# zbMATH — the first resource for mathematics

## Tao, Terence

Compute Distance To:
 Author ID: tao.terence-c Published as: Tao, T.; Tao, Terence; Tao, Terence C.; Tao, Terence C. S.; Tao, Terence Chi-Shen; Tao, Terrence; Tao, Terry Homepage: https://www.math.ucla.edu/~tao/ External Links: MGP · Math-Net.Ru · Wikidata · MathOverflow · ORCID · dblp · GND · MacTutor Awards: Clay Research Award (2003) · Fields Medal (2006) · Breakthrough Prize in Mathematics (2014)
 Documents Indexed: 341 Publications since 1992, including 29 Books Reviewing Activity: 111 Reviews Biographic References: 9 Publications
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#### Co-Authors

 127 single-authored 34 Vu, Van H. 32 Green, Ben Joseph 18 Keel, Markus 18 Thiele, Christoph Martin 16 Colliander, James E. 14 Staffilani, Gigliola 14 Takaoka, Hideo 14 Ziegler, Tamar 13 Muscalu, Camil 8 Breuillard, Emmanuel 8 Katz, Nets Hawk 6 Candès, Emmanuel J. 6 Wright, James Robert 5 Christ, Michael 5 Hassell, Andrew 5 Knutson, Allen 5 Matomäki, Kaisa Sofia 5 Radziwiłł, Maksym 5 Seeger, Andreas 5 Visan, Monica 4 Bergelson, Vitaly 4 de Gier, Jan 4 Ford, Kevin B. 4 Maynard, James 4 Praeger, Cheryl Elisabeth 4 Rodnianski, Igor 4 Teräväinen, Joni 4 Wood, David Ronald 3 Bennett, Jonathan M. 3 Carbery, Anthony 3 Demeter, Ciprian 3 Konyagin, Sergeĭ Vladimirovich 3 Łaba, Izabella 3 Vargas, Ana M. 3 Zhang, Xiaoyi 2 Austin, Tim D. 2 Castryck, Wouter 2 Eisner, Tanja 2 Grafakos, Loukas 2 Guralnick, Robert Michael 2 Harcos, Gergely 2 Iosevich, Alex 2 Khare, Apoorva 2 Kowalski, Emmanuel 2 Lacey, Michael T. 2 Michel, Philippe Gabriel 2 Naor, Assaf 2 Nielsen, Pace P. 2 Oberlin, Richard 2 Pipher, Jill Catherine 2 Romberg, Justin K. 2 Sutherland, Andrew V. 2 Woodward, Christopher T. 2 Wunsch, Jared 1 Auscher, Pascal 1 Bejenaru, Ioan 1 Bourgain, Jean 1 Chang, Sun-Yung Alice 1 Córdoba Barba, Antonio Juan 1 Cordoba, Diego 1 Costello, Kevin Patrick 1 Cowling, Michael G. 1 Croot, Ernest III 1 Ellenberg, Jordan S. 1 Elsholtz, Christian 1 Erdős, László 1 Fefferman, Charles Louis 1 Filoche, Marcel 1 Fouvry, Etienne 1 Frantzikinakis, Nikos 1 Fritz, Tobias 1 Fröhlich, Jürg Martin 1 Gadgil, Siddhartha 1 Gibson, Andrew P. 1 Gomba, Irene 1 Graham, C. Robin 1 Greengard, Leslie F. 1 Hall, Peter Gavin 1 Helfgott, Harald Andrés 1 Hofmann, Steve 1 Holden, Helge 1 Ionescu, Alex 1 Kane, Daniel M. 1 Karlsen, Kenneth Hvistendahl 1 Killip, Rowan 1 Klainerman, Sergiu 1 Klartag, Bo’az 1 Kohn, Joseph J. 1 Krishnapur, Manjunath 1 Li, Xiaochun 1 Lindblad, Hans 1 Mayboroda, Svitlana 1 Millard, Andrew C. 1 Mockenhaupt, Gerd 1 Nelson, Paul D. 1 Nguyen, Hoi H. 1 Nirenberg, Louis 1 Paldi, Eytan 1 Payne, Kevin R. 1 Petersen, Peter V ...and 27 more Co-Authors
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#### Serials

 13 Geometric and Functional Analysis. GAFA 10 Journal of the American Mathematical Society 10 Mathematical Research Letters 10 Annals of Mathematics. Second Series 8 Journal d’Analyse Mathématique 8 American Journal of Mathematics 8 Duke Mathematical Journal 8 Bulletin of the American Mathematical Society. New Series 8 Texts and Readings in Mathematics 8 Analysis & PDE 6 Journal of Functional Analysis 6 Dynamics of Partial Differential Equations 6 Contributions to Discrete Mathematics 6 Graduate Studies in Mathematics 5 Acta Mathematica 5 Mathematische Annalen 5 Revista Matemática Iberoamericana 5 Communications in Partial Differential Equations 5 Discrete and Continuous Dynamical Systems 5 Algebra & Number Theory 5 Forum of Mathematics, Sigma 4 Communications in Mathematical Physics 4 IEEE Transactions on Information Theory 4 Mathematics of Computation 4 Probability Theory and Related Fields 4 Notices of the American Mathematical Society 4 Journal of the European Mathematical Society (JEMS) 4 Journal of the Australian Mathematical Society 4 MATRIX Book Series 3 Communications on Pure and Applied Mathematics 3 Israel Journal of Mathematics 3 Advances in Mathematics 3 The Annals of Probability 3 The Australian Mathematical Society Gazette 3 Mathematika 3 Proceedings of the London Mathematical Society. Third Series 3 Combinatorica 3 Random Structures & Algorithms 3 IMRN. International Mathematics Research Notices 3 Electronic Journal of Differential Equations (EJDE) 3 The Electronic Journal of Combinatorics 3 The New York Journal of Mathematics 3 Forum of Mathematics, Pi 3 Discrete Analysis 2 Journal of Mathematical Physics 2 Collectanea Mathematica 2 Indiana University Mathematics Journal 2 Inventiones Mathematicae 2 Journal of Differential Equations 2 Mathematische Zeitschrift 2 Pacific Journal of Mathematics 2 Proceedings of the American Mathematical Society 2 Transactions of the American Mathematical Society 2 European Journal of Combinatorics 2 Discrete & Computational Geometry 2 Publicacions Matemàtiques 2 SIAM Journal on Mathematical Analysis 2 Journal de Théorie des Nombres de Bordeaux 2 Applied and Computational Harmonic Analysis 2 Combinatorics, Probability and Computing 2 The Quarterly Journal of Mathematics 2 Journal of Hyperbolic Differential Equations 2 Cambridge Studies in Advanced Mathematics 2 Electronic Research Announcements in Mathematical Sciences 2 Random Matrices: Theory and Applications 1 Bulletin of the Australian Mathematical Society 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Mitteilungen der Deutschen Mathematiker-Vereinigung (DMV) 1 Nonlinearity 1 Acta Mathematica Vietnamica 1 Annales de l’Institut Fourier 1 The Annals of Statistics 1 Glasgow Mathematical Journal 1 Publications Mathématiques 1 Journal of Combinatorial Theory. Series A 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Journal of Operator Theory 1 Ergodic Theory and Dynamical Systems 1 Forum Mathematicum 1 Pokroky Matematiky, Fyziky & Astronomie 1 Proceedings of the National Academy of Sciences of the United States of America 1 Communications in Analysis and Geometry 1 Advances in Applied Clifford Algebras 1 Electronic Journal of Probability 1 European Mathematical Society Newsletter 1 Séminaire Lotharingien de Combinatoire 1 Annals of Combinatorics 1 Journal of the Royal Statistical Society. Series B. Statistical Methodology 1 Communications in Contemporary Mathematics 1 Communications on Pure and Applied Analysis 1 Journal of the Institute of Mathematics of Jussieu 1 Oberwolfach Reports 1 Pure and Applied Mathematics Quarterly 1 Proceedings of the Steklov Institute of Mathematics 1 Groups, Geometry, and Dynamics 1 Journal of Combinatorics 1 EMS Surveys in Mathematical Sciences 1 Die Weltweit Besten Mathematischen Artikel im 21. Jahrhundert 1 Annals of PDE 1 CBMS Regional Conference Series in Mathematics
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#### Fields

 102 Number theory (11-XX) 85 Partial differential equations (35-XX) 72 Harmonic analysis on Euclidean spaces (42-XX) 47 Dynamical systems and ergodic theory (37-XX) 40 Linear and multilinear algebra; matrix theory (15-XX) 38 Combinatorics (05-XX) 33 Probability theory and stochastic processes (60-XX) 22 Group theory and generalizations (20-XX) 19 General and overarching topics; collections (00-XX) 15 Measure and integration (28-XX) 15 Functional analysis (46-XX) 13 Real functions (26-XX) 13 Global analysis, analysis on manifolds (58-XX) 12 Operator theory (47-XX) 9 History and biography (01-XX) 9 Information and communication theory, circuits (94-XX) 8 Convex and discrete geometry (52-XX) 7 Algebraic geometry (14-XX) 7 Topological groups, Lie groups (22-XX) 7 Statistics (62-XX) 7 Fluid mechanics (76-XX) 7 Quantum theory (81-XX) 6 Abstract harmonic analysis (43-XX) 6 Integral transforms, operational calculus (44-XX) 5 Differential geometry (53-XX) 5 Numerical analysis (65-XX) 4 Geometry (51-XX) 4 Operations research, mathematical programming (90-XX) 3 Mathematical logic and foundations (03-XX) 3 Category theory; homological algebra (18-XX) 2 Field theory and polynomials (12-XX) 2 Functions of a complex variable (30-XX) 2 Potential theory (31-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Ordinary differential equations (34-XX) 2 Manifolds and cell complexes (57-XX) 2 Biology and other natural sciences (92-XX) 1 Commutative algebra (13-XX) 1 Associative rings and algebras (16-XX) 1 Special functions (33-XX) 1 Difference and functional equations (39-XX) 1 Integral equations (45-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Computer science (68-XX) 1 Mechanics of deformable solids (74-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Mathematics education (97-XX)

#### Citations contained in zbMATH Open

300 Publications have been cited 12,117 times in 7,328 Documents Cited by Year
Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. Zbl 1231.94017
Candès, Emmanuel J.; Romberg, Justin K.; Tao, Terence
2006
Endpoint Strichartz estimates. Zbl 0922.35028
Keel, Markus; Tao, Terence
1998
Decoding by linear programming. Zbl 1264.94121
Candès, Emmanuel J.; Tao, Terence
2005
The Dantzig selector: statistical estimation when $$p$$ is much larger than $$n$$. (With discussions and rejoinder). Zbl 1139.62019
Candès, Emmanuel; Tao, Terence
2007
Stable signal recovery from incomplete and inaccurate measurements. Zbl 1098.94009
Candès, Emmanuel J.; Romberg, Justin K.; Tao, Terence
2006
Nonlinear dispersive equations. Local and global analysis. Zbl 1106.35001
Tao, Terence
2006
Near-optimal signal recovery from random projections: universal encoding strategies? Zbl 1309.94033
Candès, Emmanuel J.; Tao, Terence
2006
Tao, Terence; Vu, Van H.
2006
Sharp global well-posedness for KdV and modified KdV on $$\mathbb R$$ and $$\mathbb T$$. Zbl 1025.35025
Colliander, James E.; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo; Tao, Terence C.
2003
The power of convex relaxation: near-optimal matrix completion. Zbl 1366.15021
Candès, Emmanuel J.; Tao, Terence
2010
Global well-posedness and scattering for the energy-critical Schrödinger equation in $$\mathbb R^{3}$$. Zbl 1178.35345
Colliander, James; Keel, Markus; Staffilani, Gigiola; Takaoka, Hideo; Tao, Terence
2008
The primes contain arbitrarily long arithmetic progressions. Zbl 1191.11025
Green, Ben; Tao, Terence
2008
Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations. Zbl 1048.35101
Christ, Michael; Colliander, James; Tao, Terrence
2003
A sum-product estimate in finite fields, and applications. Zbl 1145.11306
Bourgain, Jean; Katz, N.; Tao, Terence C.
2004
Random matrices: universality of local eigenvalue statistics. Zbl 1217.15043
Tao, Terence; Vu, Van
2011
Multilinear weighted convolution of $$L^2$$ functions, and applications to nonlinear dispersive equations. Zbl 0998.42005
Tao, Terence
2001
The honeycomb model of $$\text{GL}_n(\mathbb C)$$ tensor products. I: Proof of the saturation conjecture. Zbl 0944.05097
Knutson, Allen; Tao, Terence
1999
Topics in random matrix theory. Zbl 1256.15020
Tao, Terence
2012
Fuglede’s conjecture is false in 5 and higher dimensions. Zbl 1092.42014
Tao, Terence
2004
Random matrices: universality of ESDs and the circular law. Zbl 1203.15025
Tao, Terence; Vu, Van; Krishnapur, Manjunath
2010
A sharp bilinear restriction estimate for paraboloids. Zbl 1068.42011
Tao, Terence C.
2003
Linear equations in primes. Zbl 1242.11071
Green, Benjamin; Tao, Terence
2010
The honeycomb model of $$\text{GL}_n({\mathbb C})$$ tensor products. II: Puzzles determine facets of the Littlewood-Richardson cone. Zbl 1043.05111
Knutson, Allen; Tao, Terence; Woodward, Christopher
2004
Scale-oblivious metric fragmentation and the nonlinear Dvoretzky theorem. Zbl 1266.46017
Naor, Assaf; Tao, Terence
2012
Global well-posedness of the Benjamin-Ono equation in $$H^ 1(R)$$. Zbl 1055.35104
Tao, Terence
2004
Random matrices: Universality of local eigenvalue statistics up to the edge. Zbl 1202.15038
Tao, Terence; Vu, Van
2010
On the multilinear restriction and Kakeya conjectures. Zbl 1203.42019
Bennett, Jonathan; Carbery, Anthony; Tao, Terence
2006
The Möbius function is strongly orthogonal to nilsequences. Zbl 1347.37019
Green, Ben; Tao, Terence
2012
The nonlinear Schrödinger equation with combined power-type nonlinearities. Zbl 1187.35245
Tao, Terence; Visan, Monica; Zhang, Xiaoyi
2007
A bilinear approach to the restriction and Kakeya conjectures. Zbl 0924.42008
Tao, Terence; Vargas, Ana; Vega, Luis
1998
The cubic nonlinear Schrödinger equation in two dimensions with radial data. Zbl 1187.35237
Killip, Rowan; Tao, Terence; Visan, Monica
2009
Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation. Zbl 1197.35265
Colliander, James E.; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo; Tao, Terence
2010
Sharp well-posedness and ill-posedness results for a quadratic nonlinear Schrödinger equation. Zbl 1090.35162
Bejenaru, Ioan; Tao, Terence
2006
Inverse Littlewood-Offord theorems and the condition number of random discrete matrices. Zbl 1250.60023
Tao, Terence; Vu, Van H.
2009
Global regularity of wave maps. II: Small energy in two dimensions. Zbl 1020.35046
Tao, Terence
2001
Puzzles and (equivariant) cohomology of Grassmannians. Zbl 1064.14063
Knutson, Allen; Tao, Terence
2003
An inverse theorem for the Gowers $$U^{s+1}[N]$$-norm. Zbl 1282.11007
Green, Ben; Tao, Terence; Ziegler, Tamar
2012
Random matrices: the circular law. Zbl 1156.15010
Tao, Terence; Van, Vu
2008
Multilinear estimates for periodic KdV equations, and applications. Zbl 1062.35109
Colliander, James E.; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo; Tao, Terence C.
2004
Global well-posedness for Schrödinger equations with derivative. Zbl 1002.35113
Colliander, James E.; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo; Tao, Terence C.
2001
A refined global well-posedness result for Schrödinger equations with derivative. Zbl 1034.35120
Colliander, James E.; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo; Tao, Terence C.
2002
Product set estimates for non-commutative groups. Zbl 1254.11017
Tao, Terence
2008
Global existence and scattering for rough solutions of a nonlinear Schrödinger equation on $$\mathbb R^3$$. Zbl 1060.35131
Colliander, James E.; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo; Tao, Terence C.
2004
Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation. Zbl 1152.35491
Colliander, James E.; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo; Tao, Terence C.
2002
The quantitative behaviour of polynomial orbits on nilmanifolds. Zbl 1251.37012
Green, Ben; Tao, Terence
2012
Multi-linear operators given by singular multipliers. Zbl 0994.42015
Muscalu, Camil; Tao, Terence; Thiele, Christoph
2002
Bi-parameter paraproducts. Zbl 1087.42016
Muscalu, Camil; Pipher, Jill; Tao, Terence; Thiele, Christoph
2004
Norm convergence of multiple ergodic averages for commuting transformations. Zbl 1181.37004
Tao, Terence
2008
Global regularity for a logarithmically supercritical hyperdissipative Navier-Stokes equation. Zbl 1190.35177
Tao, Terence
2009
The Brascamp-Lieb inequalities: Finiteness, structure and extremals. Zbl 1132.26006
Bennett, Jonathan; Carbery, Anthony; Christ, Michael; Tao, Terence
2008
An uncertainty principle for cyclic groups of prime order. Zbl 1080.42002
Tao, Terence
2005
Global well-posedness and scattering for the defocusing mass-critical nonlinear Schrödinger equation for radial data in high dimensions. Zbl 1187.35246
Tao, Terence; Visan, Monica; Zhang, Xiaoyi
2007
A bilinear approach to cone multipliers. II: Applications. Zbl 0949.42013
Tao, Terence C.; Vargas, Ana M.
2000
Approximate subgroups of linear groups. Zbl 1229.20045
Breuillard, Emmanuel; Green, Ben; Tao, Terence
2011
Some recent progress on the restriction conjecture. Zbl 1083.42008
Tao, Terence
2004
A variant of the hypergraph removal lemma. Zbl 1105.05052
Tao, Terence
2006
An introduction to measure theory. Zbl 1231.28001
Tao, Terence
2011
Minimal-mass blowup solutions of the mass-critical NLS. Zbl 1154.35085
Tao, Terence; Visan, Monica; Zhang, Xiaoyi
2008
From the Littlewood-Offord problem to the circular law: universality of the spectral distribution of random matrices. Zbl 1168.15018
Tao, Terence; Vu, Van
2009
Global regularity of wave maps. I: Small critical Sobolev norm in high dimension. Zbl 0983.35080
Tao, Terence
2001
A bilinear approach to cone multipliers. I: Restriction estimates. Zbl 0949.42012
Tao, Terence C.; Vargas, Ana M.
2000
Random covariance matrices: universality of local statistics of eigenvalues. Zbl 1247.15036
Tao, Terence; Vu, Van
2012
An inverse theorem for the Gowers $$U^3(G)$$ norm. Zbl 1202.11013
Green, Ben; Tao, Terence
2008
The Fuglede spectral conjecture holds for convex planar domains. Zbl 1087.42018
Iosevich, Alex; Katz, Nets; Tao, Terence
2003
An incidence theorem in higher dimensions. Zbl 1253.51004
Solymosi, József; Tao, Terence
2012
On the singularity probability of random Bernoulli matrices. Zbl 1116.15021
Tao, Terence; Vu, Van
2007
Random matrices: The distribution of the smallest singular values. Zbl 1210.60014
Tao, Terence; Vu, Van
2010
Stability of energy-critical nonlinear Schrödinger equations in high dimensions. Zbl 1245.35122
Tao, Terence; Visan, Monica
2005
$$L^p$$ improving bounds for averages along curves. Zbl 1080.42007
Tao, Terence; Wright, James
2003
Global well-posedness and scattering for the higher-dimensional energy-critical nonlinear Schrödinger equation for radial data. Zbl 1119.35092
Tao, Terence
2005
Restriction and Kakeya phenomena for finite fields. Zbl 1072.42007
Mockenhaupt, Gerd; Tao, Terence
2004
Spherically averaged endpoint Strichartz estimates for the two-dimensional Schrödinger equation. Zbl 0966.35027
Tao, Terence
2000
Carleson measures, trees, extrapolation, and $$T(b)$$ theorems. Zbl 1027.42009
Auscher, P.; Hofmann, S.; Muscalu, Camil; Tao, Terence C.; Thiele, Christoph
2002
Global well-posedness for KdV in Sobolev spaces of negative index. Zbl 0967.35119
Colliander, James E.; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo; Tao, Terence C.
2001
A variation norm Carleson theorem. Zbl 1246.42016
Oberlin, Richard; Seeger, Andreas; Tao, Terence; Thiele, Christoph; Wright, James
2012
Bulk universality for Wigner Hermite matrices with subexponential decay. Zbl 1277.15027
Erdős, László; Ramírez, José; Schlein, Benjamin; Tao, Terence; Vu, Van; Yau, Horng-Tzer
2010
Multi-parameter paraproducts. Zbl 1114.42005
Muscalu, Camil; Pipher, Jill; Tao, Terence; Thiele, Christoph
2006
A singularity removal theorem for Yang-Mills fields in higher dimensions. Zbl 1086.53043
Tao, Terence; Tian, Gang
2004
Convex bodies with a point of curvature do not have Fourier bases. Zbl 0998.42001
Iosevich, Alex; Katz, Nets Hawk; Tao, Terry
2001
On random $$\pm 1$$ matrices: Singularity and determinant. Zbl 1086.60008
Tao, Terence; Vu, Van
2006
The Bochner-Riesz conjecture implies the restriction conjecture. Zbl 0980.42006
Tao, Terence
1999
An averaged form of Chowla’s conjecture. Zbl 1377.11109
Matomäki, Kaisa; Radziwiłł, Maksym; Tao, Terence
2015
Effective limiting absorption principles, and applications. Zbl 1310.35204
Rodnianski, Igor; Tao, Terence
2015
The structure of approximate groups. Zbl 1260.20062
Breuillard, Emmanuel; Green, Ben; Tao, Terence
2012
Structure and randomness. Pages from year one of a mathematical blog. Zbl 1245.00024
Tao, Terence
2008
A priori bounds and weak solutions for the nonlinear Schrödinger equation in Sobolev spaces of negative order. Zbl 1136.35087
Christ, Michael; Colliander, James; Tao, Terence
2008
Honeycombs and sums of Hermitian matrices. Zbl 1047.15006
Knutson, Allen; Tao, Terence
2001
Finite time blowup for an averaged three-dimensional Navier-Stokes equation. Zbl 1342.35227
Tao, Terence
2016
Why are solitons stable? Zbl 1155.35082
Tao, Terence
2009
Some connections between Falconer’s distance set conjecture and sets of Furstenburg type. Zbl 0991.28006
Katz, Nets Hawk; Tao, Terence
2001
Random matrices: universality of local spectral statistics of non-Hermitian matrices. Zbl 1316.15042
Tao, Terence; Vu, Van
2015
Scattering for the quartic generalised Korteweg-de Vries equation. Zbl 1171.35107
Tao, Terence
2007
Endpoint bilinear restriction theorems for the cone, and some sharp null form estimates. Zbl 0992.42004
Tao, Terence
2001
Random matrices: universal properties of eigenvectors. Zbl 1248.15031
Tao, Terence; Vu, Van
2012
Operator splitting for the KdV equation. Zbl 1219.35235
Holden, Helge; Karlsen, Kenneth H.; Risebro, Nils Henrik; Tao, Terence
2011
Random symmetric matrices are almost surely nonsingular. Zbl 1110.15020
Costello, Kevin P.; Tao, Terence; Vu, Van
2006
Smooth analysis of the condition number and the least singular value. Zbl 1253.65067
Tao, Terence; Vu, Van
2010
The primes contain arbitrarily long polynomial progressions. Zbl 1230.11018
Tao, Terence; Ziegler, Tamar
2008
On sets defining few ordinary lines. Zbl 1309.51002
Green, Ben; Tao, Terence
2013
Local universality of zeroes of random polynomials. Zbl 1360.60102
Tao, Terence; Vu, Van
2015
The de Bruijn-Newman constant is non-negative. Zbl 1454.11158
2020
Sharp bounds for multilinear curved Kakeya, restriction and oscillatory integral estimates away from the endpoint. Zbl 1442.42042
Tao, Terence
2020
Fourier uniformity of bounded multiplicative functions in short intervals on average. Zbl 07177806
Matomäki, Kaisa; Radziwiłł, Maksym; Tao, Terence
2020
The structure of logarithmically averaged correlations of multiplicative functions, with applications to the Chowla and Elliott conjectures. Zbl 1436.11115
Tao, Terence; Teräväinen, Joni
2019
The structure of correlations of multiplicative functions at almost all scales, with applications to the Chowla and Elliott conjectures. Zbl 07141311
Tao, Terence; Teräväinen, Joni
2019
Correlations of the von Mangoldt and higher divisor functions. I. Long shift ranges. Zbl 1426.11107
Matomäki, Kaisa; Radziwiłł, Maksym; Tao, Terence
2019
Value patterns of multiplicative functions and related sequences. Zbl 1433.11112
Tao, Terence; Teräväinen, Joni
2019
Correlations of the von Mangoldt and higher divisor functions. II: Divisor correlations in short ranges. Zbl 1416.11138
Matomäki, Kaisa; Radziwiłł, Maksym; Tao, Terence
2019
Long gaps between primes. Zbl 1392.11071
Ford, Kevin; Green, Ben; Konyagin, Sergei; Maynard, James; Tao, Terence
2018
Odd order cases of the logarithmically averaged Chowla conjecture. Zbl 1441.11255
Tao, Terence; Teräväinen, Joni
2018
Polynomial patterns in the primes. Zbl 07087932
Tao, Terence; Ziegler, Tamar
2018
Some remarks on the lonely runner conjecture. Zbl 1451.11088
Tao, Terence
2018
An inverse theorem for an inequality of Kneser. Zbl 1426.43001
Tao, Terence
2018
Schur polynomials, entrywise positivity preservers, and weak majorization. Zbl 1411.05263
Khare, Apoorva; Tao, Terence
2018
Homogeneous length functions on groups. Zbl 06976302
Fritz, Tobias; Gadgil, Siddhartha; Khare, Apoorva; Nielsen, Pace; Silberman, Lior; Tao, Terence
2018
Finite time blowup for a supercritical defocusing nonlinear Schrödinger system. Zbl 1375.35435
Tao, Terence
2018
Equivalence of the logarithmically averaged Chowla and Sarnak conjectures. Zbl 1426.11111
Tao, Terence
2017
Random matrices have simple spectrum. Zbl 1399.60008
Tao, Terence; Vu, V.
2017
Random matrices: tail bounds for gaps between eigenvalues. Zbl 1391.15111
Nguyen, Hoi; Tao, Terence; Vu, Van
2017
New bounds for Szemerédi’s theorem. III: A polylogarithmic bound for $$r_{4}(n)$$. Zbl 1434.11037
Green, Ben; Tao, Terence
2017
An integration approach to the Toeplitz square peg problem. Zbl 1422.52001
Tao, Terence
2017
Sum-free sets in groups: a survey. Zbl 1431.11026
Tao, Terence; Vu, Van
2017
Inverse theorems for sets and measures of polynomial growth. Zbl 1400.11133
Tao, Terence
2017
On the universality of potential well dynamics. Zbl 1383.37016
Tao, Terence
2017
Finite time blowup for an averaged three-dimensional Navier-Stokes equation. Zbl 1342.35227
Tao, Terence
2016
The logarithmically averaged Chowla and Elliott conjectures for two-point correlations. Zbl 1383.11116
Tao, Terence
2016
Large gaps between consecutive prime numbers. Zbl 1338.11083
Ford, Kevin; Green, Ben; Konyagin, Sergei; Tao, Terence
2016
Sign patterns of the Liouville and Möbius functions. Zbl 1394.11066
Matomäki, Kaisa; Radziwiłł, Maksym; Tao, Terence
2016
The Erdös discrepancy problem. Zbl 1353.11087
Tao, Terence
2016
Finite time blowup for Lagrangian modifications of the three-dimensional Euler equation. Zbl 1397.35181
Tao, Terence
2016
Finite-time blowup for a supercritical defocusing nonlinear wave system. Zbl 1365.35111
Tao, Terence
2016
Concatenation theorems for anti-Gowers-uniform functions and Host-Kra characteristic factors. Zbl 1400.11028
Tao, Terence; Ziegler, Tamar
2016
Sum-avoiding sets in groups. Zbl 1400.11027
Tao, Terence; Vu, Van
2016
Cancellation for the multilinear Hilbert transform. Zbl 1369.42014
Tao, Terence
2016
Finite time blowup for high dimensional nonlinear wave systems with bounded smooth nonlinearity. Zbl 1353.35254
Tao, Terence
2016
An averaged form of Chowla’s conjecture. Zbl 1377.11109
Matomäki, Kaisa; Radziwiłł, Maksym; Tao, Terence
2015
Effective limiting absorption principles, and applications. Zbl 1310.35204
Rodnianski, Igor; Tao, Terence
2015
Random matrices: universality of local spectral statistics of non-Hermitian matrices. Zbl 1316.15042
Tao, Terence; Vu, Van
2015
Local universality of zeroes of random polynomials. Zbl 1360.60102
Tao, Terence; Vu, Van
2015
Expansion in finite simple groups of Lie type. Zbl 1331.20060
Breuillard, Emmanuel; Green, Ben; Guralnick, Robert; Tao, Terence
2015
Expanding polynomials over finite fields of large characteristic, and a regularity lemma for definable sets. Zbl 1370.11135
Tao, Terence
2015
Failure of the $$L^1$$ pointwise and maximal ergodic theorems for the free group. Zbl 1359.37010
Tao, Terence
2015
A multi-dimensional Szemerédi theorem for the primes via a correspondence principle. Zbl 1414.11019
Tao, Terence; Ziegler, Tamar
2015
Expansion in finite simple groups of Lie type. Zbl 1336.20015
Tao, Terence
2015
The Elliott-Halberstam conjecture implies the Vinogradov least quadratic nonresidue conjecture. Zbl 1319.11067
Tao, Terence
2015
Narrow progressions in the primes. Zbl 1391.11131
Tao, Terence; Ziegler, Tamar
2015
Multiple recurrence and convergence results associated to $$\mathbb F_P^\omega$$-actions. Zbl 1361.37006
Bergelson, Vitaly; Tao, Terence; Ziegler, Tamar
2015
Hilbert’s fifth problem and related topics. Zbl 1298.22001
Tao, Terence
2014
New equidistribution estimates of Zhang type. Zbl 1307.11097
Castryck, Wouter; Fouvry, Étienne; Harcos, Gergely; Kowalski, Emmanuel; Michel, Philippe; Nelson, Paul; Paldi, Eytan; Pintz, János; Sutherland, Andrew; Tao, Terence; Xie, Xiao-Feng
2014
Random matrices: The universality phenomenon for Wigner ensembles. Zbl 1310.15077
Tao, Terence; Vu, Van
2014
Algebraic combinatorial geometry: the polynomial method in arithmetic combinatorics, incidence combinatorics, and number theory. Zbl 1294.05044
Tao, Terence
2014
Every odd number greater than 1 is the sum of at most five primes. Zbl 1318.11126
Tao, Terence
2014
Multiple recurrence in quasirandom groups. Zbl 1336.37007
Bergelson, Vitaly; Tao, Terence
2014
Multi-linear multipliers associated to simplexes of arbitrary length. Zbl 1354.42006
Muscalu, Camil; Tao, Terence; Thiele, Christoph
2014
On the quantitative distribution of polynomial nilsequences – erratum. Zbl 1290.37004
Green, Ben; Tao, Terence
2014
Random matrices: the four-moment theorem for Wigner ensembles. Zbl 1327.15075
Tao, Terence; Vu, Van
2014
The “Bounded gaps between primes” Polymath project – a retrospective analysis. Zbl 1315.01078
Polymath, D. H. J.; Tao, Terence; Gibson, Andrew; Nielsen, Pace; Maynard, James; Harcos, Gergely; Roberts, David; Sutherland, Andrew; Castryck, Wouter; Kowalski, Emmanuel; Michel, Philippe
2014
Analysis I. 3rd ed. Zbl 1300.26002
Tao, Terence
2014
On sets defining few ordinary lines. Zbl 1309.51002
Green, Ben; Tao, Terence
2013
Outliers in the spectrum of iid matrices with bounded rank perturbations. Zbl 1261.60009
Tao, Terence
2013
Random matrices: sharp concentration of eigenvalues. Zbl 1296.15022
Tao, Terence; Vu, Van
2013
Counting the number of solutions to the Erdős-Straus equation on unit fractions. Zbl 1304.11018
Elsholtz, Christian; Tao, Terence
2013
The asymptotic distribution of a single eigenvalue gap of a Wigner matrix. Zbl 1280.15023
Tao, Terence
2013
Small doubling in groups. Zbl 1333.11028
Breuillard, Emmanuel; Green, Ben; Tao, Terence
2013
Localisation and compactness properties of the Navier-Stokes global regularity problem. Zbl 1287.35058
Tao, Terence
2013
Mixing for progressions in nonabelian groups. Zbl 1328.20065
Tao, Terence
2013
A nilpotent Freiman dimension lemma. Zbl 1294.22004
Breuillard, Emmanuel; Green, Ben; Tao, Terence
2013
Noncommutative sets of small doubling. Zbl 1371.11032
Tao, Terence
2013
Erratum to “The primes contain arbitrarily long polynomial progressions”. Zbl 1295.11013
Tao, Terence; Ziegler, Tamar
2013
Tao, Terence
2013
Topics in random matrix theory. Zbl 1256.15020
Tao, Terence
2012
Scale-oblivious metric fragmentation and the nonlinear Dvoretzky theorem. Zbl 1266.46017
Naor, Assaf; Tao, Terence
2012
The Möbius function is strongly orthogonal to nilsequences. Zbl 1347.37019
Green, Ben; Tao, Terence
2012
An inverse theorem for the Gowers $$U^{s+1}[N]$$-norm. Zbl 1282.11007
Green, Ben; Tao, Terence; Ziegler, Tamar
2012
The quantitative behaviour of polynomial orbits on nilmanifolds. Zbl 1251.37012
Green, Ben; Tao, Terence
2012
Random covariance matrices: universality of local statistics of eigenvalues. Zbl 1247.15036
Tao, Terence; Vu, Van
2012
An incidence theorem in higher dimensions. Zbl 1253.51004
Solymosi, József; Tao, Terence
2012
A variation norm Carleson theorem. Zbl 1246.42016
Oberlin, Richard; Seeger, Andreas; Tao, Terence; Thiele, Christoph; Wright, James
2012
The structure of approximate groups. Zbl 1260.20062
Breuillard, Emmanuel; Green, Ben; Tao, Terence
2012
Random matrices: universal properties of eigenvectors. Zbl 1248.15031
Tao, Terence; Vu, Van
2012
Strongly dense free subgroups of semisimple algebraic groups. Zbl 1266.20060
Breuillard, Emmanuel; Green, Ben; Guralnick, Robert; Tao, Terence
2012
A central limit theorem for the determinant of a Wigner matrix. Zbl 1248.60011
Tao, Terence; Vu, Van
2012
Higher order Fourier analysis. Zbl 1277.11010
Tao, Terence
2012
The inverse conjecture for the Gowers norm over finite fields in low characteristic. Zbl 1306.11015
Tao, Terence; Ziegler, Tamar
2012
Large values of the Gowers-Host-Kra seminorms. Zbl 1305.11009
Eisner, Tanja; Tao, Terence
2012
Deterministic methods to find primes. Zbl 1267.11123
Tao, Terence; Croot, Ernest III; Helfgott, Harald
2012
Asymptotic decay for a one-dimensional nonlinear wave equation. Zbl 1273.35049
2012
The Littlewood-Offord problem in high dimensions and a conjecture of Frankl and Füredi. Zbl 1289.05453
Tao, Terence; Vu, Van
2012
Random matrices: universality of local eigenvalue statistics. Zbl 1217.15043
Tao, Terence; Vu, Van
2011
Approximate subgroups of linear groups. Zbl 1229.20045
Breuillard, Emmanuel; Green, Ben; Tao, Terence
2011
An introduction to measure theory. Zbl 1231.28001
Tao, Terence
2011
Operator splitting for the KdV equation. Zbl 1219.35235
Holden, Helge; Karlsen, Kenneth H.; Risebro, Nils Henrik; Tao, Terence
2011
The Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices. Zbl 1245.15041
Tao, Terence C.; Vu, Van
2011
Global well-posedness of the Maxwell-Klein-Gordon equation below the energy norm. Zbl 1228.35241
Keel, Markus; Roy, Tristan; Tao, Terence
2011
Suzuki groups as expanders. Zbl 1247.20017
Breuillard, Emmanuel; Green, Ben; Tao, Terence
2011
A remark on primality testing and decimal expansions. Zbl 1251.11089
Tao, Terence
2011
Nonconventional ergodic averages and multiple recurrence for von Neumann dynamical systems. Zbl 1219.46058
Austin, Tim; Eisner, Tanja; Tao, Terence
2011
An inverse theorem for the Gowers $$U^4$$-norm. Zbl 1262.11013
Green, Ben; Tao, Terence; Ziegler, Tamar
2011
Random matrices: localization of the eigenvalues and the necessity of four moments. Zbl 1247.15035
Tao, Terence; Vu, Van
2011
An inverse theorem for the Gowers $$U^{s+1}[N]$$-norm. Zbl 1247.11017
Green, Ben; Tao, Terence; Ziegler, Tamar
2011
...and 200 more Documents
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#### Cited by 8,367 Authors

 129 Tao, Terence 50 Bourgain, Jean 36 Lee, Sanghyuk 35 Vu, Van H. 33 Miao, Changxing 32 Shkredov, Il’ya Dmitrievich 30 Erdős, László 29 Iosevich, Alex 28 Kenig, Carlos Eduardo 27 Oh, Tadahiro 27 Tataru, Daniel 27 Zheng, Jiqiang 26 Koh, Doowon 26 Rauhut, Holger 26 Yau, Horng-Tzer 25 Green, Ben Joseph 25 Guo, Zihua 25 Himonas, A. Alexandrou 25 Tzvetkov, Nikolay 21 Carles, Rémi 21 Shparlinski, Igor E. 21 Zhang, Junyong 20 Bez, Neal 20 Chen, Wengu 20 Staffilani, Gigliola 20 Visan, Monica 19 Candès, Emmanuel J. 19 Guo, Boling 19 Lai, Chun-Kit 19 Linares, Felipe 19 Ponce, Gustavo 18 Demeter, Ciprian 18 Lacey, Michael T. 18 Li, Song 18 Peng, Jigen 18 Thiele, Christoph Martin 18 Xiu, Naihua 18 Xu, Guixiang 18 Yin, Jun 17 Dutkay, Dorin Ervin 17 Guth, Lawrence David 17 Osher, Stanley Joel 17 Vega, Luis 17 Vinh, Le Anh 16 Bennett, Jonathan M. 16 Colliander, James E. 16 Killip, Rowan 16 Krahmer, Felix 16 Li, Yongsheng 16 Litvak, Aleksandr Evgen’evich 16 Ozawa, Tohru 16 Seo, Ihyeok 16 Serra, Oriol 16 Tomczak-Jaegermann, Nicole 16 Zhang, Xiaoyi 16 Zhao, Lifeng 15 Carvajal, Xavier Paredes 15 D’Ancona, Piero 15 Ding, Yong 15 Fan, Jianqing 15 Germain, Pierre 15 Götze, Friedrich W. 15 Grafakos, Loukas 15 Herr, Sebastian 15 Hong, Younghun 15 Ionescu, Alexandru D. 15 Knowles, Antti 15 Kutyniok, Gitta 15 Pham Van Thang 15 Rudnev, Misha 15 Saanouni, Tarek 15 Tsybakov, Alexandre B. 15 Yan, Wei 15 Ziegler, Tamar 14 Bejenaru, Ioan 14 Dinh, Van Duong 14 Fang, Daoyuan 14 Huo, Zhaohui 14 Krieger, Joachim 14 Merle, Frank 14 Murphy, Jason 14 O’Rourke, Sean D. 14 Rogers, Keith McKenzie 14 Sanders, Tom 14 Shen, Chun-Yen 14 Tikhomirov, Konstantin E. 14 Van de Geer, Sara Anna 14 Visciglia, Nicola 14 Wang, Baoxiang 13 Dodson, Benjamin G. 13 Frantzikinakis, Nikos 13 Kong, Lingchen 13 Kovač, Vjekoslav 13 Nakanishi, Kenji 13 Needell, Deanna 13 Selberg, Sigmund 13 Vershynin, Roman 13 Wang, Yuzhao 13 Zahl, Joshua 12 Antonelli, Paolo ...and 8,267 more Authors
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#### Cited in 645 Serials

 202 Journal of Mathematical Analysis and Applications 196 Journal of Functional Analysis 157 Transactions of the American Mathematical Society 156 Advances in Mathematics 155 Journal of Differential Equations 141 Proceedings of the American Mathematical Society 141 Applied and Computational Harmonic Analysis 138 Communications in Mathematical Physics 128 The Annals of Statistics 103 Communications in Partial Differential Equations 98 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 92 The Journal of Fourier Analysis and Applications 80 Journal d’Analyse Mathématique 76 Journal of Mathematical Physics 74 Discrete and Continuous Dynamical Systems 67 Linear Algebra and its Applications 66 Journal of Number Theory 59 Duke Mathematical Journal 59 Probability Theory and Related Fields 54 Journal of Combinatorial Theory. Series A 54 Mathematische Annalen 54 Revista Matemática Iberoamericana 53 Electronic Journal of Statistics 51 Comptes Rendus. Mathématique. Académie des Sciences, Paris 50 Israel Journal of Mathematics 50 Geometric and Functional Analysis. GAFA 50 Communications on Pure and Applied Analysis 49 Mathematical Problems in Engineering 49 Science China. Mathematics 48 Mathematische Zeitschrift 46 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 45 SIAM Journal on Imaging Sciences 43 Journal of the American Mathematical Society 43 SIAM Journal on Mathematical Analysis 41 Discrete & Computational Geometry 41 Annals of Mathematics. Second Series 41 Journal of the European Mathematical Society (JEMS) 41 Random Matrices: Theory and Applications 40 Inventiones Mathematicae 40 Mathematical Programming. Series A. Series B 39 Journal of Statistical Physics 39 Journal of Multivariate Analysis 39 Bulletin of the American Mathematical Society. New Series 39 Computational Statistics and Data Analysis 39 Foundations of Computational Mathematics 37 European Journal of Combinatorics 36 The Journal of Geometric Analysis 36 Computational Optimization and Applications 35 Archive for Rational Mechanics and Analysis 35 The Annals of Probability 35 Forum Mathematicum 35 Acta Mathematica Sinica. English Series 34 Journal of Computational and Applied Mathematics 34 Ergodic Theory and Dynamical Systems 34 Journal de Mathématiques Pures et Appliquées. Neuvième Série 33 Mathematics of Computation 32 Inverse Problems 32 Communications in Contemporary Mathematics 31 Communications on Pure and Applied Mathematics 31 Journal of Hyperbolic Differential Equations 30 Journal of Scientific Computing 29 Journal of Theoretical Probability 28 SIAM Journal on Optimization 28 Journal of Machine Learning Research (JMLR) 28 Forum of Mathematics, Sigma 26 Journal of Computational Physics 26 NoDEA. Nonlinear Differential Equations and Applications 26 Bernoulli 26 Annales Henri Poincaré 25 Applied Mathematics and Computation 25 Calculus of Variations and Partial Differential Equations 24 Mathematical Methods in the Applied Sciences 24 Random Structures & Algorithms 23 Annales de l’Institut Fourier 23 Mathematika 23 Combinatorica 23 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 23 SIAM Journal on Scientific Computing 22 Monatshefte für Mathematik 22 Circuits, Systems, and Signal Processing 22 Computational & Mathematical Methods in Medicine 21 Discrete Mathematics 21 Automatica 21 Journal of the American Statistical Association 21 Journal of Approximation Theory 21 Journal of Algebraic Combinatorics 21 Finite Fields and their Applications 21 Analysis & PDE 20 Mathematical Proceedings of the Cambridge Philosophical Society 20 Combinatorics, Probability and Computing 19 Information Sciences 19 Journal of Optimization Theory and Applications 19 Abstract and Applied Analysis 18 Nonlinearity 18 ZAMP. Zeitschrift für angewandte Mathematik und Physik 18 Acta Arithmetica 18 Journal of Statistical Planning and Inference 18 Journal of Complexity 18 Constructive Approximation 18 SIAM Journal on Discrete Mathematics ...and 545 more Serials
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#### Cited in 63 Fields

 2,169 Partial differential equations (35-XX) 941 Harmonic analysis on Euclidean spaces (42-XX) 846 Number theory (11-XX) 784 Information and communication theory, circuits (94-XX) 756 Statistics (62-XX) 731 Probability theory and stochastic processes (60-XX) 718 Numerical analysis (65-XX) 596 Linear and multilinear algebra; matrix theory (15-XX) 593 Combinatorics (05-XX) 537 Operations research, mathematical programming (90-XX) 464 Computer science (68-XX) 450 Dynamical systems and ergodic theory (37-XX) 335 Operator theory (47-XX) 313 Functional analysis (46-XX) 287 Quantum theory (81-XX) 269 Fluid mechanics (76-XX) 241 Convex and discrete geometry (52-XX) 216 Group theory and generalizations (20-XX) 209 Algebraic geometry (14-XX) 195 Measure and integration (28-XX) 181 Global analysis, analysis on manifolds (58-XX) 163 Statistical mechanics, structure of matter (82-XX) 132 Calculus of variations and optimal control; optimization (49-XX) 127 Biology and other natural sciences (92-XX) 126 Differential geometry (53-XX) 123 Topological groups, Lie groups (22-XX) 114 Systems theory; control (93-XX) 109 Abstract harmonic analysis (43-XX) 96 Approximations and expansions (41-XX) 93 Real functions (26-XX) 72 Mathematical logic and foundations (03-XX) 61 Optics, electromagnetic theory (78-XX) 59 Ordinary differential equations (34-XX) 58 Functions of a complex variable (30-XX) 53 Integral transforms, operational calculus (44-XX) 49 Geometry (51-XX) 49 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 32 General and overarching topics; collections (00-XX) 31 Commutative algebra (13-XX) 31 Manifolds and cell complexes (57-XX) 31 Relativity and gravitational theory (83-XX) 30 Nonassociative rings and algebras (17-XX) 30 Integral equations (45-XX) 29 Special functions (33-XX) 28 Associative rings and algebras (16-XX) 28 Mechanics of deformable solids (74-XX) 27 Potential theory (31-XX) 26 Mechanics of particles and systems (70-XX) 25 Several complex variables and analytic spaces (32-XX) 24 Geophysics (86-XX) 23 History and biography (01-XX) 22 General topology (54-XX) 19 Order, lattices, ordered algebraic structures (06-XX) 19 Field theory and polynomials (12-XX) 19 Algebraic topology (55-XX) 15 Difference and functional equations (39-XX) 9 Classical thermodynamics, heat transfer (80-XX) 7 Sequences, series, summability (40-XX) 6 Mathematics education (97-XX) 5 Category theory; homological algebra (18-XX) 5 $$K$$-theory (19-XX) 3 Astronomy and astrophysics (85-XX) 1 General algebraic systems (08-XX)

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