian circle packings and prime curvatures. Zbl 1281.52011Bourgain, J. 5 2012 Distribution of elements of cosets of small subgroups and applications. Zbl 1290.11017Bourgain, Jean; Konyagin, Sergei V.; Shparlinski, Igor E. 5 2012 A modular Szemerédi-Trotter theorem for hyperbolas. Zbl 1272.11024Bourgain, Jean 3 2012 On representation of integers by binary quadratic forms. Zbl 1294.11040Bourgain, Jean; Fuchs, Elena 2 2012 Partial quotients and representation of rational numbers. Zbl 1345.11007Bourgain, Jean 2 2012 Monotone expansion. Zbl 1286.68369Bourgain, Jean; Yehudayoff, Amir 1 2012 Bounds on oscillatory integral operators based on multilinear estimates. Zbl 1237.42010Bourgain, Jean; Guth, Larry 78 2011 Generalization of Selberg’s \(\frac {3}{16} \) theorem and affine sieve. Zbl 1276.11081Bourgain, Jean; Gamburd, Alex; Sarnak, Peter 49 2011 Explicit constructions of RIP matrices and related problems. Zbl 1236.94027Bourgain, Jean; Dilworth, Stephen; Ford, Kevin; Konyagin, Sergei; Kutzarova, Denka 41 2011 ...and 355 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 5,048 Authors 200 Bourgain, Jean 90 Shparlinski, Igor E. 52 Tao, Terence 45 Tzvetkov, Nikolay 37 Naor, Assaf 35 Oh, Tadahiro 33 Iosevich, Alex 32 Brézis, Haïm 31 Damanik, David 31 Shkredov, Il’ya Dmitrievich 30 Berti, Massimiliano 29 Kenig, Carlos Eduardo 29 Lee, Sanghyuk 27 Geng, Jiansheng 27 Himonas, A. Alexandrou 26 Miao, Changxing 25 Mironescu, Petru 25 Tomczak-Jaegermann, Nicole 24 Nguyen, Hoai-Minh 23 Guo, Zihua 23 Procesi, Michela 22 Koldobsky, Alexander L. 22 You, Jiangong 22 Zhang, Bingyu 21 Chang, Mei-Chu 21 Guo, Boling 21 Ponce, Gustavo 21 Raphael, Pierre 21 Yuan, Xiaoping 20 Cui, Shangbin 20 Jitomirskaya, Svetlana Ya. 20 Paouris, Grigoris 20 Van Schaftingen, Jean 20 Vega, Luis 19 Colliander, James E. 19 Veselić, Ivan 18 Demeter, Ciprian 18 Garaev, Moubariz Z. 18 Huo, Zhaohui 18 Koh, Doowon 18 Linares, Felipe 18 Staffilani, Gigliola 18 Yan, Wei 17 Betancor Perez, Jorge Juan 17 Carvajal, Xavier Paredes 17 Kontorovich, Alex V. 17 Panthee, Mahendra 17 Sogge, Christopher D. 16 Giannopoulos, Apostolos A. 16 Konyagin, Sergeĭ Vladimirovich 16 Korolëv, Maksim Aleksandrovich 16 Li, Yongsheng 16 Schlag, Wilhelm 16 Vinh, Le Anh 16 Wang, Baoxiang 15 Bona, Jerry Lloyd 15 Erdoğan, Mehmet Burak 15 Merle, Frank 15 Milman, Vitali D. 15 Pajor, Alain 15 Pisier, Gilles 15 Shakhmurov, Veli B. 15 Vargas, Ana M. 15 Zheng, Jiqiang 14 Acosta Vigil, María Dolores 14 Burq, Nicolas 14 Guth, Lawrence David 14 Hofmann, Steve 14 Kalton, Nigel John 14 Kim, Sun Kwang 14 Martel, Yvan 14 Mirek, Mariusz 14 Molinet, Luc 14 Pham Van Thang 14 Rudnev, Misha 14 Sanders, Tom 14 Sarnak, Peter Clive 14 Schechtman, Gideon 14 Squassina, Marco 14 Torrea, José Luis 14 Visan, Monica 13 Argyros, Spiros A. 13 Castillo, Jesús M. F. 13 Grébert, Benoît 13 Herr, Sebastian 13 Isaza, Pedro 13 Johnson, William Buhmann 13 Killip, Rowan 13 Lacey, Michael T. 13 Lee, Han Ju 13 Li, Junfeng 13 Mendel, Manor 13 Orlandi, Giandomenico 13 Tzirakis, Nikolaos 13 Wang, Wei-Min 13 Xiao, Jie 13 Xu, Junxiang 13 Zvavitch, Artem 12 Casazza, Peter George 12 Castro, Alejandro J. ...and 4,948 more Authors all top 5 Cited in 489 Serials 352 Journal of Functional Analysis 261 Journal of Mathematical Analysis and Applications 227 Israel Journal of Mathematics 227 Proceedings of the American Mathematical Society 181 Journal of Differential Equations 173 Transactions of the American Mathematical Society 156 Communications in Mathematical Physics 139 Advances in Mathematics 127 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 108 Journal d’Analyse Mathématique 102 Comptes Rendus. Mathématique. Académie des Sciences, Paris 88 Communications in Partial Differential Equations 86 Duke Mathematical Journal 73 Journal of Mathematical Physics 69 Journal of Number Theory 69 Journal of the European Mathematical Society (JEMS) 66 Mathematische Annalen 66 Geometric and Functional Analysis. GAFA 65 Mathematische Zeitschrift 62 Inventiones Mathematicae 59 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 58 Archive for Rational Mechanics and Analysis 57 Discrete and Continuous Dynamical Systems 55 Annals of Mathematics. Second Series 54 The Journal of Fourier Analysis and Applications 53 Journal of the American Mathematical Society 52 Ergodic Theory and Dynamical Systems 48 Mathematika 48 Journal de Mathématiques Pures et Appliquées. Neuvième Série 42 Revista Matemática Iberoamericana 40 Mathematical Notes 40 Calculus of Variations and Partial Differential Equations 39 Monatshefte für Mathematik 39 Acta Mathematica Sinica. 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New Series 23 Rocky Mountain Journal of Mathematics 23 Integral Equations and Operator Theory 23 Mathematische Nachrichten 22 The Annals of Probability 22 Linear Algebra and its Applications 21 Mathematical Methods in the Applied Sciences 21 Studia Mathematica 21 Physica D 21 International Journal of Number Theory 21 Analysis & PDE 20 Arkiv för Matematik 20 Topology and its Applications 19 Acta Arithmetica 19 Probability Theory and Related Fields 19 Journal of Spectral Theory 18 Nonlinearity 18 Combinatorica 18 Forum Mathematicum 18 Journal of Evolution Equations 17 Chinese Annals of Mathematics. Series B 17 Frontiers of Mathematics in China 17 Science China. Mathematics 16 Annali di Matematica Pura ed Applicata. Serie Quarta 16 European Journal of Combinatorics 16 Finite Fields and their Applications 16 NoDEA. Nonlinear Differential Equations and Applications 16 Forum of Mathematics, Sigma 15 Compositio Mathematica 15 Glasgow Mathematical Journal 15 Journal für die Reine und Angewandte Mathematik 15 Nonlinear Analysis. Real World Applications 15 Journal of Hyperbolic Differential Equations 15 Journal of Fixed Point Theory and Applications 14 Applicable Analysis 14 Mathematics of Computation 14 Proceedings of the Edinburgh Mathematical Society. Series II 14 Abstract and Applied Analysis 13 Journal of Complexity 13 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 13 St. Petersburg Mathematical Journal 12 Geometriae Dedicata 12 Journal of Combinatorial Theory. Series A 12 Advances in Applied Mathematics 12 Potential Analysis 12 Mathematical Physics, Analysis and Geometry ...and 389 more Serials all top 5 Cited in 61 Fields 2,195 Partial differential equations (35-XX) 1,287 Functional analysis (46-XX) 880 Number theory (11-XX) 813 Dynamical systems and ergodic theory (37-XX) 784 Harmonic analysis on Euclidean spaces (42-XX) 672 Operator theory (47-XX) 447 Probability theory and stochastic processes (60-XX) 403 Convex and discrete geometry (52-XX) 284 Measure and integration (28-XX) 266 Combinatorics (05-XX) 260 Fluid mechanics (76-XX) 253 Quantum theory (81-XX) 250 Statistical mechanics, structure of matter (82-XX) 217 Global analysis, analysis on manifolds (58-XX) 177 Real functions (26-XX) 155 Calculus of variations and optimal control; optimization (49-XX) 146 Computer science (68-XX) 138 Numerical analysis (65-XX) 131 Abstract harmonic analysis (43-XX) 130 Functions of a complex variable (30-XX) 115 Information and communication theory, circuits (94-XX) 112 Group theory and generalizations (20-XX) 112 General topology (54-XX) 109 Ordinary differential equations (34-XX) 107 Topological groups, Lie groups (22-XX) 97 Differential geometry (53-XX) 94 Linear and multilinear algebra; matrix theory (15-XX) 65 Potential theory (31-XX) 60 Approximations and expansions (41-XX) 58 Mathematical logic and foundations (03-XX) 56 Integral equations (45-XX) 56 Mechanics of deformable solids (74-XX) 55 Mechanics of particles and systems (70-XX) 50 Difference and functional equations (39-XX) 46 Geometry (51-XX) 45 Several complex variables and analytic spaces (32-XX) 42 Integral transforms, operational calculus (44-XX) 40 Algebraic geometry (14-XX) 34 Systems theory; control (93-XX) 30 Operations research, mathematical programming (90-XX) 29 Statistics (62-XX) 28 Optics, electromagnetic theory (78-XX) 19 Order, lattices, ordered algebraic structures (06-XX) 19 Biology and other natural sciences (92-XX) 18 History and biography (01-XX) 17 General and overarching topics; collections (00-XX) 17 Algebraic topology (55-XX) 16 Sequences, series, summability (40-XX) 15 Special functions (33-XX) 14 Manifolds and cell complexes (57-XX) 14 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 10 Field theory and polynomials (12-XX) 10 Geophysics (86-XX) 7 Nonassociative rings and algebras (17-XX) 6 Commutative algebra (13-XX) 5 Classical thermodynamics, heat transfer (80-XX) 5 Relativity and gravitational theory (83-XX) 2 Astronomy and astrophysics (85-XX) 1 Associative rings and algebras (16-XX) 1 Category theory; homological algebra (18-XX) 1 \(K\)-theory (19-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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