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 Fields Medal in 2006, the MacArthur Fellowship in 2007, the Crafoord prize in 2012, and the Breakthrough Prize in Mathematics in 2015. Terence Tao also holds the James and Carol Collins chair in mathematics at UCLA, and is a Fellow of the Royal Society, the Australian Academy of Sciences, the National Academy of Sciences, and the American Academy of Arts and Sciences. He currently serves on the President's Council of Advisors on Science and Technology.
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: | |
WWW: |
Degree | Date | Institution | Advisor | Subject | Thesis title |
Ph. D. | Jun 1996 | Elias Stein | Mathematics | ||
M. Sc. | Aug 1992 | Mathematics | Convolution operators generated by right-monogenic and harmonic kernels | ||
B. Sc. (Hons) | Dec 1991 | Mathematics | N/A |
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Primary:
| Secondary:
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1992-1994 | Assistant Researcher | |
1993-1994 | Assistant Researcher | |
1996-1998 | Hedrick Assistant Professor | |
Fall 1997 | Member | |
1999 | Acting Assistant Professor | |
1999 | Visiting Fellow | |
2000 | Assistant Professor | |
2001-2003 | ||
2000- | Full Professor | |
2000 | Visiting Professor | |
2001-2003 | Honorary Professor |
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1986 | ||
1987 | ||
1988 | ||
1992 | ||
1992-1995 | Fulbright Postgraduate Scholar | |
1995 | Post-graduate Fellowship | |
1997-2000 | ||
1999-2001 | ||
1999-2006 | ||
2000 | ||
2002 | ||
2003 | ||
2004 | Levi L. Conant Award (with Allen Knutson) | |
2005 | Robert Sorgenfrey Distinguished Teaching Award | |
2005 | ||
2005 | International Society for Analysis, its Applications, and Computation | |
2006 | ||
2006 | ||
2006 | ||
2006 | ||
2007-2011 | ||
2007 | Ostrowski Foundation | |
2007 | ||
2007- | ||
2007-2011 | ||
2007- | ||
2008-2010 | ||
2008 | ||
2008- | (Regular member since 2022) | |
2008 | Information Theory Society Paper Award (with Emmanuel Candes) | |
2008 | ||
2008 | ||
2009 | ||
2009 | SIAM | Polya Prize (with Emmanuel Candes) |
2010 | ||
2010 | ||
2012 | ||
2012 | American Philosophical Society | Member |
2012 | American Mathematical Society | Fellow |
2012-2022 | 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 |
2014 | Royal Society | Royal Medal |
2014 | Royal Swedish Academy of Sciences | Foreign Member |
2015 | Breakthrough Prize | Mathematics Breakthrough Prize |
2015 | PROSE awards | PROSE award, mathematics |
2018-2023 | National Science Foundation | NSF grant 1764034 |
2019 | RISM | Riemann prize |
2020 | The Princess of Asturias Foundation | Princess of Asturias Award for Technical and Scientific Research |
2020 | Hungarian Academy of Sciences | Janos Bolyai International Mathematical Prize |
2020 | IEEE | 2021 IEEE Jack S. Kilby Signal Processing Medal |
2021 | Istituto Lombardo Accademia de Scienze E Lettere | Foreign Member |
2022 | Harvey Mudd College | Honorary Doctorate of Science |
2022 | Advance Org | Global Australian of the Year |
2023 | Grande Médaille | French Academy of Sciences |
2023 | American Institute of Mathematics | Alexanderson Award |
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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 | |
Spring 1999 | Math 254B | |
Winter 2000 | Math 132 | |
Spring 2000 | Math 121 Math 199 | |
Winter 2001 | Math 254A Math 296G | |
Fall 2002 | Math 115A Math 296G/1 Math 296G/2 | |
Winter 2002 | Math 131AH Math 254A Math 296G/1 Math 296G/2 | Introduction to Arithmetic Combinatorics |
Spring 2003 | Math 131BH Math 296G/1 Math 296G/2 | |
Winter 2004 | Math 133 Math 245B | |
Fall 2004 | Math 245A | |
Winter 2005 | Math 245B Math 33A | |
Spring 2005 | Math 245C | |
Winter 2006 | Math 251A | |
Spring 2006 | Math 251B | |
Fall 2006 | Math 247A | |
Winter 2007 | Math 247B | |
Winter 2008 | Math 254A | |
Spring 2008 | Math 285G | |
Winter 2008 | Math 245B | |
Spring 2009 | Math 245C | |
Winter 2010 | Math 254A | |
Spring 2010 | Math 254B | |
Fall 2010 | Math 245A | |
Spring 2011 | Math 245C | |
Fall 2011 | Math 254A | |
Winter 2012 | Math 254B | |
Winter 2013 | Math 245B | |
Fall 2013 | Math 245C | |
Winter 2014 | Math 245B | |
Spring 2014 | Math 245C | |
Winter 2015 | Math 254A | |
Fall 2015 | Math 275A | Probability theory |
Spring 2016 | Math 245C | Real Analysis |
Fall 2016 | Math 246A | Complex Analysis |
Spring 2017 | Math 245C | Real Analysis |
Spring 2018 | Math 246C | Complex Analysis |
Fall 2018 | Math 254A | Incompressible fluids |
Winter 2019 | Math 255B | Incompressible Euler equations |
Fall 2019 | Math 254A | Analytic prime number theory |
Spring 2020 | Math 247C | Classical Fourier Analysis |
Fall 2020 | Math 246A | Complex analysis |
Winter 2020 | Math 246B | Complex analysis |
Fall 2021 | Math 246A | Complex analysis |
Winter 2022 | Math 246B | Complex analysis |
Spring 2022 | Math 246C | Complex analysis |
Fall 2022 | Math 246A | Complex analysis |
Spring 2023 | Math 246C | Complex analysis |
Fall 2023 | Math 246A | Complex analysis |
Winter 2024 | Math 246B | Complex analysis |
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UNSW Semester 2, 1999 | Math 2620 (lecture + tutorial) Math 1241 (2 tutorials) | Higher Mathematics 1B |
UNSW Semester 2, 2000 | Math 2620 (lecture + tutorial) Math 1241 (1 tutorial) | Higher Mathematics 1B |
ANU Semester 2, 2003 | Math 3228 (3 weeks guest lectures) |
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Deborah Cromer | Honours Undergraduate, UCLA/UNSW | 2000 | |
Honours Undergraduate, UNSW | 2000-2001 | ||
Graduate Student, UCLA (joint with John Garnett) | 2002-2004 | ||
Graduate Student, UCLA (informally supervised; formal supervisor was Sorin Popa) | Operator algebra methods in ergodic theory | 2002-2003 | |
Graduate Student, UCLA | Critical nonlinear Schrodinger equations in higher dimensions | 2003-2006 | |
Graduate Student, UCLA | 2003-2006 | ||
Umut Isik | Undergraduate Student, UCLA | 2005 | |
Graduate Student, UCLA | Restriction estimates for paraboloids and cones in the cylindrically symmetric case | 2006-2008 | |
Graduate Student, UCLA | Low-regularity problems of fifth-order KdV and modified KdV equations | 2006-2008 | |
Graduate Student, UCLA | Global wellposedness of the defocusing cubic wave equation in dimension 3 | 2006-2008 | |
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 Rodgers | Graduate Student, UCLA | The statistics of the Riemann zeta function and related topics | 2011-2013 |
Pietro Carolino | Graduate Student, UCLA | The structure of locally compact groups | 2012-2015 |
Jacques Benatar | Graduate Student, UCLA | 2012-2015 | |
Anand Rajagopalan | Graduate Student, UCLA | 2013-2015 | |
Ben Krause | Graduate Student, UCLA | 2013-2015 | |
Jordy Greenblatt | Graduate Student, UCLA | 2014-2016 | |
Nick Cook | Graduate Student, UCLA | 2013-2016 | |
Yilong Yang | Graduate Student, UCLA | Shapes of Finite Groups through Covering Properties and Cayley Graphs | 2015-2017 |
Stephen Ge | Graduate Student, UCLA | The eigenvalue spacing of IID random matrices and related least singular value results | 2015-2017 |
Zane Li | Graduate Student, UCLA | Decoupling for the parabola and connections to efficient congruencing | 2017-2019 |
Bjorn Bringmann | Graduate Student, UCLA | Probabilistic perspectives on dispersive partial differential equations | 2018-2021 |
Khang Huynh | Graduate Student, UCLA | Intrinsic harmonic analysis on manifolds with boundary, and Onsager’s conjecture | 2018-2021 |
Redmond Mcnamara | Graduate Student, UCLA | 2019-2021 | |
Alex Dobner | Graduate Student, UCLA | 2019-2021 | |
Stan Palasek | Graduate Student, UCLA | Some quantitative regularity theorems for the Navier-Stokes equations | 2020-2023 |
Jaume de Dios | Graduate Student, UCLA | 2021-2023 | |
James Leng | Graduate Student, UCLA | TBA | 2022- |
Ben Johnsrude | Graduate Student, UCLA | TBA | 2022- |
Zi Li Lim | Graduate Student, UCLA | TBA | 2022- |
Rushil Raghavan | Graduate Student, UCLA | TBA | 2023- |
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1998-2005 | Zentralblatt Math. | Reviewer |
1998-1999 | Real Analysis Quals | |
1999-2000 | Real Analysis Quals Library Committee Computing Committee | |
2000-2001 | ||
2001 | Organizing commitee | |
2002-2012 | ||
2002-2004 | ||
2002-2003 | Staff search committee Analysis Quals Library Committee Graduate Advisors committee | |
2002-2022 | ||
2002 | Southern California Analysis and Partial Differential Equations (SCAPDE) | Organizing committee |
2002- | ||
2003- | ||
2003- | Associate Editor | |
2003-2004 | Library Committee Computing Committee | |
2004 | Co-organizer | |
2004-2005 | Library Committee Staff Search Analysis Seminar Analysis Quals Colloquium (chair) | |
2005-2011 | ||
2004-2006 | IMU | Sectional Committee, Analysis |
2005-2006 | Analysis Seminar Colloquium | |
2006-2007 | Staff Search | |
2007-2020 | ||
2007- | ||
2007-2008 | Staff Search Analysis Seminar Distinguished Lecture Series | |
2008-2010 | IMU | ICM 2010 Program Committee |
2008-2009 | Staff Search Analysis Seminar Distinguished Lecture Series | |
2009 | Local organizer | |
2009-2010 | 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 | 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 | 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 SearchAnalysis Seminar DLS (chair) |
2013 | MSRI | Evaluation Visiting Team |
2013 | Caltech | Caltech PMA visiting committee |
2013- | Episciences | Epi-Math committee |
2014 | AMS/MAA | AMS-MAA Joint Lecture Committee |
2014 | 2015 Bolyai Prize | Committee member |
2014 | AMS | von Neumann symposium selection committee |
2014-2015 | UCLA | Analysis seminar |
2015-2016 | UCLA | Staff searchAnalysis seminarDLS (chair) |
2015-2021 | Royal Society | Newton fellowships committee (Physical Sciences) |
2015-2022 | MATRIX | Scientific committee |
2015- | Discrete Analysis | Editor |
2015-2017 | MSRI | Analytic Number Theory program organiser (chair) |
2016- | UCLA | Analysis seminarDLS (chair) |
2016-2022 | Bhaumik Institute, UCLA | Advisory board |
2016-2018 | International Mathematical Union | Fields Medal Committee |
2017-2018 | Clay Mathematics Institute | Conference organiser |
2017 | Bergen Research Foundation | Scientific Committee |
2017 | Caltech Mathematics Department | Visiting Committee |
2017-2022 | UCLA | Staff search |
2018-2023 | Sloan Foundation | Sloan Fellowship Committee |
2018-2023 | AMS | Committee on National Awards and Public Representation |
2018 | MSRI | Visiting evaluation committee |
2019-2025 | AMS | Doob Prize Selection Committee |
2019-2023 | MSRI / SLMath | Board of Trustees Vice-Chair |
2019-2021 | AMS | Editorial Boards Committee (and liason to Committee of Publications for 2021) |
2019-2023 | IMU | Structure Committee |
2019-2023 | SMRI | Advisory Board |
2019, 2022 | UCLA | Dissertation Year Fellowship Committee |
2020-2023 | UCLA | Chair, Math Circle Steering Committee |
2021 | Infosys Science Foundation | Infosys Mathematics Prize Jury |
2021-2024 | Office of Science and Technology Policy | President's Council of Advisors on Science and Technology |
2021- | Riemann International School of Mathematics | Scientific Board |
2021-2022 | UCLA | Analysis qual (chair) |
2021-2023 | IPAM | Organizing committee, Machine Assisted Proof (chair) |
2022-2024 | UCLA | Analysis qual |
2023- | ICMS | Mathematics for Humanity scientific committee |
2023 | AMS | Stein Memorial Prize Committee |
2023 | NAS | Planning committee, workshop in AI to assist Mathematical Reasoning |
2024- | XTX Markets | Advisory Committee, AIMO Prize |
University of Chicago, Apr 8-10, 2002 | ||
Edinburgh, Mar 27-Apr 2 2002 | ||
Caltech, Apr 1,3,8,10, 2003 | ||
Park City, Jun 29-Jul 12, 2003 | ||
Michigan State University, Apr 5-7, 2004 | ||
United Kingdom, Apr 23-Jun 18 2004 | ||
New Mexico, Jun 13-17 2005 | ||
Berkeley, Nov 7-17 2006 | Nonlinear geometric PDE | |
Tennessee, Mar 24-25 2006 | ||
Montreal, Mar 30-Apr 9 2006 | ||
UCLA, Jan 17 2007 | ||
MIT, Apr 4-6 2007 | ||
U. Washington, Dec 4-6 2007 | ||
Australia, Aug 23-Oct 2 2009 | ||
UCLA, October 9 2010 | ||
Title | With | Status |
| 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 | J. Math. Phys. 37 (1996), 5848-5857 | |
The Bochner-Riesz conjecture implies the restriction conjecture |
| Duke Math. J. 96 (1999), 363-376 |
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 |
| Comm. PDE 24 (1999), 599—630 | |
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 | ACHA 9 (2000), 72-82 | |
Local and global well-posedness of wave maps in R^{1+1} for rough data | 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 | 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 | 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 | 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 | Math Res. Letters 6 (1999), 625-630 | |
An x-ray transform estimate in R^n | Revista Mat. Iber. 17 (2001), 375-408 | |
Multilinear operators with singular multipliers | Camil Muscalu | J. Amer. Math. Soc. 15 (2002), 469-496 |
Convex bodies with a point of curvature do not admit exponential bases | Alex Iosevich | Amer. J. Math. 123 (2001), 115-120 |
Endpoint multiplier theorems of Marcinkiewicz type | Revista Mat. Iber. 17 (2001), 521-558 | |
Some connections between the Falconer and Furstenburgconjectures | New York J. Math. 7 (2001), 148-187 | |
Sharp Lorentz space estimates for rough operators | Math. Annalen 320 (2001) 2, 381-415 | |
L^p improving estimates for averages along curves | 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 | Math. Res. Letters 10 (2003), 559-570 | |
Some light on Littlewood-Paley theory | Math. Annalen 321 (2001) 4, 885-888 | |
On the Minkowski dimension of Besicovitch sets in medium dimension | 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 | Journal d'Analyse de Jerusalem 87 (2002), 369-384 |
Uniform estimates for multi-linear operators with modulation symmetry | Camil Muscalu | Journal d'Analyse de Jerusalem 88 (2002), 255-309 |
Almost conservation laws and global rough solutions to a nonlinear Schrodinger equation | 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 | 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 | 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. | Math. Annalen 329 (2004), 401-426 | |
L^p estimates for the "biest" II. The Fourier model. | Math. Annalen 329 (2004), 427-461 | |
Multi-linear multipliers associated to simplexes of arbitrary length | Advances in analysis: the legacy of Elias M. Stein, 346–401, Princeton Math. Ser., 50, Princeton Univ. Press, Princeton, NJ, 2014. | |
New bounds for Kakeya problems | Journal d'Analyse de Jerusalem, 87 (2002), 231-263 | |
Multi-linear estimates for periodic KdV equations, and applications | Gigliola Staffilani Hideo Takaoka | J. Funct. Anal. 211 (2004), 173-218 |
Global well-posedness for the Schrodinger equations with derivative | Gigliola Staffilani Hideo Takaoka | Siam J. Math. 33 (2001), 649-669 |
Endpoint mapping properties of spherical maximal functions | J. Institut Math. Jussieu 2 (2003) 1, 109-144 | |
Pointwise convergence of lacunary spherical means | Mt. Holyoke Proceedings (2001), Contemporary Mathematics (2003), 341-352 | |
Singular maximal functions and Radon transforms near L^1 | Amer. J. Math. 126 (2004), 607-647. | |
Honeycombs and sums of Hermitian matrices | Notices Amer. Math. Soc. 48 (2001) No. 2, 175-186 | |
Recent progress on the Kakeya conjecture | 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 | Duke Math. J. 119 (2003), 221-260 | |
A refined global well-posedness for the Schrodinger equations with derivative | Gigliola Staffilani Hideo Takaoka | Siam J. Math. 34 (2002), 64-86.
|
Resonant decompositions and the I-method for cubic nonlinear Schrodinger on R^2 | 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 | 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 | 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 | Gigliola Staffilani Hideo Takaoka | CPAM 57 (2004), 987-1014 |
A geometric optics approach to bilinear wave estimates | 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 | GAFA 12 (2002), 1324-1364 | |
A counterexample to a multilinear endpoint question of Christ andKiselev | Math. Res. Letters 10 (2003), 237-246 | |
Multilinear interpolation between adjoint operators | J. Funct. Anal. 199 (2003), 379-385 | |
Carleson measures, trees, extrapolation, and T(b) theorems | 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 | J. Amer. Math. Soc. 17 (2004), 557-593. | |
Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocussing equations | Amer. J. Math. 125 (2003), 1235-1293 | |
Global regularity for the Maxwell-Klein-Gordon equation in high dimensions | Comm. Math. Phys. 251 (2004), 377-426 | |
Symplectic nonsqueezing of the KdV flow | Hideo Takaoka | Acta Math. 195 (2005), 197-252 |
Upper and lower bounds for Dirichlet eigenfunctions | Math. Res. Letters 9 (2002), 289-305 | |
Ill-posedness for nonlinear Schrodinger and wave equations | Unpublished | |
Relative efficiencies of kernel and local likelihood density estimators | 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 | 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 | 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 | 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 | Math. Z. 246 (2004), 321-337 | |
Bi-parameter paraproducts | Acta Math. 193 (2004), 269–296 | |
On multilinear oscillatory integrals, singular and nonsingular | Duke Math. J. 130 (2005), 321—351. | |
Long-time decay estimates for Schrodinger equations on manifolds | 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 | Comm. PDE 30 (2004), 157-205 | |
A positive proof of the Littlewood-Richardson rule using the octahedron recurrence | 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 | Unpublished | |
Instability of the periodic nonlinear Schrodinger equation | Unpublished | |
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") | 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 | Amer. J. Math. 128 (2006), 963—1024. | |
Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information | IEEE Inf. Theory 52 (2006) Vol 2., 489—509 | |
The primes contain arbitrarily long arithmetic progressions | Annals of Math. 167 (2008), 481-547 | |
New bounds for Szemeredi's Theorem, I: Progressions of length 4 in finite field geometries | Proc. Lond. Math. Soc. 98 (2009), 365-392 | |
Restriction theory of the Selberg Sieve, with applications | 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 | GAFA 16 (2006), 230—277 | |
Multi-parameter paraproducts | 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 | IEEE Inf. Theory 52 (2006), 5406-5425 | |
Decoding by Linear Programming | IEEE Inf. Theory 51 (2005), 4203-4215 | |
Stable Signal Recovery from Incomplete and Inaccurate Measurements | 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 | 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 | J. Amer. Math. Soc. 20 (2007), 603-628 | |
An inverse theorem for the Gowers $U^3(G)$ norm | 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 | 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 | GAFA 17 (2008), 1343-1415 |
Finiteness bounds for multilinear inequalities of Brascamp-Lieb type | Jon Bennett | 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 | 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 | 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 | 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 $n$ | Annals of Statistics 35 (2007), 2313-2351 | |
Maximal multilinear operators | Trans. Amer. Math. Soc., 360 (2008), 4989-5042 | |
Breaking duality in the return times theorem | Duke Math. J. 143 (2008), 281-355 | |
Velocity averaging, kinetic formulations, and regularizing effects inquasilinear PDE | CPAM 61 (2007), 1-34 | |
The nonlinear Schr\”odinger equation with combined power-type nonlinearities | 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 | Quarterly J. Math. 57 (2006), 495-504 | |
Inverse Littlewood-Offord theorems and the condition number of random discrete matrices | 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 | 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 | 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 | J. Funct. Anal 254 (2007), 368-395 | |
The cubic nonlinear Schrödinger equation in two dimensions with radial data | 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 | Acta Math. 201 (2008), 213—305. | |
John-type theorems for generalized arithmetic progressions and iterated sumsets | Adv. in Math. 219 (2008), 428—449. | |
A note on the Freiman and Balog-Szemeredi-Gowers theorems in finite fields | J. Aust. Math. Soc. 86 (2009), 61-74. | |
On the condition number of a randomly perturbed matrix | 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 | Combin. Probab. Comput. 18 (2009), no. 3, 335--355 | |
Szemerédi's theorem | 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 | Communications in Contemporary Mathematics, 10 (2008), 261--307 | |
The quantitative behaviour of polynomial orbits on nilmanifolds | Annals of Math. Volume 175 (2012), Issue 2, 465-540. | |
The M\"obius function is asymptotically orthogonal to nilsequences | Annals of Math., 175 (2012), 541--566 | |
The distribution of polynomials over finite fields, with applications to the Gowers norms | Contrib. Discrete Math. 4 (2009), no. 2, 1--36. | |
On the testability and repair of hereditary hypergraph properties | Random Structures and Algorithms 36 (2010), 373-463 | |
A remark on primality testing and decimal expansions | 91 (2011), 405-413 | |
On the permanent of random Bernoulli matrices | Adv. Math. 220 (2009), 657—669. | |
Smooth analysis of the condition number and the least singular value | 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 | Proc. Amer. Math. Soc. 137 (2009), 2437—2440. | |
The Walsh model for $M_2^*$ Carleson | 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. | Unpublished | |
Global regularity of wave maps IV. Absence of stationary or self-similar solutions in the energy class. | Unpublished | |
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 | 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 | IEEE Information Theory Society Newsletter, Dec 2008 58 (4), 20-23 | |
The power of matrix completion: near-optimal convex relaxation | IEEE Inf. Theory 56 (2009), 2053-2080 | |
Random matrices: Universality of ESDs and the circular law | 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 | 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 | Analysis & PDE 3 (2010), 1-20 | |
An inverse theorem for the uniformity seminorms associated with the action of $F^\omega$ | Geom. Funct. Anal. 19 (2010), no. 6, 1539--1596. | |
A sharp inverse Littlewood-Offord theorem | ||
Random matrices: the distribution of smallest singular values | Geom. Funct. Anal. 19 (2010), no. 6, 1539--1596. | |
A variation norm Carleson theorem | ||
Random matrices: universality of local eigenvalue statistics | Acta Math 206 (2011), 127-204 | |
An equivalence between inverse sumset theorems and inverse conjectures for the U^3 norm | 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 | José Ramírez | Math. Res. Lett. 17 (2010), 793-794 |
Random matrices: universality of local eigenvalue statistics up to the edge | 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 | 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 | Math. Comp. 80 (2011) 821-846. | |
Global well-posedness for the Maxwell-Klein-Gordon equation below the energy norm | ||
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 | |
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 | ||
Random covariance matrices: Universality of local statistics of eigenvalues | Annals of Probability 40 (2012), 1283--1315. | |
Nonconventional ergodic averages and multiple recurrence for von Neumann dynamical systems | Pacific Journal of Mathematics 250-1 (2011), 1--60. DOI 10.2140/pjm.2011.250.1 | |
Linear approximate groups | Electronic research announcements 17 (2010), 57-67 | |
An arithmetic regularity lemma, an associated counting lemma, and applications | An Irregular Mind: Szemeredi is 70, Bolyai Society Mathematical Studies, 261-334 | |
Yet another proof of Szemeredi's theorem | 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 | Combinatorica, 32 (2012), 363-372 | |
Suzuki groups as expanders | Groups, Geometry, and Dynamics 5 (2011), no. 2, 281–-299. | |
Approximate subgroups of linear groups | ||
Strongly dense free subgroups of semisimple algebraic groups | ||
Expansion in simple groups of Lie type | J. Europ. Math. Soc. 17 (2015), 1367-1434 | |
An inverse theorem for the Gowers U^k norm | Annals of Math. 176 (2012), no. 2, 1231–1372 | |
Random matrices: Localization of the eigenvalues and the necessity of four moments | 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 | |
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 | |
A note on approximate subgroups of GL_n(C) and uniformly nonamenable groups | 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 | |
An incidence theorem in higher dimensions | Jozsef Solymosi | |
Noncommutative sets of small doubling | ||
Counting the number of solutions to the Erdös-Straus equation on unit fractions | Christian Elsholtz | |
Asymptotic decay for a one-dimensional nonlinear wave equation | Hans Lindblad | |
Effective limiting absorption principles, and applications | Igor Rodnianski | Comm. Math. Phys. 333 (2015), 1-95 |
Localisation and compactness properties of the Navier-Stokes global regularity problem | ||
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 | Pub. IHES 116 (2012), 115-221 | |
A central limit theorem for the determinant of a Wigner matrix | Adv. Math. 231 (2012), 74-101 | |
Random matrices: The Four Moment Theorem for Wigner matrices | Random matrix theory, interacting particle systems, and integrable systems, 509–528, Math. Sci. Res. Inst. Publ., 65, Cambridge Univ. Press, New York, 2014. | |
A nilpotent Freiman dimension lemma | European Journal of Combinatorics 34 (2013), 1287-1292 | |
Random matrices: Sharp concentration of eigenvalues | Random matrices: Theory and Applications 2 (2013), 1350007 | |
Every odd number greater than 1 is the sum of at most five primes | Mathematics of Computation 83 (2014), 997-1038 | |
Random matrices: The Universality phenomenon for Wigner ensembles | In: Modern Aspects of Random Matrix Theory, Proceedings of Symposia in Applied Mathematics 72 (2013), V. Vu Editor, 121--172. | |
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 | Submitted, Proc. Lond. Math. Soc. | |
Random matrices: Universality of local spectral statistics of non-Hermitian matrices | Annals of Prob. 43 (2015), 782-874 | |
On sets defining few ordinary lines | 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 | Geom. Func. Anal. 24 (2014), 1-48 | |
Mixing for progressions in nonabelian groups | Forum of Mathematics, Sigma 1 (2013), e2 | |
Multiple recurrence and convergence results associated to $\F_{p}^{\omega}$-actions | J. Anal. Math. 127 (2015), 329–378. | |
A multi-dimensional Szemer\'edi theorem for the primes via a correspondence principle | Israel J. Math., Feb 2015 | |
Local universality of zeroes of random polynomials | International Mathematics Research Notices 2014;doi: 10.1093/imrn/rnu084 | |
Finite time blowup for an averaged three-dimensional Navier-Stokes equation | J. Amer. Math. Soc. 29 (2016), no. 3, 601–674. | |
Algebraic combinatorial geometry: the polynomial method in arithmetic combinatorics, incidence combinatorics, and number theory | EMS surveys in the mathematical sciences 1 (2014), 1--46 | |
New equidistribution results of Zhang type | Algebra & Number Theory 8-9 (2014), 2067--2199 | |
Variants of the Selberg sieve, and bounded intervals containing many primes | Research in the Mathematical Sciences 1:12 (2014) | |
Large gaps between consecutive prime numbers | Sergei Konyagin | Annals Math. 183 (2016), 935--974. |
Narrow progressions in the primes | To appear, “Analytic Number Theory” in honor of Helmut Maier’s 60th birthday | |
The “bounded gaps between primes” Polymath project - a retrospective | Newsletter of the European Mathematical Society, Dec 2014. Issue 94, 13--23 | |
The Elliott-Halberstam conjecture implies the Vinogradov least quadratic nonresidue conjecture | Algebra & Number Theory 9-4 (2015), 1005--1034. DOI 10.2140/ant.2015.9.1005 | |
Random matrices have simple spectrum | Combinatorica 37 (2017), no. 3, 539–553 | |
Long gaps in the primes | J. Amer. Math. Soc. 31 (2018), no. 1, 65–105 | |
An averaged form of Chowla’s conjecture | Algebra & Number Theory 9-9 (2015), 2167--2196. DOI 10.2140/ant.2015.9.2167 | |
Cancellation in the multilinear Hilbert transform | Collectanea Mathematica 67 (2016), 1-16 | |
Random matrices: tail bounds for gaps between eigenvalues | Hoi Nguyen | Probab. Theory Related Fields 167 (2017), no. 3-4, 777–816. |
Inverse theorems for sets and measures of polynomial growth | Q. J. Math. 68 (2017), no. 1, 13–57 | |
Sign patterns for the Liouville and Mobius functions | Kaisa Matomaki Maksym Radziwill | Forum Math. Sigma 4 (2016), e14, 44 pp. |
The logarithmically averaged Chowla and Elliott conjectures for two-point correlations | Forum Math. Pi 4 (2016), e8, 36 pp. | |
The Erdos discrepancy problem | Discrete Analysis 2016:1, 26 pp. | |
Chains of large gaps between primes | Kevin Ford James Maynard | Irregularities in the distribution of prime numbers, 1–21, Springer, Cham, 2018. |
Sum-avoiding subsets in groups | Van Vu | Discrete Analysis 2016:15, 31 pp.Survey: J. Comb. 8n3, 2017, 541--552 |
Concatenation theorems for anti-Gowers-uniform functions and Host-Kra characteristic factors | Tamar Ziegler | Discrete Anal. 2016, Paper No. 13, 60 pp. |
Polynomial patterns in the primes | Tamar Ziegler | Forum Math. Pi 6 (2018), e1, 60 pp. |
Equivalence of the logarithmically averaged Chowla and Sarnak conjectures | Number theory—Diophantine problems, uniform distribution and applications, 391–421, Springer, Cham, 2017. | |
An integration approach to the Toeplitz square peg problem | Forum Math. Sigma 5(2017), e30 | |
Some remarks on the lonely runner conjecture | Contrib. Discrete Math. 13 (2018), no. 2, 1–31. | |
A bound on partitioning clusters | Daniel Kane | Electron. J. Combin. 24 (2017), no. 2, Paper 2.31, 13 pp. |
Correlations of the von Mangoldt and higher divisor functions I. Long shift ranges | Proc. Lond. Math. Soc. (3) 118 (2019), no. 2, 284–350. | |
The structure of logarithmically averaged correlations of multiplicative functions, with applications to the Chowla and Elliott conjectures | Joni Teräväinen | Duke Math. J. 168 (2019), no. 11, 1977–2027 |
Odd order cases of the logarithmically averaged Chowla conjecture | Joni Teräväinen | J. Théor. Nombres Bordeaux 30 (2018), no. 3, 997–1015. |
An inverse theorem for an inequality of Kneser | Proc. Steklov Inst. Math. 303 (2018), no. 1, 193–219 | |
Correlations of the von Mangoldt and higher divisor functions II.Divisor correlations in short ranges | Math. Ann. 374 (2019), no. 1-2, 793–840. | |
The de Bruijn-Newman constant is nonnegative | Forum Math. Pi 8 (2020), e6, 62 pp. | |
Long gaps in sieved sets | Kevin Ford Sergei Konyagin James Maynard Carl Pomerance | J. Eur. Math. Soc. (JEMS) 23 (2021), no. 2, 667–700. |
The structure of correlations of multiplicative functions at almost all scales, with applications to the Chowla and Elliott conjectures | Joni Teräväinen | Algebra Number Theory 13 (2019), no. 9, 2103–2150. |
Finite time blowup for a supercritical defocusing nonlinear wave system | Anal. PDE 9 (2016), no. 8, 1999–2030. | |
Finite time blowup for a high dimensional nonlinear wave systems with bounded smooth nonlinearity | Comm. Partial Differential Equations 41 (2016), no. 8, 1204–1229. | |
Finite time blowup for Lagrangian modifications of the three-dimensional Euler equation | Ann. PDE 2 (2016), no. 2, Art. 9, 79 pp. | |
Finite time blowup for a supercritical defocusing nonlinear Schr\"odinger system | Analysis & PDE 11-2 (2018), 383--438. DOI 10.2140/apde.2018.11.383 | |
On the universality of potential well dynamics | Dynamics of PDE 14 (2017), 219--238. | |
On the universality of the incompressible Euler equation on compact manifolds | Disc. Cont. Dynam. Sys. 38 (2018), 1553-1565 | |
Failure of the $L^1$ pointwise and maximal ergodic theorems for the free group | Forum Math. Sigma 3 (2015), e27, 19 pp. | |
On the sign patterns of entrywise positivity preservers in fixed dimension | Apoorva Khare | Amer. J. Math. 143 (2021), no. 6, 1863–1929.Extended abstract: FPSAC 2018, Volume 80B of Seminaire Lotharingien de Combinatoire (2018) |
Searching for singularities in the Navier–Stokes equations | Nature Reviews Physics 1, 418–419(2019) | |
Quantitative bounds for critically bounded solutions to the Navier-Stokes equations | Nine mathematical challenges—an elucidation, 149–193, Proc. Sympos. Pure Math., 104, Amer. Math. Soc., Providence, RI, [2021], ©2021. | |
Analysis and applications: the work of Elias Stein | Charles Fefferman Alex Ionescu Stephen Wainger | |
Pointwise ergodic theorems for non-conventional bilinear polynomial averages | Ben Krause, Mariusz Mirek | Annals Math. Pages 997-1109 from Volume 195 (2022), Issue 3 |
The Ionescu-Wainger multiplier theorem and the adeles | Mathematika 67 (2021), no. 3, 647–677 | |
Homogeneous length functions on groups | D.H.J. Polymath | Algebra & Number Theory 12-7 (2018), 1773--1786 |
Commutators close to the identity | J. Op. Thy. 82:2(2019), 369–382 | |
Embedding the Heisenberg group into a bounded dimensional Euclidean space with optimal distortion | Rev. Mat. Iberoam. 37 (2021), no. 1, 1–44. | |
A Close Call: How a Near Failure Propelled Me to Succeed | Living Proof: Stories of Resilience Along the Mathematical Journey, American Math. Society, Math. Assoc. America, 2019. A. Henderson, E. Lawrence, M. Pons, D. Taylor eds., 96--99. | |
Eigenvectors from Eigenvalues: a survey of a basic identity in linear algebra. | Peter Denton, Stephen Parke, Xining Zhang | Bull. Amer. Math. Soc. (N.S.) 59 (2022), no. 1, 31–58. |
Fractional free convolution powers. With an appendix by David Jekel | Dimitri Shlyakhtenko | To appear, Indiana U. Math. J. |
Foundational aspects of uncountable measure theory: Gelfand duality, Riesz representation, canonical models, and canonical disintegration | Asgar Jamneshan | Fundamenta Mathematicae 261 (2023), 1-98 |
Sendov's conjecture for sufficiently high degree polynomials | Acta Mathematica, Vol. 229, No. 2 (2022), pp. 347-392 | |
The effective potential of an $M$-matrix | Marcel Filoche, Svetlana Mayboroda | J. Math. Phys. 62, 041902 (2021). |
Elias M. Stein (2013-2018) | Lillian Pierce et al. | Not. Amer. Math. Soc. 68 (2021), 546-563 |
Optimal sine and sawtooth inequalities | Louis Esser, Burt Totaro, Chengxi Wang | J. Fourier Anal. Appl. (2022) 28:14 |
Perfectly packing a square by squares of nearly harmonic sidelength | Comp. Disc. Geom.(2023). https://doi.org/10.1007/s00454-023-00523-y | |
Mathematika 66 (2020), 517--576 | ||
Least singular value, circular law, and Lindeberg exchange. | Random matrices, 461–498, IAS/Park City Math. Ser., 26, Amer. Math. Soc., Providence, RI, 2019. | |
Almost all orbits of the Collatz map attain almost bounded values | Forum Math. Pi 10 (2022), Paper No. e12, 56 pp. | |
Szemeredi's proof of Szemeredi's theorem | Acta Math. Hungar. 161 (2020), no. 2, 443–487. | |
Higher uniformity of bounded multiplicative functions in short intervals on average | Kaisa Matomaki, Maksym Radziwill, Joni Teravainen, Tamar Ziegler | Annals Math Pages 739-857 from Volume 197 (2023), Issue 2 |
Zarankiewicz's problem for semilinear hypergraphs | Abdul Basit, Artem Chernikov, Sergei Starchenko, Chiu-Minh Tran | Forum of Mathematics, Sigma , Volume 9 , 2021 , e59 |
An uncountable Moore-Schmidt theorem | Asgar Jamneshan | Ergodic Theory and Dynamical Systems Volume 43 , Issue 7 , July 2023 , pp. 2376 - 2403 |
An uncountable Mackey-Zimmer theorem | Asgar Jamneshan | Studia Math. 266 (2022), no. 3, 241–289. |
The structure of translational tilings in Z^d | Rachel Greenfeld | Discrete Analysis 2021:16, 28 pp. |
Additive energy of regular measures in one and higher dimensions, and the fractional uncertainty principle | Laura Cladek | Ars Inven. Anal. 2021, Paper No. 1, 38 pp. |
Singmaster's conjecture in the interior of Pascal's triangle | Kaisa Matomaki, Maksym Radziwill, Xuansheng Shao, Joni Teravainen | The Quarterly Journal of Mathematics, haac006, https://doi.org/10.1093/qmath/haac006 |
Quantitative bounds for Gowers uniformity of the M\"obius and von Mangoldt functions | Joni Teravainen | submitted, J. Europ. Math. Soc. |
Undecidable translational tilings with only two tiles, or one nonabelian tile | Rachel Greenfeld | to appear, Disc. Comp. Geom. |
The Hardy--Littlewood--Chowla conjecture in the presence of a Siegel zero | Joni Teravainen | J. Lond. Math. Soc. JLMS12663 |
The structure of arbitrary Conze-Lesigne systems | Asgar Jamneshan, Or Shalom | submitted, Comm. AMS |
The inverse theorem for the U3 Gowers uniformity norm on arbitrary finite abelian groups: Fourier-analytic and ergodic approaches | Asgar Jamneshan | Discrete Analysis https://doi.org/10.19086/da.84268 |
Measurable tilings by abelian group actions | Jan Grebík, Rachel Greenfeld, Václav Rozhoň | IMRN, rnad048, https://doi.org/10.1093/imrn/rnad048 |
Higher uniformity of arithmetic functions in short intervals I. All intervals | Kaisa Matomaki, Xuansheng Shao, Joni Teravainen | Forum of Mathematics, Pi. 2023;11:e29. doi:10.1017/fmp.2023.28 |
The Ionescu-Wainger multiplier theorem and the adeles | Mathematika 67 (2021), no. 3, 647–677 | |
Homogenization of iterated singular integrals with applications to random quasiconformal maps | Kari Astala, Steffen Rohde, Eero Saksman | Revista Iberoamericana VOL. 38, NO. 7PP. 2285–2336 |
Adjoint Brascamp-Lieb inequalities | Jon Bennett | Submitted, Proc. Lond. Math. Soc. |
A Maclaurin type inequality | Submitted, Proc. AMS | |
Machine assisted proof | Submitted, Notices Amer. Math. Soc. | |
A counterexample to the periodic tiling conjecture | Rachel Greenfeld | submitted, Annals Math. |
Infinite partial sumsets in the primes | Tamar Ziegler | J. d'Analyse Jerusalem Volume 151, pages 375–389, (2023) 10.1007/s11854-023 |
A Host--Kra Fω2-system of order 5 that is not Abramov of order 5, and non-measurability of the inverse theorem for the U6(Fn2) norm | Asgar Jamneshan, Or Shalom | submitted,JEMS |
The structure of totally disconnected Host--Kra--Ziegler factors, and the inverse theorem for the Uk Gowers uniformity norms on finite abelian groups of bounded torsion | Asgar Jamneshan, Or Shalom | submitted |
An upper bound on the mean value of the Hooley delta function | Dimitris Koukouloupolous | To appear, Proc LMS |
Sumsets and entropy revisited | Ben Green Freddie Manners | Submitted, Random Structures and Algorithms |
The convergence of an alternating series of Erd\H{o}s, assuming the Hardy--Littlewood prime tuples conjecture | To appear, Comm. AMS | |
A lower bound on the mean value of the Hooley delta function | Kevin Ford Dimitris Koukouloupolous | Proc LMS 127, December 2023, 1865-1885http://dx.doi.org/10.1112/plms.12572 |
Monotone non-decreasing sequences of the Euler totient function | submitted, La Matematica | |
Undecidability of translational monotilings | Rachel Greenfeld | submitted, JEMS |
On a conjecture of Marton | Timothy Gowers Ben Green Freddie Manners | Submitted, Annals Math. |
Sums of GUE matrices and concentration of hives from correlation decay of eigengaps | To appear, Prob. Thy. Rel. Fields |
Patents