#932

Most Influential Person

Australian-American mathematician

Tao is arguably the greatest living mathematician, and has been called the greatest mathematician of his generation. Born in South Australia, Tao was a child prodigy, the youngest person ever to win a medal in the International Mathematical Olympiad—he was ten. He has since won the Field Medal, the “Nobel Prize” for mathematicians. Terence Tao holds the James and Carol Collins Chair in Mathematics at the University of California at Los Angeles (UCLA).

At the age of 14, Tao attended the Research Science Institute, a summer seminar for talented high school students hosted by the Massachusetts Institute of Technology (MIT). At the age of 16, he received his bachelor’s and master’s degrees in mathematics at Princeton University. He received his Ph.D. from Princeton at age 20. He joined UCLA at the age of 24 and became the youngest person ever appointed to full professor by the university.

Tao’s focus is on partial differential equations, a nonlinear area of calculus, or the mathematics of change. Those who know him are quick to point out that he has an impressive grasp of seemingly all of mathematics—a rare feat, particularly today in an age of specialization. He has also done important work in fields as diverse as probability theory to number theory. As fellow mathematician Timothy Gowers put it when reviewing one of Tao’s books, *“it is not easy to find gaps in Tao’s knowledge, and if you do then you may well find that the gaps have been filled a year later.”*

Tao has won numerous awards, including but not limited to the Field Medal (referenced above), in 2006 a MacArthur Award (the “genius” award), Fellow of the Royal Society (2007), and in 2009 he was inducted into the American Academy of Arts and Sciences.

**Featured in Top Influential Mathematicians Today**

According to Wikipedia, Terence "Terry" Chi-Shen Tao is an Australian-American 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.

- Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information (2006) (14231)
- Stable signal recovery from incomplete and inaccurate measurements (2005) (6703)
- Decoding by linear programming (2005) (6568)
- Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies? (2006) (6385)
- The Dantzig selector: Statistical estimation when P is much larger than n (2007) (3241)
- The Power of Convex Relaxation: Near-Optimal Matrix Completion (2010) (1837)
- Nonlinear dispersive equations : local and global analysis (2006) (1231)
- Additive combinatorics (2007) (838)
- Topics in Random Matrix Theory (2012) (828)
- The primes contain arbitrarily long arithmetic progressions (2004) (805)
- A sum-product estimate in finite fields, and applications (2003) (454)
- Sharp global well-posedness for KdV and modified KdV on ℝ and (2003) (405)
- The honeycomb model of _{}(ℂ) tensor products I: Proof of the saturation conjecture (1999) (390)
- Random matrices: Universality of local eigenvalue statistics (2009) (357)
- Random matrices: Universality of ESDs and the circular law (2008) (350)
- Linear equations in primes (2006) (348)
- Global well-posedness and scattering for the energy-critical nonlinear Schr\"odinger equation in R^3 (2004) (345)
- Sharp Global well-posedness for KdV and modified KdV on $\R$ and $\T$ (2001) (308)
- Multilinear weighted convolution of L2 functions, and applications to nonlinear dispersive equations (2000) (285)
- Fuglede's conjecture is false in 5 and higher dimensions (2003) (283)
- The honeycomb model of GL(n) tensor products I: proof of the saturation conjecture (1998) (282)
- A sharp bilinear restriction estimate for paraboloids (2002) (245)
- On the multilinear restriction and Kakeya conjectures (2005) (240)
- The honeycomb model of _{}(ℂ) tensor products II: Puzzles determine facets of the Littlewood-Richardson cone (2001) (234)
- A bilinear approach to the restriction and Kakeya conjectures (1998) (226)
- RANDOM MATRICES: THE CIRCULAR LAW (2007) (222)
- Random Matrices: Universality of Local Eigenvalue Statistics up to the Edge (2010) (212)
- The Brascamp–Lieb Inequalities: Finiteness, Structure and Extremals (2005) (211)
- Almost conservation laws and global rough solutions to a Nonlinear Schr (2002) (210)
- The cubic nonlinear Schr\"odinger equation in two dimensions with radial data (2007) (204)
- The Nonlinear Schrödinger Equation with Combined Power-Type Nonlinearities (2005) (203)
- Puzzles and (equivariant) cohomology of Grassmannians (2001) (202)
- Product set estimates for non-commutative groups (2008) (202)
- An uncertainty principle for cyclic groups of prime order (2003) (194)
- Norm convergence of multiple ergodic averages for commuting transformations (2008) (191)
- Global Regularity of Wave Maps¶II. Small Energy in Two Dimensions (2001) (187)
- Ill-posedness for nonlinear Schrodinger and wave equations (2003) (186)
- On the singularity probability of random Bernoulli matrices (2005) (185)
- A variant of the hypergraph removal lemma (2006) (184)
- An inverse theorem for the Gowers U^{s+1}[N]-norm (2010) (183)
- Approximate Subgroups of Linear Groups (2010) (181)
- The quantitative behaviour of polynomial orbits on nilmanifolds (2007) (180)
- GLOBAL EXISTENCE AND SCATTERING FOR ROUGH SOLUTIONS OF A NONLINEAR SCHR ¨ ODINGER EQUATION ON R 3 (2003) (175)
- Multi-linear operators given by singular multipliers (1999) (174)
- Multilinear estimates for periodic KdV equations, and applications (2001) (173)
- GLOBAL WELL-POSEDNESS OF THE BENJAMIN–ONO EQUATION IN H1(R) (2004) (170)
- AN INVERSE THEOREM FOR THE GOWERS $U^3(G)$ NORM (2008) (170)
- Honeycombs and sums of Hermitian matrices (2000) (166)
- A bilinear approach to cone multipliers I. Restriction estimates (2000) (163)
- The structure of approximate groups (2011) (163)
- A Refined Global Well-Posedness Result for Schrödinger Equations with Derivative (2002) (162)
- Error correction via linear programming (2005) (159)
- Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation (2010) (158)
- AN INVERSE THEOREM FOR THE GOWERS U4-NORM (2010) (155)
- Finite time blowup for an averaged three-dimensional Navier-Stokes equation (2014) (153)
- On random ±1 matrices: Singularity and determinant (2006) (152)
- Global Well-Posedness for Schrödinger Equations with Derivative (2001) (149)
- Error correction via linear programming (2005) (147)
- Inverse Littlewood-Offord theorems and the condition number of random discrete matrices (2005) (144)
- Global well-posedness and scattering for the defocusing mass-critical nonlinear Schrödinger equation for radial data in high dimensions (2007) (144)
- An Incidence Theorem in Higher Dimensions (2012) (143)
- Minimal-mass blowup solutions of the mass-critical NLS (2006) (142)
- The primes contain arbitrarily long polynomial progressions (2006) (139)
- Random Matrices: the Distribution of the Smallest Singular Values (2009) (139)
- Bi-parameter paraproducts (2003) (138)
- The Bochner-Riesz conjecture implies the restriction conjecture (1999) (133)
- Global well-posedness and scattering for the higher-dimensional energy-critical non-linear Schrodinger equation for radial data (2004) (132)
- The Mobius function is strongly orthogonal to nilsequences (2008) (131)
- STABILITY OF ENERGY-CRITICAL NONLINEAR SCHR¨ ODINGER EQUATIONS IN HIGH DIMENSIONS (2005) (128)
- Some Recent Progress on the Restriction Conjecture (2004) (126)
- Global regularity of wave maps, I: small critical Sobolev norm in high dimension (2000) (125)
- The distribution of polynomials over finite fields, with applications to the Gowers norms (2009) (125)
- A bilinear approach to cone multipliers II. Applications (2000) (117)
- Sharp well-posedness and ill-posedness results for a quadratic non-linear Schr (2005) (117)
- Variants of the Selberg sieve, and bounded intervals containing many primes (2014) (116)
- Global regularity for a logarithmically supercritical hyperdissipative Navier-Stokes equation (2009) (115)
- Restriction and Kakeya phenomena for finite fields (2002) (115)
- From the Littlewood-Offord problem to the Circular Law: universality of the spectral distribution of random matrices (2008) (114)
- Random covariance matrices: Universality of local statistics of eigenvalues (2012) (114)
- Expansion in finite simple groups of Lie type (2013) (111)
- Rejoinder: The Dantzig selector: Statistical estimation when $p$ is much larger than $n$ (2007) (110)
- A new proof of the density Hales-Jewett theorem (2009) (108)
- Outliers in the spectrum of iid matrices with bounded rank perturbations (2010) (108)
- Random matrices: Universality of local spectral statistics of non-Hermitian matrices (2015) (108)
- Spherically averaged endpoint Strichartz estimates for the two-dimensional Schr (1998) (107)
- An averaged form of Chowla's conjecture (2015) (107)
- Bulk universality for Wigner hermitian matrices with subexponential decay (2009) (107)
- Higher Order Fourier Analysis (2012) (107)
- From rotating needles to stability of waves; emerging connections between combinatorics, analysis and PDE (2000) (106)
- An inverse theorem for the Gowers U^{s+1}[N]-norm (announcement) (2010) (105)
- Why are solitons stable (2008) (105)
- Szemerédi's regularity lemma revisited (2006) (103)
- L p IMPROVING BOUNDS FOR AVERAGES ALONG CURVES (2001) (102)
- On Sets Defining Few Ordinary Lines (2013) (99)
- Some Connections between Falconer's Distance Set Conjecture and Sets of Furstenburg Type (2001) (98)
- A Quantitative Ergodic Theory Proof of Szemerédi's Theorem (2006) (98)
- Random symmetric matrices are almost surely nonsingular (2005) (98)
- Finite bounds for Hölder-Brascamp-Lieb multilinear inequalities (2005) (96)
- Global well-posedness for KdV in Sobolev spaces of negative index (2001) (94)
- Local and global well-posedness of wave maps on $\R^{1+1}$ for rough data (1998) (94)
- The Mobius function is strongly orthogonal to nilsequences (2012) (93)
- Multi-parameter paraproducts (2004) (93)
- The Power of Convex Relaxation (2010) (92)
- The Fuglede spectral conjecture holds for convex planar domains (2003) (90)
- Structure and randomness (2008) (89)
- Testability and repair of hereditary hypergraph properties (2010) (88)
- The inverse conjecture for the Gowers norm over finite fields via the correspondence principle (2010) (88)
- Smooth analysis of the condition number and the least singular value (2010) (88)
- Carleson measures, trees, extrapolation, and T(b) theorems (2001) (87)
- Additive Combinatorics: Contents (2006) (86)
- Random matrices: Universal properties of eigenvectors (2011) (86)
- An Arithmetic Regularity Lemma, An Associated Counting Lemma, and Applications (2010) (85)
- Hilbert's Fifth Problem and Related Topics (2014) (85)
- THE LOGARITHMICALLY AVERAGED CHOWLA AND ELLIOTT CONJECTURES FOR TWO-POINT CORRELATIONS (2016) (82)
- The dichotomy between structure and randomness, arithmetic progressions, and the primes (2005) (81)
- On the asymptotic behavior of large radial data for a focusing non-linear Schr\ (2003) (81)
- Endpoint bilinear restriction theorems for the cone, and some sharp null form estimates (1999) (79)
- A singularity removal theorem for Yang-Mills fields in higher dimensions (2002) (78)
- QUADRATIC UNIFORMITY OF THE MOBIUS FUNCTION (2006) (77)
- Local Universality of Zeroes of Random Polynomials (2013) (77)
- A Finitary Version of Gromov’s Polynomial Growth Theorem (2009) (76)
- The Inverse Conjecture for the Gowers Norm over Finite Fields in Low Characteristic (2011) (76)
- A variation norm Carleson theorem (2009) (72)
- Random matrices: The Universality phenomenon for Wigner ensembles (2012) (72)
- New bounds for Kakeya problems (2001) (71)
- Sumset and Inverse Sumset Theory for Shannon Entropy (2010) (70)
- Global regularity for a logarithmically supercritical defocusing nonlinear wave equation for spherically symmetric data (2006) (69)
- An improved bound on the Minkowski dimension of Besicovitch sets in $\mathbb{R}^3$ (2000) (69)
- Effective Limiting Absorption Principles, and Applications (2011) (68)
- Scattering for the quartic generalised Korteweg–de Vries equation (2006) (67)
- GLOBAL WELL-POSEDNESS FOR SCHR ¨ ODINGER EQUATIONS WITH DERIVATIVE ∗ (2001) (67)
- Lp estimates for the biest II. The Fourier case (2001) (64)
- Operator splitting for the KdV equation (2011) (64)
- A correspondence principle between (hyper)graph theory and probability theory, and the (hyper)graph removal lemma (2006) (63)
- Restriction theory of the Selberg sieve, with applications (2004) (63)
- BOUNDS ON ARITHMETIC PROJECTIONS, AND APPLICATIONS TO THE KAKEYA CONJECTURE (1999) (62)
- Random matrices have simple spectrum (2017) (62)
- A Positive Proof of the Littlewood-Richardson Rule using the Octahedron Recurrence (2004) (60)
- A pseudoconformal compactification of the nonlinear Schrodinger equation and applications (2006) (59)
- What is good mathematics (2007) (59)
- Freiman's theorem for solvable groups (2010) (58)
- The Gaussian primes contain arbitrarily shaped constellations (2005) (58)
- A (concentration-)compact attractor for high-dimensional non-linear Schr\ (2006) (58)
- The sum-product phenomenon in arbitrary rings (2009) (58)
- Global regularity of wave maps III. Large energy from $\R^{1+2}$ to hyperbolic spaces (2008) (58)
- Algebraic combinatorial geometry: the polynomial method in arithmetic combinatorics, incidence combinatorics, and number theory (2013) (58)
- A priori bounds and weak solutions for the nonlinear Schr (2006) (57)
- Upper and lower bounds for normal derivatives of Dirichlet eigenfunctions (2002) (57)
- Velocity averaging, kinetic formulations, and regularizing effects in quasi‐linear PDEs (2007) (56)
- The condition number of a randomly perturbed matrix (2007) (56)
- An Inverse Theorem for the Uniformity Seminorms Associated with the Action of $${{\mathbb {F}^{\infty}_{p}}}$$ (2009) (55)
- A Carleson type theorem for a Cantor group model of the scattering transform (2003) (53)
- Long gaps between primes (2014) (53)
- A central limit theorem for the determinant of a Wigner matrix (2011) (53)
- Spacetime bounds for the energy-critical nonlinear wave equation in three spatial dimensions (2006) (52)
- Recent progress on the Kakeya conjecture (2000) (52)
- Global Regularity for the Maxwell-Klein-Gordon Equation with Small Critical Sobolev Norm in High Dimensions (2003) (51)
- New equidistribution estimates of Zhang type (2014) (50)
- THE WEAK-TYPE ENDPOINT BOCHNER-RIESZ CONJECTURE AND RELATED TOPICS (1998) (50)
- Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrodinger equation (2010) (50)
- Eigenvectors from eigenvalues: A survey of a basic identity in linear algebra (2019) (50)
- The Kakeya set and maximal conjectures for algebraic varieties over finite fields (2009) (50)
- Random Martingales and localization of maximal inequalities (2009) (50)
- A counterexample to a multilinear endpoint question of Christ and Kiselev (2001) (49)
- Local well-posedness of the Yang-Mills equation in the temporal gauge below the energy norm (2000) (49)
- Resonant decompositions and the $I$-method for the cubic nonlinear Schrödinger equation on $\mathbb{R}^2$ (2008) (48)
- Expanding polynomials over finite fields of large characteristic, and a regularity lemma for definable sets (2015) (47)
- A Strichartz Inequality for the Schrödinger Equation on Nontrapping Asymptotically Conic Manifolds (2003) (47)
- Global Existence and Scattering for Rough Solutions of a Nonlinear Schr¨odinger Equation on R (2003) (47)
- The structure of logarithmically averaged correlations of multiplicative functions, with applications to the Chowla and Elliott conjectures (2019) (46)
- Low-regularity global solutions to nonlinear dispersive equations (2002) (46)
- Recent progress on the restriction conjecture (2003) (46)
- Geometric renormalization of large energy wave maps (2004) (46)
- Freiman's Theorem in Finite Fields via Extremal Set Theory (2009) (46)
- Breaking the duality in the return times theorem (2006) (45)
- A sharp inverse Littlewood-Offord theorem (2010) (45)
- Maximal multilinear operators (2005) (45)
- Structure and Randomness in Combinatorics (2007) (45)
- Random matrices: tail bounds for gaps between eigenvalues (2015) (44)
- On multilinear oscillatory integrals, nonsingular and singular (2003) (44)
- Large gaps between consecutive prime numbers (2014) (44)
- 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) (43)
- On the Almost Everywhere Convergence of Wavelet Summation Methods (1996) (42)
- An improved bound on the Minkowski dimension of Besicovitch sets in R^3 (1999) (42)
- Localisation and compactness properties of the Navier-Stokes global regularity problem (2011) (41)
- Equivalence of the Logarithmically Averaged Chowla and Sarnak Conjectures (2017) (41)
- On the maximal Bochner-Riesz conjecture in the plane for p < 2 (2002) (41)
- New bounds for Szemeredi's theorem, II: A new bound for r_4(N) (2006) (40)
- Global well-posedness of the Benjamin-Ono equation in H^1(R) (2003) (40)
- COUNTING THE NUMBER OF SOLUTIONS TO THE ERDŐS–STRAUS EQUATION ON UNIT FRACTIONS (2013) (39)
- The Wigner-Dyson-Mehta Bulk Universality Conjecture for Wigner Matrices (2011) (39)
- Random matrices: Universality of eigenvectors (2011) (39)
- The weak-type (1,1) of L \log L homogeneous convolution operators (1999) (39)
- Global regularity of wave maps IV. Absence of stationary or self-similar solutions in the energy class (2008) (39)
- Poincare's Legacies: Pages from Year Two of a Mathematical Blog (2009) (39)
- Sharp Lorentz space estimates for rough operators (1999) (37)
- Nonconventional ergodic averages and multiple recurrence for von Neumann dynamical systems (2009) (37)
- An Epsilon of Room, II: pages from year three of a mathematical blog (2011) (36)
- Global well-posedness of the Maxwell-Klein-Gordon equation below the energy norm (2009) (36)
- Uniform estimates on multi-linear operators with modulation symmetry (2001) (36)
- Global regularity of wave maps VII. Control of delocalised or dispersed solutions (2009) (35)
- Lp estimates for the biest I. The Walsh case (2001) (35)
- Suzuki groups as expanders (2010) (35)
- Insights From SMPY's Greatest Former Child Prodigies: Drs. Terence (“Terry”) Tao and Lenhard (“Lenny”) Ng Reflect on Their Talent Development (2006) (35)
- Random matrices: Sharp concentration of eigenvalues (2012) (35)
- Endpoint multiplier theorems of Marcinkiewicz type (2000) (35)
- Every odd number greater than 1 is the sum of at most five primes (2014) (35)
- COMPRESSIONS, CONVEX GEOMETRY AND THE FREIMAN–BILU THEOREM (2005) (35)
- ENDPOINT MAPPING PROPERTIES OF SPHERICAL MAXIMAL OPERATORS (2003) (34)
- Polynomial upper bounds for the orbital instability of the 1D cubic NLS below the energy norm (2002) (34)
- Classification of almost quarter-pinched manifolds (2008) (34)
- Multilinear interpolation between adjoint operators (2001) (34)
- Almost all orbits of the Collatz map attain almost bounded values (2019) (34)
- Instability of the periodic nonlinear Schrodinger equation (2003) (33)
- A VARIATION (2009) (33)
- New bounds for Szemerédi's theorem, I: progressions of length 4 in finite field geometries (2009) (33)
- Large values of the Gowers-Host-Kra seminorms (2010) (32)
- The weak-type (1,1) of Fourier integral operators of order –(n–1)/2 (2004) (32)
- John-type theorems for generalized arithmetic progressions and iterated sumsets (2006) (32)
- Singular maximal functions and Radon transforms near L1 (2002) (32)
- Global regularity of wave maps VI. Abstract theory of minimal-energy blowup solutions (2009) (32)
- Symplectic nonsqueezing of the korteweg-de vries flow (2005) (32)
- Strongly dense free subgroups of semisimple algebraic groups (2010) (32)
- Deterministic methods to find primes (2012) (31)
- A quantitative version of the Besicovitch projection theorem via multiscale analysis (2009) (31)
- An equivalence between inverse sumset theorems and inverse conjectures for the U3 norm (2010) (30)
- New equidistribution estimates of Zhang type (2014) (30)
- Resonant decompositions and the I-method for cubic nonlinear Schrodinger on R^2 (2007) (30)
- Real analysis : pages from year three of a mathematical blog (2010) (30)
- Lp bounds for a maximal dyadic sum operator (2002) (30)
- Multiple Recurrence in Quasirandom Groups (2012) (29)
- Global well-posedness and scattering for the mass-critical nonlinear Schr\"odinger equation for radial data in high dimensions (2006) (29)
- Low regularity semi—linear wave equations 1 (1999) (28)
- SIGN PATTERNS OF THE LIOUVILLE AND MÖBIUS FUNCTIONS (2016) (28)
- The "bounded gaps between primes" Polymath project - a retrospective (2014) (28)
- An improved bound for the Minkowski dimension of Besicovitch sets in medium dimension (2000) (27)
- On the permanent of random Bernoulli matrices (2008) (27)
- Low regularity semi-linear wave equations (1997) (27)
- A variation norm Carleson theorem (2010) (27)
- Finite Time Blowup for Lagrangian Modifications of the Three-Dimensional Euler Equation (2016) (26)
- Inverse theorems for sets and measures of polynomial growth (2015) (26)
- THE SATURATION CONJECTURE (AFTER A. KNUTSON (2006) (26)
- Additive Combinatorics: Graph-theoretic methods (2006) (26)
- Quantitative bounds for critically bounded solutions to the Navier-Stokes equations (2019) (26)
- PERELMAN'S PROOF OF THE POINCAR´ E CONJECTURE: A NONLINEAR PDE PERSPECTIVE (2006) (26)
- Global regularity of wave maps V. Large data local wellposedness and perturbation theory in the energy class (2008) (26)
- The Littlewood-Offord problem in high dimensions and a conjecture of Frankl and Füredi (2012) (25)
- A nilpotent Freiman dimension lemma (2013) (25)
- A NOTE ON THE FREIMAN AND BALOG–SZEMERÉDI–GOWERS THEOREMS IN FINITE FIELDS (2009) (25)
- The bi-Carleson operator (2004) (25)
- Density Hales-Jewett and Moser Numbers (2010) (24)
- Weak-type endpoint bounds for Riesz means (1996) (24)
- Global behaviour of nonlinear dispersive and wave equations (2006) (24)
- THE DE BRUIJN–NEWMAN CONSTANT IS NON-NEGATIVE (2020) (24)
- Odd order cases of the logarithmically averaged Chowla conjecture (2017) (24)
- The Erdos discrepancy problem (2015) (23)
- Ill-posedness for one-dimensional wave maps at the critical regularity (1998) (23)
- Compactness and Contradiction (2013) (23)
- Almost Everywhere Behavior of General Wavelet Shrinkage Operators (2000) (23)
- A new bound for finite field besicovitch sets in four dimensions (2002) (22)
- Arithmetic progressions and the primes (2006) (22)
- Linear Approximate Groups (2010) (22)
- Weakly turbulent solutions for the cubic defocusing nonlinear Schr\"odinger equation (2008) (22)
- A Converse Extrapolation Theorem for Translation-Invariant Operators (1999) (22)
- The asymptotic distribution of a single eigenvalue gap of a Wigner matrix (2012) (22)
- Solving mathematical problems - a personal perspective (2006) (21)
- AN INTEGRATION APPROACH TO THE TOEPLITZ SQUARE PEG PROBLEM (2017) (21)
- On the universality of the incompressible Euler equation on compact manifolds (2017) (21)
- Structure and Randomness in the Prime Numbers (2011) (20)
- Poincare's Legacies, Part II: pages from year two of a mathematical blog (2009) (20)
- Obstructions to uniformity, and arithmetic patterns in the primes (2005) (20)
- A physical space approach to wave equation bilinear estimates (2001) (19)
- Asymptotic decay for a one-dimensional nonlinear wave equation (2010) (19)
- Random matrices: Localization of the eigenvalues and the necessity of four moments (2010) (19)
- Correlations of the von Mangoldt and higher divisor functions I. Long shift ranges (2018) (19)
- Two remarks on the generalised Korteweg de-Vries equation (2006) (19)
- New equidistribution estimates of Zhang type, and bounded gaps between primes (2014) (19)
- An X-ray transform estimate in "Rn" (2001) (18)
- Concatenation theorems for anti-Gowers-uniform functions and Host-Kra characteristic factors (2016) (18)
- Yet Another Proof Of Szemerédi's Theorem (2010) (18)
- A REMARK ON PARTIAL SUMS INVOLVING THE MÖBIUS FUNCTION (2010) (18)
- Scale-oblivious metric fragmentation and the nonlinear Dvoretzky theorem (2010) (18)
- Testability and repair of hereditary hypergraph properties (2010) (18)
- New bounds for Szemeredi's theorem, Ia: Progressions of length 4 in finite field geometries revisited (2012) (17)
- On the sign patterns of entrywise positivity preservers in fixed dimension (2021) (17)
- Works Title An Inverse Theorem for the Uniformity Seminorms Associated with the Action of (2010) (17)
- A COUNTEREXAMPLE TO AN ENDPOINT BILINEAR STRICHARTZ INEQUALITY (2006) (16)
- A REMARK ON PRIMALITY TESTING AND DECIMAL EXPANSIONS (2011) (16)
- A quantitative formulation of the global regularity problem for the periodic Navier-Stokes equation (2007) (16)
- A multi-dimensional Szemerédi theorem for the primes via a correspondence principle (2013) (15)
- Uniform estimates on paraproducts (2001) (15)
- Small Doubling in Groups (2013) (15)
- Searching for singularities in the Navier–Stokes equations (2019) (15)
- A global compact attractor for high-dimensional defocusing non-linear Schr (2008) (15)
- Cancellation for the multilinear Hilbert transform (2015) (15)
- Nonlinear Fourier Analysis (2012) (15)
- POLYNOMIAL PATTERNS IN THE PRIMES (2018) (14)
- The Lang-Weil bound (2015) (14)
- Long-time decay estimates for the Schr\"odinger equation on manifolds (2004) (14)
- On the universality of potential well dynamics (2017) (14)
- Erratum for "Upper and lower bounds for normal derivatives of Dirichlet eigenfunctions" (2010) (14)
- BOUNDS FOR A MAXIMAL DYADIC SUM OPERATOR (2002) (14)
- On random plus/minus 1 matrices: Singularity and determinant (2006) (14)
- FINITE TIME BLOWUP FOR A SUPERCRITICAL DEFOCUSING NONLINEAR WAVE SYSTEM (2016) (14)
- Szemerédi's Theorem (2007) (13)
- WELL-POSEDNESS AND SCATTERING FOR THE MASS-CRITICAL NONLINEAR SCHRÖDINGER EQUATION FOR RADIAL DATA IN HIGH DIMENSIONS (2008) (13)
- WAVE MAPS (2007) (13)
- A Discrete Model for the Bi-Carleson Operator (2002) (13)
- AN INVERSE THEOREM FOR THE BILINEAR L 2 STRICHARTZ ESTIMATE FOR THE WAVE EQUATION (2009) (13)
- Relative efficiencies of kernel and local likelihood density estimators (2002) (12)
- Random matrices: The Four Moment Theorem for Wigner ensembles (2011) (12)
- Polynomial upper bounds for the instability of the Nonlinear Schr (2002) (12)
- A sharp inverse Littlewood-Offord theorem (2010) (12)
- Correlations of the von Mangoldt and higher divisor functions II: divisor correlations in short ranges (2019) (12)
- Fourier uniformity of bounded multiplicative functions in short intervals on average (2019) (11)
- E pluribus unum: From Complexity, Universality (2012) (11)
- New bounds for Szemer\'edi's theorem, III: A polylogarithmic bound for $r_4(N)$ (2017) (11)
- An x-ray estimate in $R^n$ (1999) (11)
- Multi-linear multipliers associated to simplexes of arbitrary length (2007) (10)
- Pointwise convergence of lacunary spherical means (2002) (10)
- UNIVERSALITY OF ESDS AND THE CIRCULAR LAW (2009) (10)
- The structure of correlations of multiplicative functions at almost all scales, with applications to the Chowla and Elliott conjectures (2018) (10)
- On multilinear oscillatory integrals, nonsingular and singular (2005) (10)
- An Inverse Theorem for an Inequality of Kneser (2018) (10)
- Sum-avoiding sets in groups (2016) (10)
- Sumfree sets in groups: a survey (2016) (9)
- A note on approximate subgroups of GL_n(C) and uniformly nonamenable groups (2011) (9)
- Noncommutative sets of small doubling (2013) (9)
- Arithmetic progressions and the primes - El Escorial lectures (2004) (9)
- MIXING FOR PROGRESSIONS IN NONABELIAN GROUPS (2013) (9)
- Pointwise ergodic theorems for non-conventional bilinear polynomial averages (2020) (9)
- FAILURE OF THE $L^{1}$ POINTWISE AND MAXIMAL ERGODIC THEOREMS FOR THE FREE GROUP (2015) (9)
- Effective approximation of heat flow evolution of the Riemann $$\xi $$ function, and a new upper bound for the de Bruijn–Newman constant (2019) (8)
- The Elliott-Halberstam conjecture implies the Vinogradov least quadratic nonresidue conjecture (2014) (8)
- Some remarks on the lonely runner conjecture (2018) (8)
- On random pm 1 matrices: singularity and determinant (2005) (8)
- Random Matrices: a General Approach for the Least Singular Value Problem (7)
- On the quantitative distribution of polynomial nilsequences — erratum (2013) (7)
- Foundational aspects of uncountable measure theory: Gelfand duality, Riesz representation, canonical models, and canonical disintegration (2020) (7)
- Erratum to “The primes contain arbitrarily long polynomial progressions” (2013) (7)
- An uncountable Moore-Schmidt theorem (2019) (7)
- Global existence and uniqueness results for weak solutions of the focusing mass-critical non-linear Schr\"odinger equation (2008) (7)
- Narrow Progressions in the Primes (2015) (7)
- Chapter 11. Longtime Decay Estimates for the Schrödinger Equation on Manifolds (2007) (7)
- An uncountable Mackey-Zimmer theorem (2020) (7)
- SHARP BOUNDS FOR MULTILINEAR CURVED KAKEYA, RESTRICTION AND OSCILLATORY INTEGRAL ESTIMATES AWAY FROM THE ENDPOINT (2019) (6)
- A Bound on Partitioning Clusters (2017) (6)
- DIFFERENTIAL FORMS AND INTEGRATION (2008) (6)
- Large prime gaps and probabilistic models (2019) (6)
- A SHORT PROOF OF THE COIFMAN-MEYER MULTILINEAR THEOREM (6)
- Finite time blowup for a supercritical defocusing nonlinear Schrödinger system (2018) (6)
- The structure of locally compact groups (2014) (6)
- The honeycomb model of the Berenstein-Zelevinsky polytope I. Klyachko's saturation conjecture (1998) (5)
- Exploring the toolkit of Jean Bourgain (2020) (5)
- A PHYSICAL SPACE PROOF OF THE BILINEAR STRICHARTZ AND LOCAL SMOOTHING ESTIMATES FOR THE SCHRÖDINGER EQUATION (2010) (5)
- 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)
- The Walsh model for $M_2^*$ Carleson (2007) (5)
- THE IONESCU–WAINGER MULTIPLIER THEOREM AND THE ADELES (2020) (4)
- VALUE PATTERNS OF MULTIPLICATIVE FUNCTIONS AND RELATED SEQUENCES (2019) (4)
- The nonlinear Schr (2005) (4)
- POLYNOMIAL UPPER BOUNDS FOR THE ORBITAL INSTABILITY OF THE 1 D CUBIC NLS BELOW THE ENERGY (2002) (4)
- Restriction and Kakeya Phenomena for Finite Field (1982) (4)
- Apiary views of the Berenstein-Zelevinsky polytope, and Klyachko's saturation conjecture (1998) (4)
- 2016 MATRIX Annals (2018) (4)
- Erratum to: Outliers in the spectrum of iid matrices with bounded rank perturbations (2013) (4)
- Sendov's conjecture for sufficiently high degree polynomials. (2020) (4)
- The high exponent limit p →∞ for the one-dimensional nonlinear wave equation (2009) (4)
- J un 2 00 9 AN INVERSE THEOREM FOR THE UNIFORMITY SEMINORMS ASSOCIATED WITH THE ACTION OF F (2018) (4)
- Zarankiewicz’s problem for semilinear hypergraphs (2021) (4)
- Finite time blowup for high dimensional nonlinear wave systems with bounded smooth nonlinearity (2016) (4)
- The Hardy--Littlewood--Chowla conjecture in the presence of a Siegel zero (2021) (4)
- Additive energy of regular measures in one and higher dimensions, and the fractal uncertainty principle (2020) (3)
- Chains of large gaps between primes (2018) (3)
- Global well-posedness of the Benjamin-Ono equation in H¹(R) (2003) (3)
- Embedding the Heisenberg group into a bounded-dimensional Euclidean space with optimal distortion (2018) (3)
- Least singular value, circular law, and Lindeberg exchange (2019) (3)
- Multiple recurrence and convergence results associated to $${\text{F}}_P^\omega $$-actions (2015) (3)
- The $T(b)$ theorem and its variants (2003) (3)
- A SHARP BILINEAR RESTRICTION ESTIMATE FOR ELLIPTIC SURFACES (3)
- The Mobius and Nilsequences Conjecture (2008) (3)
- Ad Honorem Charles Fefferman (2017) (3)
- Bochner-Riesz Summability for analytic functions on the m-complex unit sphere and for cylindrically symmetric functions on R^n-1 x R (2002) (3)
- The inverse theorem for the $U^3$ Gowers uniformity norm on arbitrary finite abelian groups: Fourier-analytic and ergodic approaches (2021) (3)
- The structure of arbitrary Conze-Lesigne systems (2021) (3)
- THE PROBABILITY THAT A RANDOM TRIPLE OF DICE IS TRANSITIVE (2017) (3)
- A ] 2 3 Ja n 20 01 Some connections between Falconer ’ s distance set conjecture , and sets of Furstenburg type Nets (2001) (3)
- LECTURE NOTES 4 FOR 247A (2015) (3)
- Analysis I: Third Edition (2006) (2)
- Additive Combinatorics: The Littlewood–Offord problem (2006) (2)
- Commutators close to the identity (2018) (2)
- 2019-20 MATRIX Annals (2021) (2)
- Notes on symplectic non-squeezing of the KdV flow (2005) (2)
- AND REGULARIZING EFFECTS IN QUASILINEAR PDES (2006) (2)
- LECTURE NOTES 8 FOR 247B (2015) (2)
- Homogeneous length functions on groups (2018) (2)
- On the bi-carleson operator I. The Walsh case (2002) (2)
- Correction to: Fourier uniformity of bounded multiplicative functions in short intervals on average (2019) (2)
- Homogeneous length functions on groups (2018) (2)
- Symplectic nonsqueezing of the KdV flow (2004) (2)
- Ado’s theorem (2014) (1)
- Sumfree sets in groups (2016) (1)
- Polymath and Small Gaps Between Primes (2015) (1)
- PUZZLES AND ( EQUIVARIANT ) (2003) (1)
- 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) (1)
- The Jordan-Schur theorem (2014) (1)
- Polynomial bounds via nonstandard analysis (2014) (1)
- Szemerédi’s proof of Szemerédi’s theorem (2020) (1)
- LECTURE NOTES 2 FOR 247A (2015) (1)
- Remembering Jean Bourgain (1954–2018) (2021) (1)
- Quantitative bounds for Gowers uniformity of the M\"obius and von Mangoldt functions (2021) (1)
- DENSITY HALES-JEWETT AND MOSER NUMBERS IN LOW DIMENSIONS (2009) (1)
- LECTURE NOTES 6 FOR 247B (2015) (1)
- 1 Arithmetic progressions in primes I after (2006) (1)
- 1/3 Bounded gaps between primes Download (2014) (1)
- Multiple recurrence and convergence results associated to $\mathbb{F}_{p}^ω$-actions (2013) (1)
- Additive Combinatorics: Prologue (2006) (1)
- LECTURE NOTES 1 FOR 247A (2015) (1)
- Analysis and applications: The mathematical work of Elias Stein (2020) (1)
- Undecidable translational tilings with only two tiles, or one nonabelian tile (2021) (1)
- 2017 MATRIX Annals (2019) (1)
- The effective potential of an M-matrix (2021) (1)
- Analysis II: Third Edition (2016) (1)
- On the number of solutions to $\frac{4}{p}=\frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}$ (2011) (1)
- Erratum (2001) (1)
- Several Variable Differential Calculus (2016) (1)
- 2 2 Se p 20 07 QUADRATIC UNIFORMITY OF THE MÖBIUS FUNCTION (2005) (0)
- Expander graphs: Basic theory (2015) (0)
- Tools from harmonic analysis (2006) (0)
- Sieving and expanders (2015) (0)
- The Peter-Weyl theorem and nonabelian Fourier analysis (2014) (0)
- Cayley graphs the algebra of groups (2015) (0)
- HARMONIC ANALYSIS (2007) (0)
- III.83 The Schrödinger Equation (2010) (0)
- Continuous functions on metric spaces (2016) (0)
- LECTURE NOTES 5 FOR 247A (2015) (0)
- A variation norm Carleson theorem (2010) (0)
- Models of ultra approximate groups (2014) (0)
- A remark on circular means of Fourier transforms of measures (2000) (0)
- Building Lie structure from representations and metrics (2014) (0)
- The Hilbert-Smith conjecture (2014) (0)
- III.9 Compactness and Compactification (2010) (0)
- SYMPLECTIC NON-SQUEEZING OF THE KDV FLOW (2004) (0)
- Differentiation of functions (2016) (0)
- IV.11 Harmonic Analysis (2010) (0)
- N T ] 4 J un 2 00 6 QUADRATIC UNIFORMITY OF THE MÖBIUS FUNCTION (2005) (0)
- Logic and foundations (2013) (0)
- III.16 Differential Forms and Integration (2010) (0)
- THE T (b) THEOREM AND ITS VARIANTS (2003) (0)
- OF A DOUBLEROTOR DOUBLEROTOR DOUBLEROTOR MICRO FLYING ROBOT (2009) (0)
- Fe b 19 99 THE HONEYCOMB MODEL OF GL n ( C ) TENSOR PRODUCTS I : PROOF OF THE SATURATION (0)
- The spectral theorem and its converses for unbounded self-adjoint operators (2015) (0)
- Additive Combinatorics: Szemerédi' theorem for k = 3 (2006) (0)
- COMBINATORIAL AND ERGODIC APPROACHES TO SZEMERÉDI 3 where (0)
- A COUNTEREXAMPLE TO AN ENDPOINT BILINEAR (2006) (0)
- Clay Research Conference (2007) (0)
- C A ] 1 4 M ay 2 00 2 ENDPOINT MAPPING PROPERTIES OF SPHERICAL MAXIMAL OPERATORS (0)
- Book Review: Polynomial methods in combinatorics (2017) (0)
- THE THEORY OF NONLINEAR SCHRÖDINGER (2009) (0)
- Two notes on Lie groups (2014) (0)
- Homogenization of iterated singular integrals with applications to random quasiconformal maps. (2020) (0)
- Book Reviews. (2020) (0)
- Additive Combinatorics: Incidence geometry (2006) (0)
- DISCREPANCY THEOREMS AND REPRESENTING DIAGONAL MATRICES (2010) (0)
- Deterministic methods to find primes (2010) (0)
- Ju l 2 00 8 GLOBAL EXISTENCE AND UNIQUENESS RESULTS FOR WEAK SOLUTIONS OF THE FOCUSING MASS-CRITICAL NON-LINEAR SCHRÖDINGER EQUATION (0)
- Upper bounds for the k = 3 Moser problem in small dimensions (2009) (0)
- Multiple recurrence and convergence results associated to $\mathbb{F}_{p}^{\omega}$-actions (2013) (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)
- An inverse theorem for the Kemperman inequality (2017) (0)
- The Korteweg de Vries equation (2006) (0)
- Associativity of the Baker-Campbell-Hausdorff-Dynkin law (2014) (0)
- Implementation of Spectrum Sensing Techniques in Cognitive Radio Networks (2017) (0)
- Challenges in Geometry , Analysis and Computation : High Dimensional Synthesis (2012) (0)
- ON THE PERMANENT OF A RANDOM BERNOULLI MATRIX (2008) (0)
- Additive Combinatorics: Fourier-analytic methods (2006) (0)
- C A ] 1 3 D ec 1 99 9 SHARP LORENTZ SPACE ESTIMATES FOR ROUGH OPERATORS (2008) (0)
- Lie groups, Lie algebras, and the Baker-Campbell-Hausdorff formula (2014) (0)
- Additive Combinatorics: Sum set estimates (2006) (0)
- Additive Combinatorics: Long arithmetic progressions in sum sets (2006) (0)
- ENDPOINT STRICHARTZ ESTIMATES By MARKUS KEEL and TERENCE TAO (1998) (0)
- The Riemann Integral (2015) (0)
- Lectures in additive prime number theory (2009) (0)
- Central extensions of Lie groups, and cocycle averaging (2014) (0)
- Additive Combinatorics: Inverse sum set theorems (2006) (0)
- Loeb measure and the triangle removal lemma (2014) (0)
- Optimal sine and sawtooth inequalities (2021) (0)
- The Mathematics of Cathleen Synge Morawetz (2018) (0)
- Energy-critical semilinear dispersive equations (2006) (0)
- The structure of translational tilings in $\mathbb{Z}^d$ (2020) (0)
- Seven days: 20–26 January 2012 (2012) (0)
- A remark on primality testing and the binary expansion (2008) (0)
- LECTURE NOTES 7 FOR 247B (2015) (0)
- Book Reviews (1870) (0)
- Product theorems, pivot arguments, and the Larsen-Pink non-concentration inequality (2015) (0)
- Continuous functions on R (2016) (0)
- Starting at the beginning: The natural numbers (2016) (0)
- Notes on groups of Lie type (2015) (0)
- Notes on Lie algebras (2015) (0)
- BOOK REVIEWS (2006) (0)
- Integers and Rationals (2016) (0)
- BOUNDS FOR NORMAL DERIVATIVES OF DIRICHLET EIGENFUNCTIONS (2003) (0)
- LECTURE NOTES 3 FOR 247A (2015) (0)
- Constant coefficient linear dispersive equations (2006) (0)
- Title A Finitary Version of Gromov ’ s Polynomial Growth Theorem Permalink (2010) (0)
- Long gaps in sieved sets (2018) (0)
- Additive Combinatorics: Bibliography (2006) (0)
- The high exponent limit $p \to \infty$ for the one-dimensional nonlinear wave equation (2009) (0)
- Additive Combinatorics: Additive geometry (2006) (0)
- ENDPOINT STRICHARTZ ESTIMATESMARKUS KEEL (0)
- Building metrics on groups, and the Gleason-Yamabe theorem (2014) (0)
- Singmaster's conjecture in the interior of Pascal's triangle (2021) (0)
- Elias M. Stein (1931–2018) (2021) (0)
- Three regularity results in harmonic analysis (1996) (0)
- Non-concentration in subgroups (2015) (0)
- Limits of sequences (2016) (0)
- III.29 Function Spaces (2010) (0)
- Applications of the structural theory of approximate groups (2014) (0)
- Orbital Instability Bounds for the Non-linear Schr¨odinger Equation below the Energy Norm (2005) (0)
- Fourier Transform (2009) (0)
- Additive Combinatorics: Algebraic methods (2006) (0)
- III.18 Distributions (2010) (0)
- The real numbers (2016) (0)
- A ug 2 00 7 RANDOM MATRICES : THE CIRCULAR LAW (0)
- Additive Combinatorics: The probabilistic method (2006) (0)
- Haar measure, the Peter-Weyl theorem, and compact or abelian groups (2014) (0)
- En:primes in Arithmetic Progression#largest Known Primes in ap (2018) (0)
- Jean Bourgain, problem solver (2019) (0)
- Tao, Terence - University of California, Los Angeles (2006) (0)
- III.35 Hamiltonians (2010) (0)
- Nilpotent groups and nilprogressions (2014) (0)
- LECTURE NOTES 9 FOR 247B (2015) (0)
- ON ZHANG ’ S PRIME GAPS PAPER (2013) (0)
- The microscopic structure of approximate groups (2014) (0)
- TERENCE TAO GLOBAL REGULARITY FOR A LOGARITHMICALLY SUPERCRITICAL HYPERDISSIPATIVE NAVIER–STOKES EQUATION (2010) (0)
- 2018 MATRIX Annals (2020) (0)
- The Saturation Conjecture (after A. Knutson and T. Tao) (2008) (0)
- C A ] 9 D ec 2 00 9 RANDOM MARTINGALES AND LOCALIZATION OF MAXIMAL INEQUALITIES (0)
- C A ] 1 4 M ay 2 00 2 POINTWISE CONVERGENCE OF LACUNARY SPHERICAL MEANS (2002) (0)
- L2 Bounds for Normal Derivatives of Dirichlet Eigenfunctions (2003) (0)
- Expansion in Cayley graphs, and Kazhdan’s property (T) (2015) (0)
- On a problem by Arens, Goldberg, and Luxemburg (2002) (0)
- The Balog-Szemerédi-Gowers lemma, and the Bourgain-Gamburd expansion machine (2015) (0)
- Zero-Viscosity Limit of the Navier-Stokes Equations with the Navier Friction Boundary Condition (2020) (0)
- III.27 The Fourier Transform (2010) (0)
- The Averaging lemma and regularizing effect (2005) (0)
- LECTURE NOTES 10 FOR 247B (2015) (0)
- VARIETIES OF GENERAL TYPE WITH MANY VANISHING PLURIGENERA, AND OPTIMAL SINE AND SAWTOOTH INEQUALITIES (2021) (0)
- Book Review: Combinatorics and random matrix theory; Dynamical approach to random matrix theory (2019) (0)
- Construction of ground states (2006) (0)
- FUNCTION SPACES (2008) (0)
- The Poincaré conjecture (2009) (0)
- Book Review: Concentration compactness for critical wave maps (2012) (0)
- Arbeitsgemeinschaft: Ergodic Theory and Combinatorial Number Theory (2012) (0)
- Perfectly packing a square by squares of nearly harmonic sidelength (2022) (0)
- An Invitation to Mathematics-ReadingSample (2016) (0)
- A variation norm Carleson theorem (2010) (0)
- A variation norm Carleson theorem (2010) (0)
- Semilinear dispersive equations (2006) (0)

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