Vitae and Bibliography for Terence Tao

Last updated:  Oct 12, 2009

Short biography

Terence Tao was born in Adelaide, Australia in 1975. He has been a professor of mathematics at UCLA since 1999, having completed his PhD under Elias Stein at Princeton in 1996.  Tao's areas of research include harmonic analysis, PDE, combinatorics, and number theory.  He has received a number of awards, including the Salem Prize in 2000, the Bochner Prize in 2002, the Fields Medal and SASTRA Ramanujan Prize in 2006, the MacArthur Fellowship and Ostrowski Prize in 2007, and the Waterman Award in 2008.  Terence Tao also currently holds the James and Carol Collins chair in mathematics at UCLA, and is a Fellow of the Royal Society, the Australian Academy of Sciences (Corresponding Member), the National Academy of Sciences (Foreign member), and the American Academy of Arts and Sciences.

Personal

Date of Birth:	July 17, 1975
Birthplace:	Adelaide, Australia
Citizenship:	Australian & US
Marital status:	Married
Address	Dept. of Math. UCLA 405 Hilgard Ave 90095 LA, CA
Phone:	1-310-206-4844
Fax:	1-310-206-6673
E-mail:	tao@math.ucla.edu
WWW:	http://www.math.ucla.edu/~tao

Education

Degree	Date	Institution	Advisor	Subject	Thesis title
Ph. D.	Jun 1996	Princeton University	Elias Stein	Mathematics	Three regularity results in harmonic analysis
M. Sc.	Aug 1992	Flinders University	Garth Gaudry	Mathematics	Convolution operators generated by right-monogenic and harmonic kernels
B. Sc. (Hons)	Dec 1991	Flinders University	Garth Gaudry	Mathematics	N/A

Research interests

Primary:  Oscillatory integrals and Kakeya maximal functions Non-linear dispersive equations Multilinear operators (e.g. Bilinear Hilbert Transform) Arithmetic combinatorics and connections with number theory and ergodic theory Compressed sensing

Secondary:  Representation and symplectic theory of U(n); honeycombs Geometric PDE (e.g. Yang-Mills) General Relativity General harmonic analysis Inverse scattering, nonlinear Fourier transforms, and integrable systems for rough data

Experience

1992-1994	Flinders Medical Centre	Assistant Researcher
1993-1994	Princeton University	Assistant Researcher
1996-1998	UCLA	Hedrick Assistant Professor
Fall 1997	MSRI	Member
1999	UCLA	Acting Assistant Professor
1999	UNSW	Visiting Fellow
2000	UCLA	Assistant Professor
2001-2003	Clay Mathematical Institute	CMI Long-term Prize Fellow
2000-	UCLA	Full Professor
2000	UNSW	Visiting Professor
2001-2003	ANU	Honourary Professor

Awards and Honours

1986	International Mathematical Olympiad	Bronze Medal
1987	International Mathematical Olympiad	Silver Medal
1988	International Mathematical Olympiad	Gold Medal
1992	Flinders University	University Medal
1992-1995	Australian-American Fulbright Commission	Fulbright Postgraduate Scholar
1995	Sloan Foundation	Post-graduate Fellowship
1997-2000	National Science Foundation	Summer grant DMS 9706964
1999-2001	Sloan Foundation	Research Fellowship
1999-2006	David and Lucille Packard Foundation	Foundation Fellowship
2000	Salem Prize	2000 Salem Prize
2002	American Mathematical Society	Bocher Memorial Prize
2003	Clay Mathematical Institute	Clay Research Award
2004	American Mathematical Society	Levi L. Conant Award (with Allen Knutson)
2005	UCLA	Robert Sorgenfrey Distinguished Teaching Award
2005	Australian Mathematical Society	Australian Mathematical Society Medal
2005	International Society for Analysis, its Applications, and Computation	ISAAC award
2006	International Congress of Mathematicians	Plenary Speaker
2006	International Mathematical Union	Fields Medal
2006	Australian Academy of Science	Corresponding Member
2006	SASTRA	SASTRA Ramanujan prize
2007-2011	MacArthur Foundation	MacArthur Fellowship
2007	Ostrowski Foundation	Ostrowski Prize
2007	National Australia Day Council	SA finalist, Australian of the Year
2007-	UCLA	James and Carol Collins Chair
2007-2012	National Science Foundation	Research Award DMS-0649473
2007-	The Royal Society	Fellow
2008-2010	National Science Foundation	Waterman Award
2008	CESASC	Achievement Award
2008-	National Academy of Sciences	Foreign Affiliate
2008	Information Theory Society	Information Theory Society Paper Award (with Emmanuel Candes)
2008	Flinders University Alumni Association	Convocation Award
2008	Onsager Lecture	Onsager medal
2009	American Academy of Arts and Sciences	Member

 Teaching at UCLA

Fall 1996	Math 132	Complex Analysis
Winter 1997	Math 31B (Hons)	Calculus and Analytic Geometry
Spring 1997	Math 132  Math 121	Complex Analysis  Introduction to Topology
Winter 1998	Math 32A	Calculus of Several Variables
Spring 1998	Math 32A  Math 132	Calculus of Several Variables  Complex Analysis
Fall 1998	Math 132	Complex Analysis
Winter 1999	Math 254A	Topics in Analysis: Oscillatory Integrals and applications
Spring 1999	Math 254B	Topics in Analysis: Restriction theorems and applications
Winter 2000	Math 132	Complex Analysis
Spring 2000	Math 121  Math 199	Introduction to Topology Problem Solving
Winter 2001	Math 254A Math 296G	Topics in Analysis: Harmonic Analysis in the Phase Plane Analysis seminar
Fall 2002	Math 115A Math 296G/1 Math 296G/2	Linear Algebra Participating Analysis Seminar Analysis seminar
Winter 2002	Math 131AH Math 254A Math 296G/1 Math 296G/2	Analysis (Hons) Introduction to Arithmetic Combinatorics Participating Analysis Seminar Analysis seminar
Spring 2003	Math 131BH Math 296G/1 Math 296G/2	Analysis (Hons) Participating Analysis Seminar Analysis seminar
Winter 2004	Math 133 Math 245B	Introduction to Fourier Analysis Graduate Real Analysis
Fall 2004	Math 245A	Graduate Real Analysis
Winter 2005	Math 245B Math 33A	Graduate Real Analysis Linear Algebra
Spring 2005	Math 245C	Graduate Real Analysis
Winter 2006	Math 251A	Graduate Partial Differential Equations
Spring 2006	Math 251B	Graduate Partial Differential Equations
Fall 2006	Math 247A	Graduate Fourier Analysis
Winter 2007	Math 247B	Graduate Fourier Analysis
Winter 2008	Math 254A	Ergodic theory
Spring 2008	Math 285G	Poincare conjecture
Winter 2008	Math 245B	Graduate Real Analysis
Spring 2009	Math 245C	Graduate Real Analysis

Teaching at UNSW/ANU

UNSW Semester 2, 1999	Math 2620 (lecture + tutorial)  Math 1241 (2 tutorials)	Higher Complex Analysis Higher Mathematics 1B
UNSW Semester 2, 2000	Math 2620 (lecture + tutorial)  Math 1241 (1 tutorial)	Higher Complex Analysis Higher Mathematics 1B
ANU Semester 2, 2003	Math 3228 (3 weeks guest lectures)	Complex Variables (Hons)

Students

Deborah Cromer	Honours Undergraduate, UCLA/UNSW	Uniform distribution of sequences mod 1	2000
Thomas Lam	Honours Undergraduate, UNSW	Cycles of even length in graphs	2000-2001
Julia Garibaldi	Graduate Student, UCLA (joint with John Garnett)	Erdos distance problem for convex metrics	2002-2004
Roman Sasyk	Graduate Student, UCLA (informally supervised; formal supervisor was Sorin Popa)	Operator algebra methods in ergodic theory	2002-2003
Monica Visan	Graduate Student, UCLA	Critical nonlinear Schrodinger equations in higher dimensions	2003-2006
Jon Bueti	Graduate Student, UCLA	Finite field x-ray and k-plane estimates	2003-2006
Umut Isik	Undergraduate Student, UCLA	Maximal non-commuting subsets of groups	2005
Shuanglin Shao	Graduate Student, UCLA	Restriction estimates for paraboloids and cones in the cylindrically symmetric case	2006-2008
Soonsik Kwon	Graduate Student, UCLA	Low-regularity problems of fifth-order KdV and modified KdV equations	2006-2008
Tristan Roy	Graduate Student, UCLA	Global wellposedness of the defocusing cubic wave equation in dimension 3	2006-2008
Tim Austin	Graduate Student, UCLA	Szemeredi’s theorem and related topics	2006-
Le Thai Hoang	Graduate Student, UCLA	Additive combinatorics in finite fields	2007-
Paul Smith	Graduate Student, UCLA	TBA	2008-
Zaher Hani	Graduate Student, UCLA	TBA	2008-
Kenny Maples	Graduate Student, UCLA (joint with John Garnett)	TBA	2008-
Josh Zahl	Graduate Student, UCLA	TBA	2009-

Miscellaneous Duties

1998-2005	Zentralblatt Math.	Reviewer
1998-1999	UCLA	Putnam Committee Real Analysis Quals
1999-2000	UCLA	Putnam Committee Real Analysis Quals Library Committee  Computing Committee
2000-2001	www.arXiv.org	math.AP moderator
2001	Workshop in oscillatory integrals and non-linear PDE	Organizing commitee
2002-	www.arXiv.org	Global moderator / math.CA moderator
2002-2004	J. Amer. Math. Soc.	Associate editor
2002-2003	UCLA	Staff search committee  Analysis Quals Library Committee Graduate Advisors committee Analysis seminar (Fall)
2002-	Australian Mathematical Sciences Institute	Scientific Advisory Board
2002	Southern California Analysis and Partial Differential Equations (SCAPDE)	Organizing committee
2002-	American Journal of Mathematics	Associate Editor
2003-	International Mathematical Research Surveys (IMRS)	Advisory Board
2003-	Dynamics of Partial Differential Equations	Associate Editor
2003-2004	UCLA	Library Committee Computing Committee Analysis Seminar (Winter)
2004	Workshop: Recent Trends in Additive Combinatorics	Co-organizer
2004-2005	UCLA	Library Committee Staff Search Analysis Seminar Analysis Quals Colloquium (chair)
2005-2010	J. Amer. Math. Soc.	Full Editor
2004-2006	IMU	Sectional Committee, Analysis
2005-2006	UCLA	Analysis Seminar Colloquium
2006-2007	UCLA	Staff Search
2007-	IPAM	Scientific Advisory Board
2007-	Analysis & PDE	Editor
2007-2008	UCLA	Staff Search Analysis Seminar Distinguished Lecture Series
2008-2009	UCLA	Staff Search Analysis Seminar Distinguished Lecture Series
2009	SCAPDE	Local organizer
2009-2010	UCLA	Staff Search Analysis Seminar Distinguished Lecture Series
2009	IPAM	Organising committee: “Combinatorics: Methods and Applications in Mathematics and Computer Science”

Selected Lectures

Zygmund-Calderon lectures in Analysis	University of Chicago, Apr 8-10, 2002	Low-regularity behavior of the Korteweg-de Vries equations
Edinburgh lectures	Edinburgh, Mar 27-Apr 2 2002	The Kakeya problem
Wolff memorial lectures	Caltech, Apr 1,3,8,10, 2003	Long-time behavior of semi-linear dispersive equations
Park City lectures	Park City, Jun 29-Jul 12, 2003	Recent progress on the restriction conjecture
Phillips lectures	Michigan State University, Apr 5-7, 2004	The nonlinear Fourier transform
Hardy Lectures	United Kingdom, Apr 23-Jun 18 2004	Various
CBMS lectures	New Mexico, Jun 13-17 2005	Nonlinear dispersive and wave equations
Chern Lectures	Berkeley, Nov 7-17 2006	Nonlinear geometric PDE
Erdos lectures	Tennessee, Mar 24-25 2006	Arithmetic Progressions and the Primes
Aisenstadt lectures	Montreal, Mar 30-Apr 9 2006	Szemeredi’s theorem and related topics
Science Faculty Research Colloquium	UCLA, Jan 17 2007	Structure and randomness in the prime numbers
Simons Lectures	MIT, Apr 4-6 2007	The dichotomy between structure and randomness
Milliman Lectures	U. Washington, Dec 4-6 2007	Recent developments in arithmetic combinatorics
Mahler Lectures	Australia, Aug 23-Oct 2 2009	Various

Articles published, submitted, or in preparation

Title	With	Status
Weak-type endpoint bounds for Riesz means		Proc. Amer. Math. Soc. 124 (1996), 2797-2805
On the almost-everywhere convergence of wavelet summation methods		ACHA 3 (1996), 384-387
Harmonic convolution operators on Lipschitz graphs		Adv. Appl. Clifford Alg. 6 (1996), 207-218
On the Structure of Projective Group Representations in Quaternionic Hilbert Space	Andrew Millard	J. Math. Phys. 37 (1996), 5848-5857
The Bochner-Riesz conjecture implies the restriction conjecture		Duke Math. J. 96 (1999), 363-376
Endpoint Strichartz Estimates	Mark Keel	Amer. J. Math., 120 (1998), 955-980
The weak-type endpoint Bochner-Riesz conjecture and related topics		Indiana U. Math. J. 47 (1998), 1097-1124
Low regularity semi-linear wave equations		Comm. PDE 24 (1999), 599—630
Small data blowup for semilinear Klein-Gordon equations	Mark Keel	Amer. J. Math. 121 (1999), 629-669
A bilinear approach to the restriction and Kakeya conjectures	Ana Vargas  Luis Vega	J. Amer. Math. Soc. 11 (1998), 967-1000
On the Maximal Bochner-Riesz conjecture in the plane, for p<2		Trans. Amer. Math. Soc. 354 (2002), 1947-1959
Almost everywhere convergence of general wavelet shrinkage estimators	Brani Vidakovic	ACHA 9 (2000), 72-82
Local and global well-posedness of wave maps in R^{1+1} for rough data	Mark Keel	IMRN 21 (1998), 1117-1156
A bilinear approach to cone multipliers I. Restriction theorems	Ana Vargas	GAFA 10 (2000), 185-215
A bilinear approach to cone multipliers II. Applications	Ana Vargas	GAFA 10 (2000), 216-258
The honeycomb model of GL_n(C) tensor products I. Proof of the saturation conjecture	Allen Knutson	J. Amer. Math. Soc.12 (1999), 1055—1090
Spherically averaged endpoint Strichartz estimates for the two-dimensional Schrödinger equation		Comm. PDE 25 (2000), 1471-1485
Ill-posedness for one-dimensional wave maps at the critical regularity		Amer. J. Math., 122 (2000), 451-463
An improved bound on the Minkowski dimension of Besicovitch sets in R^3	Nets Katz Izabella Laba	Annals of Math. 152 (2000),  383-446
Weak-type endpoint bounds for homogeneous convolution operators		Indiana U. Math. J., 48 (1999), 1547-1584
The honeycomb model of GL_n(C) tensor products II. Facets of the Littlewood-Richardson cone	Allen Knutson Chris Woodward	J. Amer. Math. Soc. 17 (2004), 19-48.
Endpoint bilinear restriction theorems for the cone, and some sharp null form estimates		Math. Z. 238 (2001), 215-268
Bounds on arithmetic projections, and applications to the Kakeya conjecture	Nets Katz	Math Res. Letters 6 (1999), 625-630
An x-ray transform estimate in R^n	Izabella Laba	Revista Mat. Iber. 17 (2001), 375-408
Multilinear operators with singular multipliers	Camil Muscalu Christoph Thiele	J. Amer. Math. Soc. 15 (2002), 469-496
Convex bodies with a point of curvature do not admit exponential bases	Alex Iosevich Nets Katz	Amer. J. Math. 123 (2001), 115-120
Endpoint multiplier theorems of Marcinkiewicz type	Jim Wright	Revista Mat. Iber. 17 (2001), 521-558
Some connections between the Falconer and Furstenburg conjectures	Nets Katz	New York J. Math. 7 (2001), 148-187
Sharp Lorentz space estimates for rough operators	Andreas Seeger	Math. Annalen 320 (2001) 2, 381-415
L^p improving estimates for averages along curves	Jim Wright	J. Amer. Math. Soc. 16 (2003), 605-638
A converse extrapolation theorem for translation-invariant operators		J. Funct. Anal. 180 (2001), 1-10
Kakeya and restriction phenomena for finite fields	Gerd Mockenhaupt	Duke Math. J. 121 (2004), 35-74
The Fuglede spectral conjecture holds for convex bodies in the plane	Alex Iosevich Nets Katz	Math. Res. Letters 10 (2003), 559-570
Some light on Littlewood-Paley theory	Michael Cowling	Math. Annalen 321 (2001) 4, 885-888
On the Minkowski dimension of Besicovitch sets in medium dimension	Izabella Laba	GAFA 11 (2001), 773-806
Local well-posedness for the Yang-Mills equation below the energy norm		JDE 189 (2003), 366-382
Uniform estimates for paraproducts	Camil Muscalu Christoph Thiele	Journal d'Analyse de Jerusalem 87 (2002), 369-384
Uniform estimates for multi-linear operators with modulation symmetry	Camil Muscalu Christoph Thiele	Journal d'Analyse de Jerusalem 88 (2002), 255-309
Almost conservation laws and global rough solutions to a nonlinear Schrodinger equation	Jim Colliander Mark Keel Gigliola Staffilani Hideo Takaoka	Math. Res. Letters 9 (2002), 659-682.
Multilinear weighted convolution of $L^2$ functions, and applications to non-linear dispersive equations		Amer. J. Math. 123 (2001), 839-908
Global well-posedness result for KdV in Sobolev spaces of negative index	Jim Colliander Mark Keel Gigliola Staffilani Hideo Takaoka	EJDE 2001 (2001) No 26, 1-7
Sharp global well-posedness results for periodic and non-periodic KdV and modified KdV on R and T	Jim Colliander Mark Keel Gigliola Staffilani Hideo Takaoka	J. Amer. Math. Soc 16 (2003), 705-749.
From rotating needles to stability of waves: emerging connections between combinatorics, analysis, and PDE.		Notices Amer. Math. Soc. 48 (2001) No 3, 294-303
Three regularity results in harmonic analysis (Ph. D. Thesis)		Topics in Analysis and Applications, World Scientific.
L^p estimates for the "biest" I.  The Walsh model.	Camil Muscalu Christoph Thiele	Math. Annalen 329 (2004), 401-426
L^p estimates for the "biest" II.  The Fourier model.	Camil Muscalu Christoph Thiele	Math. Annalen 329 (2004), 427-461
Multi-linear multipliers associated to simplexes of arbitrary length	Camil Muscalu Christoph Thiele	Submitted, Analysis & PDE
New bounds for Kakeya problems	Nets Katz	Journal d'Analyse de Jerusalem,  87 (2002), 231-263
Multi-linear estimates for periodic KdV equations, and applications	Jim Colliander Mark Keel Gigliola Staffilani Hideo Takaoka	J. Funct. Anal. 211 (2004), 173-218
Global well-posedness for the Schrodinger equations with derivative	Jim Colliander Mark Keel Gigliola Staffilani Hideo Takaoka	Siam J. Math. 33 (2001), 649-669
Endpoint mapping properties of spherical maximal functions	Andreas Seeger Jim Wright	J. Institut Math. Jussieu 2 (2003) 1, 109-144
Pointwise convergence of lacunary spherical means	Andreas Seeger Jim Wright	Mt. Holyoke Proceedings (2001), Contemporary Mathematics (2003), 341-352
Singular maximal functions and Radon transforms near L^1	Andreas Seeger Jim Wright	Amer. J. Math. 126 (2004), 607-647.
Honeycombs and sums of Hermitian matrices	Allen Knutson	Notices Amer. Math. Soc. 48 (2001) No. 2, 175-186
Recent progress on the Kakeya conjecture	Nets Katz	Publicacions Matematiques, Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, U. Barcelona 2002, 161-180
Global regularity of wave maps I.  Small critical Sobolev norm in high dimension		IMRN 7 (2001), 299-328
Global regularity of wave maps II.  Small energy in two dimensions		Comm. Math. Phys. 224 (2001), 443-544
Puzzles and (equivariant) cohomology of Grassmanians	Allen Knutson	Duke Math. J. 119 (2003), 221-260
A refined global well-posedness for the Schrodinger equations with derivative	Jim Colliander Mark Keel Gigliola Staffilani Hideo Takaoka	Siam J. Math. 34 (2002), 64-86.
Resonant decompositions and the I-method for cubic nonlinear Schrodinger on R^2	Jim Colliander Mark Keel Gigliola Staffilani Hideo Takaoka	Disc. Cont. Dynam. Systems A 21 (2008), 665-686
Polynomial upper bounds for the orbital instability of the 1D cubic NLS below the energy norm	Jim Colliander Mark Keel Gigliola Staffilani Hideo Takaoka	Discrete Cont. Dynam. Systems 9 (2003), 31-54
Polynomial growth and orbital instability bounds for $L^2$-subcritical NLS below the energy norm	Jim Colliander Mark Keel Gigliola Staffilani Hideo Takaoka	Comm. Pure Appl. Anal. 2 (2003), 33-50
Global existence and scattering for rough solutions of a nonlinear Schrodinger equation in R^3	Jim Colliander Mark Keel Gigliola Staffilani Hideo Takaoka	CPAM 57 (2004), 987-1014
A geometric optics approach to bilinear wave estimates	Sergiu Klainerman Igor Rodnianski	J. Anal. Math. 87 (2002), 299—336
Bochner-Riesz summability for analytic functions on the  m-complex unit sphere and for cylindrically symmetric functions on R^{n-1} \times R	Adam Sikora	Comm. Anal. Geom. 12 (2004), 43-57
A new bound for finite field Besicovitch sets in four dimensions		Pacific J. Math 222 (2005), 337-363
A discrete model for the bi-carleson operator	Camil Muscalu Christoph Thiele	GAFA 12 (2002), 1324-1364
A counterexample to a multilinear endpoint question of Christ and Kiselev	Camil Muscalu Christoph Thiele	Math. Res. Letters 10 (2003), 237-246
Multilinear interpolation between adjoint operators	Loukas Grafakos	J. Funct. Anal. 199 (2003), 379-385
Carleson measures, trees, extrapolation, and T(b) theorems	Pascal Auscher Steve Hofman Camil Muscalu Christoph Thiele	Publications Matematiques Barcelona 46 (2002), 257-325
Weak-type (1,1) bounds for Fourier integral operators		J. Aust. Math. Soc. 76 (2004), 1-21
A singularity removal theorem for Yang-Mills fields in higher dimensions	Gang Tian	J. Amer. Math. Soc. 17 (2004), 557-593.
Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocussing equations	Michael Christ Jim Colliander	Amer. J. Math. 125 (2003), 1235-1293
Global regularity for the Maxwell-Klein-Gordon equation in high dimensions	Igor Rodnianski	Comm. Math. Phys. 251 (2004), 377-426
Symplectic nonsqueezing of the KdV flow	Jim Colliander Mark Keel Gigliola Staffilani Hideo Takaoka	Acta Math. 195 (2005), 197-252
Upper and lower bounds for Dirichlet eigenfunctions	Andrew Hassell	Math. Res. Letters 9 (2002), 289-305
Ill-posedness for nonlinear Schrodinger and wave equations	Michael Christ Jim Colliander	to appear, Annales IHP
Relative efficiencies of kernel and local likelihood density estimators	Peter Hall	J. R. Stat. Soc. Ser. B Stat. Methodol. 64 (2002), 537-547
A sharp bilinear restriction estimate for paraboloids		GAFA 13 (2003), 1359-1384
A Carleson-type theorem for a Cantor group model of the Scattering Transform	Camil Muscalu Christoph Thiele	Nonlinearity 19 (2003), 219-246
Local and global well-posedness for nonlinear dispersive equations		Proc. Centre Math. Appl. Austral. Nat. Univ. 40 (2002), 19-48
Existence globale et diffusion pour l'équation de Schrödinger nonlinéaire répulsive cubique sur R^3 en dessous l'espace d'énergie	Jim Colliander Mark Keel Gigliola Staffilani Hideo Takaoka	Journées "Équations aux Dérivées Partielles" (Forges-les-Eaux, 2002), Exp. No. X, 14 pp., Univ. Nantes, Nantes, 2002
A sum-product estimate for finite fields, and applications	Jean Bourgain Nets Katz	GAFA 14 (2004), 27-57
Some recent progress on the Restriction conjecture		Fourier analysis and convexity, 217-243, Appl. Numer. Harmon. Anal., Birkhäuser Boston, Boston, MA, 2004.
L^p bounds for a maximal dyadic sum operator	Loukas Grafakos Erin Terwilleger	Math. Z. 246 (2004), 321-337
Bi-parameter paraproducts	Camil Muscalu Jill Pipher Christoph Thiele	Acta Math. 193 (2004), 269–296
On multilinear oscillatory integrals, singular and nonsingular	Michael Christ Xiaochun Li Christoph Thiele	Duke Math. J. 130 (2005), 321—351.
Long-time decay estimates for Schrodinger equations on manifolds	Igor Rodnianski	Mathematical aspects of nonlinear dispersive equatoins, 223-253, Ann. of Math. Stud. 163, Princeton University Press, Princeton NJ 2007
A Strichartz inequality for the Schrodinger equation on non-trapping asymptotically conic manifolds	Andrew Hassell Jared Wunsch	Comm. PDE 30 (2004), 157-205
A positive proof of the Littlewood-Richardson rule using the octahedron recurrence	Allen Knutson Chris Woodward	Electron. J. Combin. 11 (2004), Research Paper 61, 18 pp. (electronic);
Global well-posedness of the Benjamin-Ono equation in H^1(R)		J. Hyperbolic Diff. Eq. 1 (2004) 27-49
Fuglede's conjecture is false in 5 and higher dimensions		Math. Res. Letters 11 (2004), 251-258
An uncertainty principle for cyclic groups of prime order		Math. Res. Letters 12 (2005), 121-127
Nonlinear Fourier Analysis	Christoph Thiele	to appear, Park City proceedings
Instability of the periodic nonlinear Schrodinger equation	Michael Christ Jim Colliander	Submitted,
On the asymptotic behavior of large radial data for a focusing non-linear Schr\"odinger equation		J. Hyperbolic Diff. Eq. 1 (2004) 27-49
Global well-posedness and scattering for the higher-dimensional energy-critical non-linear Schrodinger equation for radial data		Dynamics of PDE 1 (2004), 1-48
Global well-posedness and scattering in the energy space for the critical nonlinear Schrodinger equation in R^3 ("Project Gopher")	Jim Colliander Mark Keel Gigliola Staffilani Hideo Takaoka	Annals of Math. 167 (2007), 767-865
Recent progress on the Restriction conjecture		to appear,  Park City proceedings
Sharp Strichartz estimates on non-trapping asymptotically conic manifolds	Andrew Hassell Jared Wunsch	Amer. J. Math. 128 (2006), 963—1024.
Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information	Emmanuel Candes Justin Romberg	IEEE Inf. Theory 52 (2006) Vol 2., 489—509
The primes contain arbitrarily long arithmetic progressions	Ben Green	Annals of Math. 167 (2008), 481-547
New bounds for Szemeredi's Theorem, I: Progressions of length 4 in finite field geometries	Ben Green	to appear,  Proc. Lond. Math. Soc.
Restriction theory of the Selberg Sieve, with applications	Ben Green	Journal de Théorie des Nombres de Bordeaux 18 (2006), 137—172
A quantitative ergodic theory proof of Szemer\'edi's theorem		Electron. J. Combin. 13 (2006). 1 No. 99, 1-49.
The Bi-Carleson operator	Camil Muscalu Christoph Thiele	GAFA 16 (2006), 230—277
Multi-parameter paraproducts	Camil Muscalu Jill Pipher Christoph Thiele	Revista Mat. Iber. 22 (2006), 963-976
Geometric renormalization of large energy wave maps		Journees “Equations aux derives partielles”, Forges les Eaux, 7-11 June 2004, XI 1-32
Near Optimal Signal Recovery From Random Projections And Universal Encoding Strategies	Emmanuel Candes	IEEE Inf. Theory 52 (2006), 5406-5425
Decoding by Linear Programming	Emmanuel Candes	IEEE Inf. Theory 51 (2005), 4203-4215
Stable Signal Recovery from Incomplete and Inaccurate Measurements	Emmanuel Candes Justin Romberg	Comm. Pure Appl. Math. 59 (2006), 1207-1223
A quantitative ergodic theory proof of Szemer\'edi's theorem		Electron. J. Combin. 13 (2006). 1 No. 99, 1-49.
On random $\pm 1$ matrices: Singularity and Determinant	Van Vu	Random Structures and Algorithms 28 (2006),  1—23. [An extended abstracted is also in: STOC’05: Proceedings of the 37^th annual ACM symposium on the theory of computing, 431—440, New York 2005.]
Arithmetic progressions and the primes		Collectanea Mathematica (2006), Vol. Extra., 37-88. [Proceedings, 7th International Conference on Harmonic Analysis and Partial Differential Equations]
On the singularity probability of random Bernoulli matrices	Van Vu	J. Amer. Math. Soc. 20 (2007), 603-628
An inverse theorem for the Gowers $U^3(G)$ norm	Ben Green	Proc. Edin. Math. Soc. 51 (2008), 73-153
A variant of the hypergraph removal lemma		J. Combin. Thy. A 113 (2006), 1257—1280
Error Correction via Linear Programming	Emmanuel Candes Mark Rudelson Roman Vershynin	Proc. 46^th Annual IEEE Symposium on Foundations of Computer Science (FOCS05), IEEE, 2005.  pp. 295-308
The Brascamp--Lieb Inequalities: Finiteness, Structure and Extremals	Jon Bennett Tony Carbery Michael Christ	GAFA 17 (2008), 1343-1415
Finiteness bounds for multilinear inequalities of Brascamp-Lieb type	Jon Bennett Tony Carbery Michael Christ	Submitted, Math. Res. Letters
Szemer\’edi’s regularity lemma revisited		Contrib. Discrete Math. 1 (2006), 8-28
Random symmetric matrices are almost surely non-singular	Kevin Costello Van Vu	Duke Math. J. 135 (2006), 395-413
Obstructions to uniformity, and arithmetic patterns in the primes		Quarterly J. Pure Appl. Math. 2 (2006), 199-217 [Special issue in honour of John H. Coates, Vol. 1 of 2]
Stability of energy-critical nonlinear Schr\"odinger equations in high dimensions	Monica Visan	Electron. J. Diff. Eq. Vol. 2005 (2005), No. 118, 1-28.
Sharp well-posedness and ill-posedness results for a quadratic non-linear Schr\"odinger equation	Ioan Bejenaru	J. Funct. Anal. Vol. 233 (2006), 228-259
On the Multilinear Restriction and Kakeya conjectures	Jon Bennett Tony Carbery	Acta Math.  196 (2006) 261—302
The Gaussian primes contain arbitrarily shaped constellations		J. d’Analyse Mathematique 99 (2006), 109-176
The Dantzig selector: statistical estimation when $p$ is much larger than $n$	Emmanuel Candes	Annals of Statistics 35 (2007),  2313-2351
Maximal multilinear operators	Ciprian Demeter Christoph Thiele	Trans. Amer. Math. Soc.,  360 (2008),  4989-5042
Breaking duality in the return times theorem	Ciprian Demeter Michael Lacey Christoph Thiele	Duke Math. J. 143 (2008), 281-355
Velocity averaging, kinetic formulations, and regularizing effects in quasilinear PDE	Eitan Tadmor	CPAM 61 (2007), 1-34
The nonlinear Schr\”odinger equation with combined power-type nonlinearities	Monica Visan Xiaoyi Zhang	Comm. PDE 32 (2007), 1281-1343.
Spacetime bounds for the energy-critical nonlinear wave equation in three spatial dimensions		Dynamics of PDE 3 (2006), 93-110
Compressions, convex geometry, and the Freiman-Bilu theorem	Ben Green	Quarterly J. Math. 57 (2006), 495-504
Inverse Littlewood-Offord theorems and the condition number of random discrete matrices	Van Vu	To appear, Annals of Math.
The dichotomy between structure and randomness, arithmetic progressions, and the primes		2006 ICM proceedings, Vol. I., 581--608
Product set estimates in noncommutative groups		To appear, Combinatorica
A correspondence principle between (hyper)graph theory and probability theory, and the (hyper)graph removal lemma		J. d’Analyse Mathematique 103 (2007), 1--45.
Scattering for the quartic generalised Korteweg-de Vries equation		J. Diff. Eq. 232 (2007), 623—651
Global regularity for a logarithmically supercritical defocusing nonlinear wave equation for spherically symmetric data		J. Hyperbolic Diff. Eq. 4 (2007),  259-266
Two remarks on the generalised Korteweg-de Vries equation		Discrete Cont. Dynam. Systems 18 (2007), 1-14
A pseudoconformal compactification of the nonlinear Schrodinger equation and applications		To appear, New York Journal of Mathematics
Global behaviour of nonlinear dispersive and wave equations		Current Developments in Mathematics 2006, International Press.  255-340.
Minimal-mass blowup solutions of the mass-critical NLS	Monica Visan Xiaoyi Zhang	Forum Mathematicum 20 (2008), 881-919
Global well-posedness and scattering for the mass-critical nonlinear Schr\”odinger equation for radial data in high dimensions	Monica Visan Xiaoyi Zhang	Duke Math J. 140 (2007), 165-202
A counterexample to an endpoint bilinear Strichartz inequality		Electron. J. Diff. Eq. 2006 (2006) 151, 1—6.
A (concentration-)compact attractor for high-dimensional non-linear Schr\"odinger equations		Dynamics of PDE 4 (2007), 1-53
A priori bounds and weak solutions for the nonlinear Schrodinger equation in Sobolev spaces of negative order	Michael Christ Jim Colliander	J. Funct. Anal  254 (2007), 368-395
The cubic nonlinear Schrödinger equation in two dimensions with radial data	Rowan Killip Monica Visan	To appear, J. Europ. Math. Soc.
A quantitative version of the Besicovitch projection theorem via multiscale analysis		Proc. Lond. Math. Soc. doi:10.112/plms/pdn037
The primes contain arbitrarily long polynomial progressions	Tamar Ziegler	Acta Math. 201 (2008), 213—305.
John-type theorems for generalized arithmetic progressions and iterated sumsets	Van Vu	Adv. in Math. 219 (2008), 428—449.
A note on the Freiman and Balog-Szemeredi-Gowers theorems in finite fields	Ben Green	J. Aust. Math. Soc. 86 (2009), 61-74.
On the condition number of a randomly perturbed matrix	Van Vu	Proceedings of the thirty-ninth annual ACM symposium on Theory of computing  (STOC) 2007, 248-255
Freiman's theorem in finite fields via extremal set theory	Ben Green	To appear, Combinatorics, Probability, and Computing
Szemerédi's theorem	Ben Green	Scholarpedia, p. 15573
Norm convergence of multiple ergodic averages for commuting transformations		Ergodic Theory and Dynamical Systems 28 (2008), 657-688
Structure and randomness in combinatorics		Proceedings of the 48th annual symposium on Foundations of Computer Science (FOCS) 2007, 3-18
Random Matrices: The circular Law	Van Vu	Communications in Contemporary Mathematics, 10 (2008), 261--307
The quantitative behaviour of polynomial orbits on nilmanifolds	Ben Green	Submitted, Annals of Math.
The M\"obius and nilsequences conjectures	Ben Green	Submitted, Annals of Math.
The distribution of polynomials over finite fields, with applications to the Gowers norms	Ben Green	Submitted, Contributions to Discrete Mathematics
On the testability and repair of hereditary hypergraph properties	Tim Austin	To appear, Random Structures and Algorithms
A remark on primality testing and decimal expansions		To appear, J. Aust. Math. Soc.
On the permanent of random Bernoulli matrices	Van Vu	Adv. Math. 220 (2009), 657—669.
Smooth analysis of the condition number and the least singular value	Van Vu	To appear, Mathematics of Computation
The sum-product phenomenon in arbitrary rings		To appear, Contributions to Discrete Mathematics
What is good mathematics?		Mathematical Perspectives, Bull. Amer. Math. Soc. 44 (2007), 623-634.
Classification of almost quarter-pinched manifolds	Peter Petersen	Proc. Amer. Math. Soc. 137 (2009), 2437—2440.
The Walsh model for $M_2^*$ Carleson	Ciprian Demeter Michael Lacey Christoph Thiele	Revista Mat. Iber. 24 (2008), 721-744
Why are solitons stable?		Bull. Amer. Math. Soc. 46 (2009), 1-33
A global compact attractor for high-dimensional defocusing non-linear Schrödinger equations with potential		Dynamics of PDE 5 (2008), 101—116.
Global regularity of wave maps III.  Large energy from $R^{1+2}$ to hyperbolic spaces.		To be submitted,
Global regularity of wave maps IV. Absence of stationary or self-similar solutions in the energy class.		To be submitted,
Global existence and uniqueness results for weak solutions of the focusing mass-critical non-linear Schrödinger equation		To appear, Analysis & PDE
The Kakeya set and maximal conjectures for algebraic varieties over finite fields	Jordan Ellenberg Richard Oberlin	To appear, Mathematika
The high exponent limit $p \to \infty$ for the one-dimensional nonlinear wave equation		To appear, Analysis & PDE
Reflections on compressed sensing	Emmanuel Candes	IEEE Information Theory Society Newsletter, Dec 2008 58 (4), 20-23
The power of matrix completion: near-optimal convex relaxation	Emmanuel Candes	To appear, IEEE Inf. Theory
Random matrices: Universality of ESDs and the circular law	Van Vu	To appear, Annals of Probability
From the Littlewood-Offord problem to the circular law: universality of the spectral distribution of random matrices	Van Vu	To appear, Bull. Amer. Math. Soc.
The inverse conjecture for the Gowers norm over finite fields via the correspondence principle	Tamar Ziegler	Submitted, Analysis & PDE
An inverse theorem for the uniformity seminorms associated with the action of $F^\omega$	Vitaly Bergelson Tamar Ziegler	To appear, GAFA
A sharp inverse Littlewood-Offord theorem	Van Vu	Submitted, Random Structures and Algorithms
Random matrices: the distribution of smallest singular values	Van Vu	To appear, GAFA
A variation norm Carleson theorem	Richard Oberlin Andreas Seeger Christoph Thiele Jim Wright	Submitted, J. Europ. Math. Soc.
Random matrices: universality of local eigenvalue statistics	Van Vu	To appear, Acta Math.
An equivalence between inverse sumset theorems and inverse conjectures for the U^3 norm	Ben Green	To appear, Math. Proc. Camb. Phil. Soc.
Freiman’s theorem for solvable groups		Submitted, Contributions to Discrete Mathematics
Sumset and inverse sumset theorems for Shannon entropy		Submitted, Combinatorics, Probability, and Computing
Bulk universality for Wigner hermitian matrices with subexponential decay	László Erdős José Ramírez Benjamin Schlein Van Vu Horng-Tzer Yau	To appear, Math. Res. Lett.
Random matrices: universality of local eigenvalue statistics up to the edge	Van Vu	Submitted, Communications in Mathematical Physics
A remark on partial sums involving the Mobius function		To appear, Bull. Aust. Math. Soc.
Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrodinger equation	Jim Colliander Mark Keel Gigliola Staffilani Hideo Takaoka	To appear, Inventiones Math.
The high exponent limit p \to \infty for the one-dimensional nonlinear wave equation		To appear, Analysis & PDE
Global regularity for a logarithmically supercritical hyperdissipative Navier-Stokes equation		Submitted, Analysis & PDE
Operator splitting for the KdV equation	Helge Holden Kenneth Karlsen Nils Risebro	Submitted, Math. Comp.
Global well-posedness for the Maxwell-Klein-Gordon equation below the energy norm	Mark Keel Tristan Roy	Submitted, Discrete Cont. Dynam. Systems

Books published

• "Solving Mathematical Problems: A Personal Perspective", Deakin University Press, 1992.  Reprinted, Oxford University Press, 2006.
• “Analysis Vol. I”, “Analysis Vol. II”.  Hindustan Book Agency, 2006.
• “Additive Combinatorics”, with Van Vu, Cambridge University Press, 2006.
• “Nonlinear dispersive equations: local and global analysis”, CBMS regional conference series in mathematics, 2006
• “Structure and Randomness: pages from year one of a mathematical blog”, American Mathematical Society, 2008.
• “Poincare’s legacies: pages from year two of a mathematical blog”, Vols. I and II, American Mathematical Society, 2009

Patents

• E. Candes, T. Tao, "A computer-implemented method for correcting transmission errors using linear programming", US Patent 20070016837