Vitae and Bibliography for Terence Tao

Last updated:  Dec 20, 2013

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, the Waterman Award in 2008, the Nemmers Prize in 2010, and the Crafoord prize in 2012.  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: 

Secondary: 

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

Honorary 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

2007-2011

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

2009

SIAM

Polya Prize (with Emmanuel Candes)

2010

King Faisal Foundation

King Faisal International Prize (Mathematics)

2010

Northwestern University

Nemmers Prize

2012

Royal Swedish Academy of Sciences

Crafoord Prize (Mathematics)

2012

American Philosophical Society

Member

2012

American Mathematical Society

Fellow

2012-2016

Simons Foundation

Simons Investigator

2013

Spanish Royal Academy of Sciences

Overseas member

2013

National Science Foundation

NSF grant 1301620

2013-2018

National Science Foundation

NSF grant 1266164

2013

Center for Excellence in Education

Joseph Lieberman Award

2013

Center for Talented Youth

Distinguished alumni award

 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

Winter 2010

Math 254A

Random matrices

Spring 2010

Math 254B

Higher order Fourier analysis

Fall 2010

Math 245A

Graduate Real Analysis

Spring 2011

Math 245C

Graduate Real Analysis

Fall 2011

Math 254A

Hilbert's Fifth Problem

Winter 2012

Math 254B

Expansion in groups of Lie type

Winter 2013

Math 245B

Graduate Real Analysis

Fall 2013

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

Multiple recurrence and the structure of probability-preserving systems

2006-2010     

Le Thai Hoang

Graduate Student, UCLA

Topics in additive combinatorics in finite fields 

2007-2010

Paul Smith

Graduate Student, UCLA

Subthreshold geometric renormalization

and energy-critical Schrodinger maps

2008-2011

Zaher Hani

Graduate Student, UCLA

Global and dynamical aspects of nonlinear

Schrodinger equations on compact manifolds

2008-2011

Kenny Maples

Graduate Student, UCLA 

Arithmetic Properties of Random Matrices

2008-2011

Josh Zahl

Graduate Student, UCLA

Some algebraic and geometric variants of Restriction and Kakeya problems   

2009-2013

Brad Rogers

Graduate Student, UCLA

The statistics of the Riemann zeta function and related topics

2011-2013

Pietro Carolino

Graduate Student, UCLA

TBA

2012-

Jacques Benatar

Graduate Student, UCLA

TBA

2012-

Anand Rajagopalan

Graduate Student, UCLA

TBA

2013-

Ben Krause

Graduate Student, UCLA

TBA

2013-

Nick Cook

Graduate Student, UCLA

TBA

2013-

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)

2005-2011

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

2008-2010

IMU

ICM 2010 Program Committee

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”

2009

Prize Jose Luis Rubio de Francia

Committee member

2009

AMS

Steele Prize committee

2010

UCLA

SCAPDE organiser

Analysis Seminar

Distinguished Lecture Series

2010

AMS

Steele Prize committee

2010

Prize Jose Luis Rubio de Francia

Committee member

2011-2012

UCLA

Staff Search

Analysis Seminar

Distinguished Lecture Series

2012-2013

UCLA

SCAPDE organiser

Staff Search

Analysis Seminar

Analysis qual

2011-2013

Norwegian Academy of Sciences

Abel prize committee

2012-2013

National Academy of Sciences

Scientific Reviewing award committee

2012-

Cambridge University Press

Editor, Forum of Mathematics

2012-2013

National Committee for the Mathematical Sciences

Subcommittee chair, decadal plan for the mathematical sciences

2013-2014

UCLA

Staff Search

Analysis Seminar

DLS (chair)

2013

MSRI

Evaluation Visiting Team

2013

Caltech

Caltech PMA visiting committee

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 

Einstein Lecture

UCLA, October 9 2010

The cosmic distance ladder

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 inQuaternionic 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 Besicovitchsets 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 Kakeyaconjecture

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 Furstenburgconjectures

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 

ChristophThiele

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

SubmittedAnalysis & 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 andKiselev

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 Schrödingernonlinéaire répulsive cubique sur R^3 en dessous l'espaced'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

LoukasGrafakos 

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 

ChristophThiele

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

Proc. Lond. Math. Soc. 98 (2009), 365-392

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 37th 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. 46th 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

Math. Res. Letters, 17 (2010), 647-666

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 inquasilinear 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

Annals of Math. 169 (2009), 595-632

The dichotomy between structure and randomness, arithmetic progressions, and the primes

 

2006 ICM proceedings, Vol. I., 581--608

Product set estimates in noncommutative groups

 

Combinatorica 28 (2008), 547-594

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 Vriesequation

 

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

 

New York J. Math. 15 (2009), 265--282. 

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

J. Eur. Math. Soc. (JEMS) 11 (2009), no. 6, 1203--1258. 

A quantitative version of the Besicovitch projection theorem viamultiscale 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

Combin. Probab. Comput. 18 (2009), no. 3, 335--355

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

Annals of Math. Volume 175 (2012), Issue 2, 465-540.

The M\"obius function is asymptotically orthogonal to nilsequences

Ben Green

Annals of Math., 175 (2012), 541--566 

The distribution of polynomials over finite fields, with applications to the Gowers norms

Ben Green

Contrib. Discrete Math. 4 (2009), no. 2, 1--36.

On the testability and repair of hereditary hypergraph properties

Tim Austin

Random Structures and Algorithms 36 (2010), 373-463

A remark on primality testing and decimal expansions

J. Aust. Math. Soc.

91 (2011), 405-413

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

Mathematics of Computation, 79 (2010), 2333-2352

The sum-product phenomenon in arbitrary rings

Contrib. Discrete Math. 4 (2009), no. 2, 59--82.

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

 Anal. PDE 2 (2009), no. 1, 61--81.

The Kakeya set and maximal conjectures for algebraic varieties over finite fields

Jordan Ellenberg

Richard Oberlin

Mathematika 56 (2010) 1-25

The high exponent limit $p \to \infty$ for the one-dimensional nonlinear wave equation

 

Anal. PDE 2 (2009), no. 2, 235--259.

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

IEEE Inf. Theory 56 (2009), 2053-2080

Random matrices: Universality of ESDs and the circular law

Van Vu

Annals of Probability 38 (2010), no. 5, 2023--2065.

From the Littlewood-Offord problem to the circular law: universality of the spectral distribution of random matrices

Van Vu

Bull. Amer. Math. Soc. (N.S.) 46 (2009), no. 3, 377--396. 

The inverse conjecture for the Gowers norm over finite fields via the correspondence principle

Tamar Ziegler

Analysis & PDE 3 (2010), 1-20

An inverse theorem for the uniformity seminorms associated with the action of $F^\omega$

Vitaly Bergelson

Tamar Ziegler

Geom. Funct. Anal. 19 (2010), no. 6, 1539--1596.

A sharp inverse Littlewood-Offord theorem

Van Vu

Random Structures and Algorithms

37 (2010), 525-539

Random matrices: the distribution of smallest singular values

Van Vu

Geom. Funct. Anal. 19 (2010), no. 6, 1539--1596.

A variation norm Carleson theorem

Richard Oberlin

Andreas Seeger

Christoph Thiele

Jim Wright

J. Europ. Math. Soc. 14 (2012), 421-464.

Random matrices: universality of local eigenvalue statistics

Van Vu

Acta Math 206 (2011), 127-204

An equivalence between inverse sumset theorems and inverse conjectures for the U^3 norm

Ben Green

Math. Proc. Camb. Phil. Soc.  149 (2010), 1-19

Freiman’s theorem for solvable groups

 

Contributions to Discrete Mathematics 5 (2010), no. 2, 137–184,

Sumset and inverse sumset theorems for Shannon entropy

 

Combinatorics, Probability, and Computing 19 (2010), 603-639

Bulk universality for Wigner hermitian matrices with subexponential decay

László Erdős

José Ramírez

Benjamin Schlein

Van Vu

Horng-Tzer Yau

Math. Res. Lett. 17 (2010), 793-794 

Random matrices: universality of local eigenvalue statistics up to the edge

Van Vu

Communications in Mathematical Physics, 298 (2010), 549-572 

A remark on partial sums involving the Mobius function

 

Bull. Aust. Math. Soc. 81 (2010), 343-349

Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrodinger equation

Jim Colliander 

Mark Keel 

Gigliola Staffilani 

Hideo Takaoka           

Inventiones Math.181 (2010), 39-113

The high exponent limit p \to \infty for the one-dimensional nonlinear wave equation

 

Anal. PDE 2 (2009), no. 2, 235--259.

Global regularity for a logarithmically supercritical hyperdissipative Navier-Stokes equation

 

Analysis & PDE 2 (2009), 361-366

Operator splitting for the KdV equation

Helge Holden

Kenneth Karlsen

Nils Risebro

Math. Comp. 80 (2011) 821-846. 

Global well-posedness for the Maxwell-Klein-Gordon equation below the energy norm

Mark Keel

Tristan Roy

Discrete Cont. Dynam. Systems 30 (2011), 573-621

Random Martingales and localization of maximal inequalities

Assaf Naor

J. Funct. Anal. 259 (2010), 731-779

Scale-oblivious metric fragmentation and the nonlinear Dvoretzky theorem

Assaf Naor

Israel J. Math. 192 (2012), 489-504

A new proof of the density Hales-Jewett theorem

D.H.J. Polymath

An Irregular Mind: Szemeredi is 70, Bolyai Society Mathematical Studies, 689-754

A finitary version of Gromov's polynomial growth theorem

Yehuda Shalom

GAFA 20 (2010), no. 6, 1502–1547.

An inverse theorem for the Gowers U^4 norm

Ben Green

Tamar Ziegler

Glasgow Mathematical Journal 53(2011), no. 1, 1–50

Random covariance matrices: Universality of local statistics of  eigenvalues

Van Vu

Annals of Probability 40 (2012), 1283--1315.

Nonconventional ergodic averages and multiple recurrence for von Neumann dynamical systems

Tim Austin

Tanja Eisner

Pacific Journal of Mathematics 250-1 (2011), 1--60. DOI 10.2140/pjm.2011.250.1

Linear approximate groups

Emmanuel Breuillard

Ben Green

Electronic research announcements 17 (2010), 57-67

An arithmetic regularity lemma, an associated counting lemma, and applications

Ben Green

An Irregular Mind: Szemeredi is 70, Bolyai Society Mathematical Studies, 261-334 

Yet another proof of Szemeredi's theorem

Ben Green

An Irregular Mind: Szemeredi is 70, Bolyai Society Mathematical Studies, 335-342

The Littlewood-Offord problem in high dimensions and a conjecture of Frankl and F\"uredi

Van Vu

Combinatorica, 32 (2012), 363-372

Suzuki groups as expanders

Emmanuel Breuillard

Ben Green

Groups, Geometry, and Dynamics 

5 (2011), no. 2, 281–-299.

Approximate subgroups of linear groups

Emmanuel Breuillard

Ben Green

GAFA  21 (2011), 774-819

Strongly dense free subgroups of semisimple algebraic groups

Emmanuel Breuillard

Ben Green

Bob Guralnick

Israel J. Math. 192 (2012), 347-379

Expansion in simple groups of Lie type

Emmanuel Breuillard

Ben Green

Submitted, J. Europ. Math. Soc.

An inverse theorem for the Gowers U^k norm

Ben Green

Tamar Ziegler

Annals of Math. 176 (2012), no. 2, 1231–1372

Random matrices: Localization of the eigenvalues and the necessity of four moments

Van Vu

Acta Mathematica Vietnamica 36 (2011), 431--449

Deterministic methods to find primes

Ernie Croot

Harald Helfgott

Mathematics of Computation 81 (2012), 1233-1246

Large values of the Gowers-Host-Kra seminorms

Tanja Eisner

J. d’Analyse Mathematique 117 (2012), 133-186

Outliers in the spectrum of iid matrices with bounded rank permutations

Probability theory and related fields

155 (2013), 231-263

The inverse conjecture for the Gowers norm over finite fields in low characteristic

Tamar Ziegler

Annals of Combinatorics 16 (2012), 121-188

A note on approximate subgroups of GL_n(C) and uniformly nonamenable groups

Emmanuel Breuillard

Ben Green

Submitted, 

The Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices

Van Vu

Electronic Journal of Probability 16 (2011), 2104-2121

Random matrices: Universal properties of Eigenvectors

Van Vu

Random matrices: Theory and Applications 1 (2012), 1150001

An incidence theorem in higher dimensions

Jozsef Solymosi

Disc. Comp. Geom. 48 (2012), 255-280

Noncommutative sets of small doubling

European Journal of Combinatorics 34 (2013), 1459-1465

Counting the number of solutions to the Erdös-Straus equation on unit fractions

Christian Elsholtz

J. Aust. Math. Soc. 94 (2013), 50-105

Asymptotic decay for a one-dimensional nonlinear wave equation

Hans Lindblad

Analysis & PDE 5-2 (2012), 411--422

Effective limiting absorption principles, and applications

Igor Rodnianski

SubmittedComm. Math. Phys

Localisation and compactness properties of the Navier-Stokes global regularity problem

Analysis & PDE 6 (2013), 25-107

Concentration compactness for critical wave maps, by Joachim Krieger and Wilhelm Schlag.

Bull. Amer. Math. Soc. 50 (2013), 655-662

The structure of approximate groups

Emmanuel Breuillard

Ben Green

To appearPub. IHES

A central limit theorem for the determinant of a Wigner matrix

Van Vu

Adv. Math. 231 (2012), 74-101

Random matrices: The Four Moment Theorem for Wigner matrices

Van Vu

Submitted, MSRI Book series

A nilpotent Freiman dimension lemma

Emmanuel Breuillard

Ben Green

European Journal of Combinatorics 34 (2013), 1287-1292

Random matrices: Sharp concentration of eigenvalues

Van Vu

To appear,  Random matrices: Theory and Applications

Every odd number greater than 1 is the sum of at most five primes

To appearMathematics of Computation 

Random matrices:  The Universality phenomenon for Wigner ensembles

To appear, Probability Theory and Related Fields

E pluribus unum: from complexity, universality

Daedalus 141 (3) (Summer 2012)

New bounds for Szemeredi's theorem, Ia: Progressions of length 4 in finite field geometries revisited

Ben Green

Submitted, Proc. Lond. Math. Soc.

Random matrices: Universality of local spectral statistics of non-Hermitian matrices

Van Vu

To appear, Annals of Prob.

On sets defining few ordinary lines

Ben Green

To appear, Disc. Comp. Geom. 50 (2013), 409-468

Expanding polynomials over finite fields of large characteristic, and a regularity lemma for definable sets

Submitted, Disc. Comp. Geom. 

Multiple recurrence in quasirandom groups

Vitaly Bergelson

To appear, Geom. Func. Anal.

Mixing for progressions in nonabelian groups

To appear, Forum of Mathematics, Sigma

Multiple recurrence and convergence results associated to $\F_{p}^{\omega}$-actions

Vitaly Bergelson

Tamar Ziegler

To appear, J. d’Analyse Mathematique

A multi-dimensional Szemer\'edi theorem for the primes via a correspondence principle

Tamar Ziegler

Submitted, Israel J. Math.

Local universality of zeroes of random polynomials

Van Vu

Submitted, IMRN

Algebraic combinatorial geometry: the polynomial method in arithmetic combinatorics, incidence combinatorics, and number theory

Submitted, EMS surveys in the mathematical sciences

Books published

Patents