Terence Tao | Academic Influence

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Terence Tao

Mathematics

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Harmonic Analysis

#1

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Combinatorics

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Number Theory

#5

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#12

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Mathematics

Terence Tao's Degrees

PhD Mathematics Princeton University
Masters Mathematics Flinders University
Bachelors Mathematics Flinders University

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Why Is Terence Tao Influential?

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According to Wikipedia, Terence Chi-Shen Tao is an Australian mathematician. He is a professor of mathematics at the University of California, Los Angeles , where he holds the James and Carol Collins chair. His research includes topics in harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, probability theory, compressed sensing and analytic number theory.

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Terence Tao's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information (2004) (15311)
Stable signal recovery from incomplete and inaccurate measurements (2005) (7244)
Decoding by linear programming (2005) (7123)
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies? (2004) (6813)
The Power of Convex Relaxation: Near-Optimal Matrix Completion (2009) (2116)
Endpoint Strichartz estimates (1998) (1798)
Nonlinear dispersive equations : local and global analysis (2006) (1458)
Additive combinatorics (2007) (1036)
Topics in Random Matrix Theory (2012) (964)
The primes contain arbitrarily long arithmetic progressions (2004) (881)
A sum-product estimate in finite fields, and applications (2003) (498)
Random matrices: Universality of local eigenvalue statistics (2009) (475)
Sharp Global well-posedness for KdV and modified KdV on $\R$ and $\T$ (2001) (438)
The honeycomb model of GL(n) tensor products I: proof of the saturation conjecture (1998) (424)
Random matrices: Universality of ESDs and the circular law (2008) (409)
Sharp global well-posedness for KdV and modified KdV on ℝ and (2003) (403)
Linear equations in primes (2006) (399)
The honeycomb model of _{}(ℂ) tensor products I: Proof of the saturation conjecture (1999) (387)
Global well-posedness and scattering for the energy-critical nonlinear Schr\"odinger equation in R^3 (2004) (361)
Multilinear weighted convolution of L2 functions, and applications to nonlinear dispersive equations (2000) (344)
Fuglede's conjecture is false in 5 and higher dimensions (2003) (340)
On the multilinear restriction and Kakeya conjectures (2005) (286)
A sharp bilinear restriction estimate for paraboloids (2002) (270)
A bilinear approach to the restriction and Kakeya conjectures (1998) (263)
Random Matrices: Universality of Local Eigenvalue Statistics up to the Edge (2009) (262)
The honeycomb model of _{}(ℂ) tensor products II: Puzzles determine facets of the Littlewood-Richardson cone (2001) (262)
RANDOM MATRICES: THE CIRCULAR LAW (2007) (258)
The Nonlinear Schrödinger Equation with Combined Power-Type Nonlinearities (2005) (252)
The Brascamp–Lieb Inequalities: Finiteness, Structure and Extremals (2005) (249)
AN INVERSE THEOREM FOR THE GOWERS $U^3(G)$ NORM (2008) (245)
An inverse theorem for the Gowers U^{s+1}[N]-norm (announcement) (2010) (242)
The Mobius function is strongly orthogonal to nilsequences (2008) (240)
Almost conservation laws and global rough solutions to a Nonlinear Schr (2002) (235)
Product set estimates for non-commutative groups (2006) (232)
Global Regularity of Wave Maps¶II. Small Energy in Two Dimensions (2000) (229)
Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation (2010) (226)
The cubic nonlinear Schr\"odinger equation in two dimensions with radial data (2007) (222)
Puzzles and (equivariant) cohomology of Grassmannians (2001) (221)
Approximate Subgroups of Linear Groups (2010) (217)
Norm convergence of multiple ergodic averages for commuting transformations (2007) (216)
An uncertainty principle for cyclic groups of prime order (2003) (215)
Ill-posedness for nonlinear Schrodinger and wave equations (2003) (215)
The quantitative behaviour of polynomial orbits on nilmanifolds (2007) (213)
Multilinear estimates for periodic KdV equations, and applications (2001) (202)
The structure of approximate groups (2011) (197)
Inverse Littlewood-Offord theorems and the condition number of random discrete matrices (2005) (197)
A variant of the hypergraph removal lemma (2005) (195)
AN INVERSE THEOREM FOR THE GOWERS U4-NORM (2005) (194)
On the singularity probability of random Bernoulli matrices (2005) (193)
Finite time blowup for an averaged three-dimensional Navier-Stokes equation (2014) (190)
A bilinear approach to cone multipliers I. Restriction estimates (2000) (188)
GLOBAL WELL-POSEDNESS OF THE BENJAMIN–ONO EQUATION IN H1(R) (2004) (186)
Honeycombs and sums of Hermitian matrices (2000) (185)
Multi-linear operators given by singular multipliers (1999) (185)
A Refined Global Well-Posedness Result for Schrödinger Equations with Derivative (2001) (183)
Global existence and scattering for rough solutions of a nonlinear Schrödinger equation on ℝ3 (2003) (181)
Global Well-Posedness for Schrödinger Equations with Derivative (2001) (173)
Sharp well-posedness and ill-posedness results for a quadratic non-linear Schr (2005) (166)
Bi-parameter paraproducts (2003) (165)
Random Matrices: the Distribution of the Smallest Singular Values (2009) (163)
An Incidence Theorem in Higher Dimensions (2011) (161)
The Bochner-Riesz conjecture implies the restriction conjecture (1999) (157)
Minimal-mass blowup solutions of the mass-critical NLS (2006) (156)
Global well-posedness and scattering for the defocusing mass-critical nonlinear Schrödinger equation for radial data in high dimensions (2007) (155)
Variants of the Selberg sieve, and bounded intervals containing many primes (2014) (154)
Global regularity for a logarithmically supercritical hyperdissipative Navier-Stokes equation (2009) (152)
Some Recent Progress on the Restriction Conjecture (2003) (149)
Global regularity of wave maps, I: small critical Sobolev norm in high dimension (2000) (147)
The primes contain arbitrarily long polynomial progressions (2006) (145)
Random matrices: Universality of local spectral statistics of non-Hermitian matrices (2012) (144)
Global well-posedness and scattering for the higher-dimensional energy-critical non-linear Schrodinger equation for radial data (2004) (142)
STABILITY OF ENERGY-CRITICAL NONLINEAR SCHR¨ ODINGER EQUATIONS IN HIGH DIMENSIONS (2005) (142)
The distribution of polynomials over finite fields, with applications to the Gowers norms (2007) (141)
On random ±1 matrices: Singularity and determinant (2004) (140)
Higher Order Fourier Analysis (2012) (139)
A bilinear approach to cone multipliers II. Applications (2000) (136)
Random covariance matrices: Universality of local statistics of eigenvalues (2009) (135)
Expansion in finite simple groups of Lie type (2013) (135)
An averaged form of Chowla's conjecture (2015) (133)
Outliers in the spectrum of iid matrices with bounded rank perturbations (2010) (132)
From the Littlewood-Offord problem to the Circular Law: universality of the spectral distribution of random matrices (2008) (130)
Why are solitons stable (2008) (129)
Restriction and Kakeya phenomena for finite fields (2002) (125)
Bulk universality for Wigner hermitian matrices with subexponential decay (2009) (118)
Some Connections between Falconer's Distance Set Conjecture and Sets of Furstenburg Type (2001) (116)
On Sets Defining Few Ordinary Lines (2012) (116)
Szemerédi's regularity lemma revisited (2005) (116)
A new proof of the density Hales-Jewett theorem (2009) (115)
Smooth analysis of the condition number and the least singular value (2008) (115)
Spherically averaged endpoint Strichartz estimates for the two-dimensional Schr (1998) (113)
L p IMPROVING BOUNDS FOR AVERAGES ALONG CURVES (2001) (111)
From rotating needles to stability of waves; emerging connections between combinatorics, analysis and PDE (2000) (111)
Random matrices: Universal properties of eigenvectors (2011) (110)
Finite bounds for Hölder-Brascamp-Lieb multilinear inequalities (2005) (110)
A variation norm Carleson theorem (2009) (110)
The Fuglede spectral conjecture holds for convex planar domains (2003) (108)
Multi-parameter paraproducts (2004) (107)
Random symmetric matrices are almost surely nonsingular (2005) (106)
THE LOGARITHMICALLY AVERAGED CHOWLA AND ELLIOTT CONJECTURES FOR TWO-POINT CORRELATIONS (2015) (105)
Local and global well-posedness of wave maps on $\R^{1+1}$ for rough data (1998) (104)
Hilbert's Fifth Problem and Related Topics (2014) (104)
A Quantitative Ergodic Theory Proof of Szemerédi's Theorem (2004) (103)
Global well-posedness for KdV in Sobolev spaces of negative index (2001) (101)
Carleson measures, trees, extrapolation, and T(b) theorems (2001) (101)
The inverse conjecture for the Gowers norm over finite fields via the correspondence principle (2008) (99)
Local Universality of Zeroes of Random Polynomials (2013) (98)
On the asymptotic behavior of large radial data for a focusing non-linear Schr\ (2003) (97)
An Arithmetic Regularity Lemma, An Associated Counting Lemma, and Applications (2010) (96)
Endpoint bilinear restriction theorems for the cone, and some sharp null form estimates (1999) (95)
A Finitary Version of Gromov’s Polynomial Growth Theorem (2009) (92)
A singularity removal theorem for Yang-Mills fields in higher dimensions (2002) (92)
Testability and repair of hereditary hypergraph properties (2008) (92)
Structure and randomness (2008) (89)
The Inverse Conjecture for the Gowers Norm over Finite Fields in Low Characteristic (2011) (87)
Random matrices: The Universality phenomenon for Wigner ensembles (2012) (86)
Additive Combinatorics: Contents (2006) (86)
Eigenvectors from eigenvalues: A survey of a basic identity in linear algebra (2019) (85)
Effective Limiting Absorption Principles, and Applications (2011) (84)
The dichotomy between structure and randomness, arithmetic progressions, and the primes (2005) (83)
Sharp Strichartz estimates on nontrapping asymptotically conic manifolds (2004) (82)
QUADRATIC UNIFORMITY OF THE MOBIUS FUNCTION (2006) (80)
New bounds for Kakeya problems (2001) (80)
Sumset and Inverse Sumset Theory for Shannon Entropy (2009) (79)
New equidistribution estimates of Zhang type (2014) (78)
Lp estimates for the biest II. The Fourier case (2001) (76)
Random matrices have simple spectrum (2014) (76)
Restriction theory of the Selberg sieve, with applications (2004) (76)
Operator splitting for the KdV equation (2009) (75)
Global regularity of wave maps III. Large energy from $\R^{1+2}$ to hyperbolic spaces (2008) (75)
Scattering for the quartic generalised Korteweg–de Vries equation (2006) (74)
Global regularity for a logarithmically supercritical defocusing nonlinear wave equation for spherically symmetric data (2006) (73)
A pseudoconformal compactification of the nonlinear Schrodinger equation and applications (2006) (72)
An improved bound on the Minkowski dimension of Besicovitch sets in R^3 (1999) (71)
An improved bound on the Minkowski dimension of Besicovitch sets in $\mathbb{R}^3$ (2000) (71)
Long gaps between primes (2014) (69)
A Positive Proof of the Littlewood-Richardson Rule using the Octahedron Recurrence (2003) (69)
A priori bounds and weak solutions for the nonlinear Schr (2006) (68)
A central limit theorem for the determinant of a Wigner matrix (2011) (67)
Erratum for "Upper and lower bounds for normal derivatives of Dirichlet eigenfunctions" (2002) (67)
Velocity averaging, kinetic formulations, and regularizing effects in quasi‐linear PDEs (2007) (67)
What is good mathematics (2007) (67)
The sum-product phenomenon in arbitrary rings (2008) (67)
BOUNDS ON ARITHMETIC PROJECTIONS, AND APPLICATIONS TO THE KAKEYA CONJECTURE (1999) (66)
GLOBAL WELL-POSEDNESS FOR SCHR ¨ ODINGER EQUATIONS WITH DERIVATIVE ∗ (2001) (66)
A correspondence principle between (hyper)graph theory and probability theory, and the (hyper)graph removal lemma (2006) (65)
The condition number of a randomly perturbed matrix (2007) (64)
Freiman's theorem for solvable groups (2009) (64)
Algebraic combinatorial geometry: the polynomial method in arithmetic combinatorics, incidence combinatorics, and number theory (2013) (64)
The Gaussian primes contain arbitrarily shaped constellations (2005) (63)
On multilinear oscillatory integrals, nonsingular and singular (2003) (63)
Random Martingales and localization of maximal inequalities (2009) (62)
Global Regularity for the Maxwell-Klein-Gordon Equation with Small Critical Sobolev Norm in High Dimensions (2003) (60)
A Carleson type theorem for a Cantor group model of the scattering transform (2002) (60)
The Kakeya set and maximal conjectures for algebraic varieties over finite fields (2009) (60)
Local well-posedness of the Yang-Mills equation in the temporal gauge below the energy norm (2000) (60)
The structure of logarithmically averaged correlations of multiplicative functions, with applications to the Chowla and Elliott conjectures (2017) (59)
Geometric renormalization of large energy wave maps (2004) (58)
An Inverse Theorem for the Uniformity Seminorms Associated with the Action of $${{\mathbb {F}^{\infty}_{p}}}$$ (2009) (57)
Large gaps between consecutive prime numbers (2014) (57)
A counterexample to a multilinear endpoint question of Christ and Kiselev (2001) (57)
Recent progress on the Kakeya conjecture (2000) (56)
A sharp inverse Littlewood‐Offord theorem (2009) (56)
Spacetime bounds for the energy-critical nonlinear wave equation in three spatial dimensions (2006) (55)
THE WEAK-TYPE ENDPOINT BOCHNER-RIESZ CONJECTURE AND RELATED TOPICS (1998) (55)
Expanding polynomials over finite fields of large characteristic, and a regularity lemma for definable sets (2012) (55)
Low-regularity global solutions to nonlinear dispersive equations (2002) (54)
Breaking the duality in the return times theorem (2006) (54)
Recent progress on the restriction conjecture (2003) (53)
Random matrices: tail bounds for gaps between eigenvalues (2015) (52)
A (concentration-)compact attractor for high-dimensional non-linear Schr\ (2006) (52)
AN INVERSE THEOREM FOR THE UNIFORMITY SEMINORMS ASSOCIATED WITH THE ACTION OF Fp (2010) (52)
Freiman's Theorem in Finite Fields via Extremal Set Theory (2007) (51)
Almost all orbits of the Collatz map attain almost bounded values (2019) (50)
A Strichartz Inequality for the Schrödinger Equation on Nontrapping Asymptotically Conic Manifolds (2003) (50)
On the maximal Bochner-Riesz conjecture in the plane for p < 2 (2002) (50)
Structure and Randomness in Combinatorics (2007) (50)
The Wigner-Dyson-Mehta Bulk Universality Conjecture for Wigner Matrices (2011) (49)
Global regularity of wave maps IV. Absence of stationary or self-similar solutions in the energy class (2008) (49)
Equivalence of the Logarithmically Averaged Chowla and Sarnak Conjectures (2016) (49)
On the Almost Everywhere Convergence of Wavelet Summation Methods (1996) (48)
Resonant decompositions and the $I$-method for the cubic nonlinear Schrödinger equation on $\mathbb{R}^2$ (2008) (47)
COUNTING THE NUMBER OF SOLUTIONS TO THE ERDŐS–STRAUS EQUATION ON UNIT FRACTIONS (2011) (46)
The weak-type (1,1) of L \log L homogeneous convolution operators (1999) (46)
Maximal multilinear operators (2005) (46)
Localisation and compactness properties of the Navier-Stokes global regularity problem (2011) (46)
A VARIATION (2009) (46)
Random matrices: Sharp concentration of eigenvalues (2012) (45)
Poincare's Legacies: Pages from Year Two of a Mathematical Blog (2009) (44)
Global regularity of wave maps VII. Control of delocalised or dispersed solutions (2009) (44)
Small data blow-up for semilinear Klein-Gordon equations (1999) (43)
Lp estimates for the biest I. The Walsh case (2001) (43)
Endpoint multiplier theorems of Marcinkiewicz type (2000) (43)
COMPRESSIONS, CONVEX GEOMETRY AND THE FREIMAN–BILU THEOREM (2005) (42)
Global well-posedness of the Benjamin-Ono equation in H^1(R) (2003) (42)
Uniform estimates on multi-linear operators with modulation symmetry (2001) (40)
Every odd number greater than 1 is the sum of at most five primes (2012) (40)
An Epsilon of Room, II: pages from year three of a mathematical blog (2011) (40)
John-type theorems for generalized arithmetic progressions and iterated sumsets (2006) (40)
Quantitative bounds for critically bounded solutions to the Navier-Stokes equations (2019) (40)
Strongly dense free subgroups of semisimple algebraic groups (2010) (40)
Suzuki groups as expanders (2010) (40)
Global well-posedness and scattering for the mass-critical nonlinear Schr\"odinger equation for radial data in high dimensions (2006) (40)
The ergodic and combinatorial approaches to Szemerédi's theorem (2006) (40)
Global well-posedness of the Maxwell-Klein-Gordon equation below the energy norm (2009) (40)
Sharp Lorentz space estimates for rough operators (1999) (40)
New bounds for Szemerédi's theorem, I: progressions of length 4 in finite field geometries (2005) (39)
New bounds for Szemeredi's theorem, II: A new bound for r_4(N) (2006) (38)
ENDPOINT MAPPING PROPERTIES OF SPHERICAL MAXIMAL OPERATORS (2002) (38)
Polynomial upper bounds for the orbital instability of the 1D cubic NLS below the energy norm (2002) (37)
Lp bounds for a maximal dyadic sum operator (2002) (37)
Global regularity of wave maps VI. Abstract theory of minimal-energy blowup solutions (2009) (37)
Large values of the Gowers-Host-Kra seminorms (2010) (37)
Symplectic nonsqueezing of the korteweg-de vries flow (2005) (37)
Deterministic methods to find primes (2011) (37)
A quantitative version of the Besicovitch projection theorem via multiscale analysis (2007) (36)
The weak-type (1,1) of Fourier integral operators of order –(n–1)/2 (2002) (36)
Classification of almost quarter-pinched manifolds (2008) (36)
Instability of the periodic nonlinear Schrodinger equation (2003) (36)
Singular maximal functions and Radon transforms near L1 (2002) (36)
Real analysis : pages from year three of a mathematical blog (2010) (36)
Insights From SMPY's Greatest Former Child Prodigies: Drs. Terence (“Terry”) Tao and Lenhard (“Lenny”) Ng Reflect on Their Talent Development (2006) (35)
Multilinear interpolation between adjoint operators (2001) (35)
THE DE BRUIJN–NEWMAN CONSTANT IS NON-NEGATIVE (2018) (34)
An equivalence between inverse sumset theorems and inverse conjectures for the U3 norm (2009) (34)
The "bounded gaps between primes" Polymath project - a retrospective (2014) (33)
Resonant decompositions and the I-method for cubic nonlinear Schrodinger on R^2 (2007) (32)
On the universality of the incompressible Euler equation on compact manifolds (2017) (32)
SIGN PATTERNS OF THE LIOUVILLE AND MÖBIUS FUNCTIONS (2015) (32)
Odd order cases of the logarithmically averaged Chowla conjecture (2017) (32)
Multiple Recurrence in Quasirandom Groups (2012) (32)
Low regularity semi-linear wave equations (1997) (32)
Low regularity semi—linear wave equations 1 (1999) (31)
Global regularity of wave maps V. Large data local wellposedness and perturbation theory in the energy class (2008) (31)
The asymptotic distribution of a single eigenvalue gap of a Wigner matrix (2012) (31)
An improved bound for the Minkowski dimension of Besicovitch sets in medium dimension (2000) (30)
The bi-Carleson operator (2004) (30)
AN INTEGRATION APPROACH TO THE TOEPLITZ SQUARE PEG PROBLEM (2016) (30)
Compactness and Contradiction (2013) (29)
Correlations of the von Mangoldt and higher divisor functions I. Long shift ranges (2017) (29)
On the permanent of random Bernoulli matrices (2008) (29)
Finite Time Blowup for Lagrangian Modifications of the Three-Dimensional Euler Equation (2016) (28)
Scale-oblivious metric fragmentation and the nonlinear Dvoretzky theorem (2010) (27)
PERELMAN'S PROOF OF THE POINCAR´ E CONJECTURE: A NONLINEAR PDE PERSPECTIVE (2006) (27)
A NOTE ON THE FREIMAN AND BALOG–SZEMERÉDI–GOWERS THEOREMS IN FINITE FIELDS (2007) (27)
The Littlewood-Offord problem in high dimensions and a conjecture of Frankl and Füredi (2010) (27)
Inverse theorems for sets and measures of polynomial growth (2015) (27)
Weak-type endpoint bounds for Riesz means (1996) (27)
A nilpotent Freiman dimension lemma (2011) (26)
Ill-posedness for one-dimensional wave maps at the critical regularity (1998) (26)
Additive Combinatorics: Graph-theoretic methods (2006) (26)
Asymptotic decay for a one-dimensional nonlinear wave equation (2010) (26)
Two remarks on the generalised Korteweg de-Vries equation (2006) (26)
Global behaviour of nonlinear dispersive and wave equations (2006) (26)
Concatenation theorems for anti-Gowers-uniform functions and Host-Kra characteristic factors (2016) (25)
Structure and Randomness in the Prime Numbers (2011) (25)
A new bound for finite field besicovitch sets in four dimensions (2002) (25)
Almost Everywhere Behavior of General Wavelet Shrinkage Operators (2000) (24)
Linear Approximate Groups (2010) (24)
The Erdos discrepancy problem (2015) (24)
Nonconventional ergodic averages and multiple recurrence for von Neumann dynamical systems (2009) (24)
Correlations of the von Mangoldt and higher divisor functions II: divisor correlations in short ranges (2017) (24)
A Converse Extrapolation Theorem for Translation-Invariant Operators (1999) (24)
Poincare's Legacies, Part II: pages from year two of a mathematical blog (2009) (23)
New equidistribution estimates of Zhang type, and bounded gaps between primes (2014) (23)
On the universality of potential well dynamics (2017) (23)
Density Hales-Jewett and Moser Numbers (2010) (23)
New bounds for Szemeredi's theorem, Ia: Progressions of length 4 in finite field geometries revisited (2012) (23)
Solving mathematical problems - a personal perspective (2006) (23)
Arithmetic progressions and the primes (2006) (22)
A physical space approach to wave equation bilinear estimates (2001) (22)
A REMARK ON PARTIAL SUMS INVOLVING THE MÖBIUS FUNCTION (2009) (22)
Searching for singularities in the Navier–Stokes equations (2019) (22)
Random matrices: Localization of the eigenvalues and the necessity of four moments (2010) (22)
A REMARK ON PRIMALITY TESTING AND DECIMAL EXPANSIONS (2008) (21)
Weakly turbulent solutions for the cubic defocusing nonlinear Schr\"odinger equation (2008) (21)
A COUNTEREXAMPLE TO AN ENDPOINT BILINEAR STRICHARTZ INEQUALITY (2006) (21)
Yet Another Proof Of Szemerédi's Theorem (2010) (21)
A global compact attractor for high-dimensional defocusing non-linear Schr (2008) (20)
On the sign patterns of entrywise positivity preservers in fixed dimension (2017) (20)
The structure of correlations of multiplicative functions at almost all scales, with applications to the Chowla and Elliott conjectures (2018) (20)
Small Doubling in Groups (2013) (20)
Some remarks on the lonely runner conjecture (2017) (19)
An X-ray transform estimate in "Rn" (2001) (19)
Szemerédi's Theorem (2007) (19)
A multi-dimensional Szemerédi theorem for the primes via a correspondence principle (2013) (19)
WAVE MAPS (2007) (18)
The Lang-Weil bound (2015) (18)
Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrodinger equation (2010) (18)
Obstructions to uniformity, and arithmetic patterns in the primes (2005) (18)
A P ] 2 8 M ay 2 00 8 A GLOBAL COMPACT ATTRACTOR FOR HIGH-DIMENSIONAL DEFOCUSING NON-LINEAR SCHRÖDINGER EQUATIONS WITH POTENTIAL (2008) (17)
Chapter 11. Longtime Decay Estimates for the Schrödinger Equation on Manifolds (2007) (17)
A quantitative formulation of the global regularity problem for the periodic Navier-Stokes equation (2007) (17)
Random matrices: The Four Moment Theorem for Wigner ensembles (2011) (17)
Uniform estimates on paraproducts (2001) (17)
Cancellation for the multilinear Hilbert transform (2015) (17)
BOUNDS FOR A MAXIMAL DYADIC SUM OPERATOR (2002) (17)
AN INVERSE THEOREM FOR THE BILINEAR L 2 STRICHARTZ ESTIMATE FOR THE WAVE EQUATION (2009) (16)
Sumfree sets in groups: a survey (2016) (16)
FINITE TIME BLOWUP FOR A SUPERCRITICAL DEFOCUSING NONLINEAR WAVE SYSTEM (2016) (16)
REMARK ON THE PAPER “SHARP WELL-POSEDNESS AND ILL-POSEDNESS RESULTS FOR A QUADRATIC NON-LINEAR SCHRÖDINGER EQUATION” BY I. BEJENARU AND T. TAO (2010) (15)
POLYNOMIAL PATTERNS IN THE PRIMES (2016) (15)
Fourier uniformity of bounded multiplicative functions in short intervals on average (2018) (15)
Pointwise ergodic theorems for non-conventional bilinear polynomial averages (2020) (15)
UNIVERSALITY OF ESDS AND THE CIRCULAR LAW (2009) (15)
Long-time decay estimates for the Schr\"odinger equation on manifolds (2004) (14)
A Discrete Model for the Bi-Carleson Operator (2002) (14)
An Inverse Theorem for an Inequality of Kneser (2017) (14)
Foundational aspects of uncountable measure theory: Gelfand duality, Riesz representation, canonical models, and canonical disintegration (2020) (13)
E pluribus unum: From Complexity, Universality (2012) (13)
New equidistribution estimates of Zhang type (2014) (13)
Pointwise convergence of lacunary spherical means (2002) (13)
Some light on Littlewood–Paley theory (2000) (12)
Random matrices: Universality of eigenvectors (2011) (12)
Multi-linear multipliers associated to simplexes of arbitrary length (2007) (12)
An x-ray estimate in $R^n$ (1999) (12)
A Bound on Partitioning Clusters (2017) (12)
New bounds for Szemer\'edi's theorem, III: A polylogarithmic bound for $r_4(N)$ (2017) (12)
Polynomial upper bounds for the instability of the Nonlinear Schr (2002) (12)
A note on approximate subgroups of GL_n(C) and uniformly nonamenable groups (2011) (11)
An uncountable Mackey–Zimmer theorem (2020) (11)
An uncountable Moore–Schmidt theorem (2019) (11)
Global Existence and Scattering for Rough Solutions of a Nonlinear Schr¨odinger Equation on R (2003) (11)
Sum-avoiding sets in groups (2016) (11)
Nonlinear Fourier Analysis (2012) (11)
A SHORT PROOF OF THE COIFMAN-MEYER MULTILINEAR THEOREM (10)
Large prime gaps and probabilistic models (2019) (10)
Exploring the toolkit of Jean Bourgain (2020) (10)
Sendov’s conjecture for sufficiently-high-degree polynomials (2020) (10)
The structure of locally compact groups (2014) (10)
Noncommutative sets of small doubling (2011) (10)
Effective approximation of heat flow evolution of the Riemann $$\xi $$ function, and a new upper bound for the de Bruijn–Newman constant (2019) (10)
Zarankiewicz’s problem for semilinear hypergraphs (2020) (9)
THE IONESCU–WAINGER MULTIPLIER THEOREM AND THE ADELES (2020) (9)
Random Matrices: a General Approach for the Least Singular Value Problem (9)
FAILURE OF THE $L^{1}$ POINTWISE AND MAXIMAL ERGODIC THEOREMS FOR THE FREE GROUP (2015) (9)
Narrow Progressions in the Primes (2014) (9)
THE SATURATION CONJECTURE (AFTER A. KNUTSON (2006) (9)
Quantitative bounds for Gowers uniformity of the M\"obius and von Mangoldt functions (2021) (9)
A PHYSICAL SPACE PROOF OF THE BILINEAR STRICHARTZ AND LOCAL SMOOTHING ESTIMATES FOR THE SCHRÖDINGER EQUATION (2010) (9)
MIXING FOR PROGRESSIONS IN NONABELIAN GROUPS (2012) (8)
SHARP BOUNDS FOR MULTILINEAR CURVED KAKEYA, RESTRICTION AND OSCILLATORY INTEGRAL ESTIMATES AWAY FROM THE ENDPOINT (2019) (8)
The effective potential of an M-matrix (2021) (8)
On the quantitative distribution of polynomial nilsequences — erratum (2013) (8)
Arithmetic progressions and the primes - El Escorial lectures (2004) (8)
The Elliott-Halberstam conjecture implies the Vinogradov least quadratic nonresidue conjecture (2014) (8)
The inverse theorem for the $U^3$ Gowers uniformity norm on arbitrary finite abelian groups: Fourier-analytic and ergodic approaches (2021) (7)
Global existence and uniqueness results for weak solutions of the focusing mass-critical non-linear Schr\"odinger equation (2008) (7)
A variation norm Carleson theorem (2010) (7)
Erratum to “The primes contain arbitrarily long polynomial progressions” (2013) (7)
Additive energy of regular measures in one and higher dimensions, and the fractal uncertainty principle (2020) (7)
A counterexample to the periodic tiling conjecture (2022) (7)
DIFFERENTIAL FORMS AND INTEGRATION (2008) (6)
A P ] 2 7 Ja n 20 14 A ( CONCENTRATION-) COMPACT ATTRACTOR FOR HIGH-DIMENSIONAL NON-LINEAR SCHRÖDINGER EQUATIONS (2021) (6)
The probability that a random triple of dice is transitive (2022) (6)
Perfectly packing a square by squares of nearly harmonic sidelength (2022) (6)
Apiary views of the Berenstein-Zelevinsky polytope, and Klyachko's saturation conjecture (1998) (6)
A new bound on partial sum-sets and difference-sets, and applications to the Kakeya conjecture (1999) (5)
Erratum to: Variants of the Selberg sieve, and bounded intervals containing many primes (2015) (5)
Multiple recurrence and convergence results associated to $${\text{F}}_P^\omega $$-actions (2015) (5)
Higher uniformity of arithmetic functions in short intervals I. All intervals (2022) (5)
The structure of arbitrary Conze-Lesigne systems (2021) (5)
The honeycomb model of the Berenstein-Zelevinsky polytope I. Klyachko's saturation conjecture (1998) (5)
The high exponent limit p →∞ for the one-dimensional nonlinear wave equation (2009) (5)
Erratum to: Outliers in the spectrum of iid matrices with bounded rank perturbations (2010) (5)
VALUE PATTERNS OF MULTIPLICATIVE FUNCTIONS AND RELATED SEQUENCES (2019) (5)
J un 2 00 9 AN INVERSE THEOREM FOR THE UNIFORMITY SEMINORMS ASSOCIATED WITH THE ACTION OF F (2018) (5)
WELL-POSEDNESS AND SCATTERING FOR THE MASS-CRITICAL NONLINEAR SCHRÖDINGER EQUATION FOR RADIAL DATA IN HIGH DIMENSIONS (2008) (5)
The Walsh model for $M_2^*$ Carleson (2007) (5)
2016 MATRIX Annals (2018) (5)
Finite time blowup for a supercritical defocusing nonlinear Schrödinger system (2016) (5)
Undecidable Translational Tilings with Only Two Tiles, or One Nonabelian Tile (2021) (5)
Chains of large gaps between primes (2015) (4)
The Hardy–Littlewood–Chowla conjecture in the presence of a Siegel zero (2021) (4)
Finite time blowup for high dimensional nonlinear wave systems with bounded smooth nonlinearity (2016) (4)
Analysis and applications: The mathematical work of Elias Stein (2020) (4)
Homogeneous length functions on groups (2018) (4)
The nonlinear Schr (2005) (4)
POLYNOMIAL UPPER BOUNDS FOR THE ORBITAL INSTABILITY OF THE 1 D CUBIC NLS BELOW THE ENERGY (2002) (4)
Bochner-Riesz Summability for analytic functions on the m-complex unit sphere and for cylindrically symmetric functions on R^n-1 x R (2002) (4)
Least singular value, circular law, and Lindeberg exchange (2019) (4)
Embedding the Heisenberg group into a bounded-dimensional Euclidean space with optimal distortion (2018) (3)
On the bi-carleson operator I. The Walsh case (2002) (3)
A counterexample to the periodic tiling conjecture (announcement) (2022) (3)
The $T(b)$ theorem and its variants (2003) (3)
Commutators close to the identity (2018) (3)
LECTURE NOTES 4 FOR 247A (2015) (3)
Analysis I: Third Edition (2006) (3)
Title : An Inverse Theorem for the Uniformity Seminorms Associated with the Action of (2010) (3)
Long gaps in sieved sets (2018) (3)
LECTURE NOTES 8 FOR 247B (2015) (3)
Analysis II: Third Edition (2016) (3)
A SHARP BILINEAR RESTRICTION ESTIMATE FOR ELLIPTIC SURFACES (3)
LECTURE NOTES 6 FOR 247B (2015) (3)
2019-20 MATRIX Annals (2021) (3)
Ad Honorem Charles Fefferman (2017) (3)
BOUNDS FOR NORMAL DERIVATIVES OF DIRICHLET EIGENFUNCTIONS (2003) (2)
The Mobius and Nilsequences Conjecture (2008) (2)
AND REGULARIZING EFFECTS IN QUASILINEAR PDES (2006) (2)
2017 MATRIX Annals (2019) (2)
Global well-posedness of the Benjamin-Ono equation in H¹(R) (2003) (2)
Homogeneous length functions on groups (2018) (2)
The structure of translational tilings in $\mathbb{Z}^d$ (2020) (2)
Notes on symplectic non-squeezing of the KdV flow (2005) (2)
LECTURE NOTES 1 FOR 247A (2015) (2)
Correction to: Fourier uniformity of bounded multiplicative functions in short intervals on average (2019) (2)
Symplectic nonsqueezing of the KdV flow (2004) (2)
Measurable Tilings by Abelian Group Actions (2022) (1)
DENSITY HALES-JEWETT AND MOSER NUMBERS IN LOW DIMENSIONS (2009) (1)
The Jordan-Schur theorem (2014) (1)
Restriction and Kakeya Phenomena for Finite Field (1982) (1)
Polymath and Small Gaps Between Primes (2015) (1)
Sumfree sets in groups (2016) (1)
LECTURE NOTES 2 FOR 247A (2015) (1)
Additive Combinatorics: The Littlewood–Offord problem (2006) (1)
A ] 2 3 Ja n 20 01 Some connections between Falconer ’ s distance set conjecture , and sets of Furstenburg type Nets (2001) (1)
Remembering Jean Bourgain (1954–2018) (2021) (1)
Optimal Sine and Sawtooth Inequalities (2021) (1)
Multiple recurrence and convergence results associated to $\mathbb{F}_{p}^ω$-actions (2013) (1)
LECTURE NOTES 7 FOR 247B (2015) (1)
Several Variable Differential Calculus (2016) (1)
PUZZLES AND ( EQUIVARIANT ) (2003) (1)
Ado’s theorem (2014) (1)
Zero-Viscosity Limit of the Navier-Stokes Equations with the Navier Friction Boundary Condition (2018) (1)
Book Review: Combinatorics and random matrix theory; Dynamical approach to random matrix theory (2019) (1)
Erratum (2001) (1)
Polynomial bounds via nonstandard analysis (2014) (1)
Variants of the Selberg sieve, and bounded intervals containing many primes (2014) (1)
On the number of solutions to $\frac{4}{p}=\frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}$ (2011) (1)
A P ] 2 9 O ct 2 00 7 SHARP WELL-POSEDNESS AND ILL-POSEDNESS RESULTS FOR A QUADRATIC NON-LINEAR SCHRÖDINGER EQUATION (2022) (0)
A COUNTEREXAMPLE TO AN ENDPOINT BILINEAR (2006) (0)
Homogenization of iterated singular integrals with applications to random quasiconformal maps (2020) (0)
OF A DOUBLEROTOR DOUBLEROTOR DOUBLEROTOR MICRO FLYING ROBOT (2009) (0)
Information theory, relative versions of the hypergraph regularity and removal lemmas, the Szemer\'edi-Furstenberg-Katznelson theorem, and prime constellations in number fields (2005) (0)
C A ] 1 4 M ay 2 00 2 ENDPOINT MAPPING PROPERTIES OF SPHERICAL MAXIMAL OPERATORS (0)
The Averaging lemma and regularizing effect (2005) (0)
A ug 2 00 7 RANDOM MATRICES : THE CIRCULAR LAW (0)
IV.11 Harmonic Analysis (2010) (0)
Title A Finitary Version of Gromov ’ s Polynomial Growth Theorem Permalink (2010) (0)
Three regularity results in harmonic analysis (2000) (0)
Multiple recurrence and convergence results associated to $\mathbb{F}_{p}^{\omega}$-actions (2013) (0)
Lie groups, Lie algebras, and the Baker-Campbell-Hausdorff formula (2014) (0)
The Mathematics of Cathleen Synge Morawetz (2018) (0)
N T ] 4 J un 2 00 6 QUADRATIC UNIFORMITY OF THE MÖBIUS FUNCTION (2005) (0)
2 J an 2 02 0 CORRELATIONS OF THE VON MANGOLDT AND HIGHER DIVISOR FUNCTIONS II (2022) (0)
Additive Combinatorics: Sum set estimates (2006) (0)
Additive Combinatorics: Inverse sum set theorems (2006) (0)
III.29 Function Spaces (2010) (0)
Expansion in Cayley graphs, and Kazhdan’s property (T) (2015) (0)
1 Arithmetic progressions in primes I after (2006) (0)
THE THEORY OF NONLINEAR SCHRÖDINGER (2009) (0)
Seven days: 20–26 January 2012 (2012) (0)
DISCREPANCY THEOREMS AND REPRESENTING DIAGONAL MATRICES (2010) (0)
Elias M. Stein (1931–2018) (2021) (0)
Upper bounds for the k = 3 Moser problem in small dimensions (2009) (0)
Deterministic methods to find primes (2010) (0)
Book Review: Polynomial methods in combinatorics (2017) (0)
2 2 Se p 20 07 QUADRATIC UNIFORMITY OF THE MÖBIUS FUNCTION (2005) (0)
Robert Israel “Bob” Jewett (1937–2022) (2023) (0)
Limits of sequences (2016) (0)
Expander graphs: Basic theory (2015) (0)
Multiple Recurrence in Quasirandom Groups (2014) (0)
Haar measure, the Peter-Weyl theorem, and compact or abelian groups (2014) (0)
Continuous functions on metric spaces (2016) (0)
A remark on primality testing and the binary expansion (2008) (0)
Logic and foundations (2013) (0)
A variation norm Carleson theorem (2010) (0)
A P ] 2 0 O ct 2 00 4 SPHERICALLY AVERAGED ENDPOINT STRICHARTZ ESTIMATES FOR THE TWO-DIMENSIONAL SCHRÖDINGER EQUATION 1 (2022) (0)
An inverse theorem for the Kemperman inequality (2017) (0)
Fourier Transform (2009) (0)
Ju l 2 00 8 GLOBAL EXISTENCE AND UNIQUENESS RESULTS FOR WEAK SOLUTIONS OF THE FOCUSING MASS-CRITICAL NON-LINEAR SCHRÖDINGER EQUATION (0)
Models of ultra approximate groups (2014) (0)
The Hilbert-Smith conjecture (2014) (0)
Two notes on Lie groups (2014) (0)
2018 MATRIX Annals (2020) (0)
Continuous functions on R (2016) (0)
Notes on groups of Lie type (2015) (0)
The microscopic structure of approximate groups (2014) (0)
The Korteweg de Vries equation (2006) (0)
III.16 Differential Forms and Integration (2010) (0)
C A ] 1 3 D ec 1 99 9 SHARP LORENTZ SPACE ESTIMATES FOR ROUGH OPERATORS (2008) (0)
SYMPLECTIC NON-SQUEEZING OF THE KDV FLOW (2004) (0)
The spectral theorem and its converses for unbounded self-adjoint operators (2015) (0)
Cayley graphs the algebra of groups (2015) (0)
Construction of ground states (2006) (0)
A remark on circular means of Fourier transforms of measures (2000) (0)
BOOK REVIEWS (2006) (0)
Product theorems, pivot arguments, and the Larsen-Pink non-concentration inequality (2015) (0)
ORBITAL INSTABILITY BOUNDS FOR THE NON-LINEAR SCHR¨ODINGER EQUATION BELOW THE ENERGY NORM (2005) (0)
Building metrics on groups, and the Gleason-Yamabe theorem (2014) (0)
LECTURE NOTES 3 FOR 247A (2015) (0)
Lectures in additive prime number theory (2009) (0)
Applications of the structural theory of approximate groups (2014) (0)
Singmaster's conjecture in the interior of Pascal's triangle (2021) (0)
Additive Combinatorics: Additive geometry (2006) (0)
ON THE PERMANENT OF A RANDOM BERNOULLI MATRIX (2008) (0)
Constant coefficient linear dispersive equations (2006) (0)
En:primes in Arithmetic Progression#largest Known Primes in ap (2018) (0)
C A ] 1 4 M ay 2 00 2 POINTWISE CONVERGENCE OF LACUNARY SPHERICAL MEANS (2002) (0)
The Poincaré conjecture (2009) (0)
THE T (b) THEOREM AND ITS VARIANTS (2003) (0)
HARMONIC ANALYSIS (2007) (0)
Starting at the beginning: The natural numbers (2016) (0)
TERENCE TAO GLOBAL REGULARITY FOR A LOGARITHMICALLY SUPERCRITICAL HYPERDISSIPATIVE NAVIER–STOKES EQUATION (2010) (0)
An Invitation to Mathematics-ReadingSample (2016) (0)
Non-concentration in subgroups (2015) (0)
Integers and Rationals (2016) (0)
Additive Combinatorics: Prologue (2006) (0)
The Riemann Integral (2015) (0)
A variation norm Carleson theorem (2010) (0)
III.9 Compactness and Compactification (2010) (0)
LECTURE NOTES 10 FOR 247B (2015) (0)
ON ZHANG ’ S PRIME GAPS PAPER (2013) (0)
III.35 Hamiltonians (2010) (0)
The real numbers (2016) (0)
Additive Combinatorics: Incidence geometry (2006) (0)
Additive Combinatorics: Algebraic methods (2006) (0)
The high exponent limit $p \to \infty$ for the one-dimensional nonlinear wave equation (2009) (0)
Additive Combinatorics: Fourier-analytic methods (2006) (0)
Tools from harmonic analysis (2006) (0)
ENDPOINT STRICHARTZ ESTIMATESMARKUS KEEL (0)
LECTURE NOTES 9 FOR 247B (2015) (0)
The Balog-Szemerédi-Gowers lemma, and the Bourgain-Gamburd expansion machine (2015) (0)
LECTURE NOTES 5 FOR 247A (2015) (0)
Arbeitsgemeinschaft: Ergodic Theory and Combinatorial Number Theory (2012) (0)
III.27 The Fourier Transform (2010) (0)
On a problem by Arens, Goldberg, and Luxemburg (2002) (0)
Associativity of the Baker-Campbell-Hausdorff-Dynkin law (2014) (0)
C A ] 9 D ec 2 00 9 RANDOM MARTINGALES AND LOCALIZATION OF MAXIMAL INEQUALITIES (0)
Building Lie structure from representations and metrics (2014) (0)
Central extensions of Lie groups, and cocycle averaging (2014) (0)
Loeb measure and the triangle removal lemma (2014) (0)
Nilpotent groups and nilprogressions (2014) (0)
Additive Combinatorics: The probabilistic method (2006) (0)
Notes on Lie algebras (2015) (0)
Additive Combinatorics: Bibliography (2006) (0)
Sieving and expanders (2015) (0)
Tao, Terence - University of California, Los Angeles (2006) (0)
FUNCTION SPACES (2008) (0)
Energy-critical semilinear dispersive equations (2006) (0)
VARIETIES OF GENERAL TYPE WITH MANY VANISHING PLURIGENERA, AND OPTIMAL SINE AND SAWTOOTH INEQUALITIES (2021) (0)
Corrigendum: Long gaps in sieved sets (2023) (0)
Jean Bourgain, problem solver (2019) (0)
Differentiation of functions (2016) (0)
Semilinear dispersive equations (2006) (0)
Book Review: Concentration compactness for critical wave maps (2012) (0)
Book Reviews. (2020) (0)
Additive Combinatorics: Szemerédi' theorem for k = 3 (2006) (0)
Fe b 19 99 THE HONEYCOMB MODEL OF GL n ( C ) TENSOR PRODUCTS I : PROOF OF THE SATURATION (0)
The Peter-Weyl theorem and nonabelian Fourier analysis (2014) (0)
ENDPOINT STRICHARTZ ESTIMATES By MARKUS KEEL and TERENCE TAO (1998) (0)
III.83 The Schrödinger Equation (2010) (0)
III.18 Distributions (2010) (0)
1/3 Bounded gaps between primes Download (2014) (0)
L2 Bounds for Normal Derivatives of Dirichlet Eigenfunctions (2003) (0)
Simply-laced isomonodromy systems . On the functions counting walks with small steps in the quarter plane . The structure of approximate groups . On stably free modules over affine algebras . Perfectoid spaces (2012) (0)
Clay Research Conference (2007) (0)
Additive Combinatorics: Long arithmetic progressions in sum sets (2006) (0)
A variation norm Carleson theorem (2010) (0)

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