Vitae and Bibliography for Terence Tao

Last updated: Aug 21, 2003

Personal

Date of Birth:	1975
Birthplace:	Adelaide, Australia
Citizenship:	Australian
Marital status:	Married
Visa status:	O-1
Permanent Address:	6 Jennifer Ave, Bellevue Heights, SA 5050, Australia
Current Address	Dept. of Math. UCLA 405 Hilgard Ave 90095 LA, CA
Phone:	1-310-206-4844
Fax:	1-310-206-6673
E-mail:	tao@math.ucla.edu
WWW:	http://www.math.ucla.edu/~tao

Education

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

Research interests

Primary:  Oscillatory integrals and Kakeya maximal functions Arithmetic and geometric combinatorics; geometric analysis Non-linear dispersive equations Multilinear operators (e.g. Bilinear Hilbert Transform) Representation and symplectic theory of U(n); honeycombs Inverse scattering and integrable systems for rough data

Secondary:  Geometric PDE (e.g. Yang-Mills) Analytic number theory and harmonic analysis General Relativity

Experience

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

Awards

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	Fulbright Association	Post-graduate award
1995	Sloan Foundation	Post-graduate Fellowship
1997-2000	National Science Foundation	Summer grant DMS 9706964
1999-2001	Sloan Foundation	Research Fellowship
1999-2004	David and Lucille Packard Foundation	Foundation Fellowship
2000	Salem Prize	2000 Salem Prize
2002	American Mathematical Society	Bocher Prize

 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

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)	Distance set problems	2002-
Roman Sasyk	Graduate Student, UCLA (joint with Sorin Popa)	Szemeredi's theorem	2002-
Monica Visan	Graduate Student, UCLA	Schrodinger operators with potential	2003-
Jon Bueti	Graduate Student, UCLA	Finite field x-ray and k-plane estimates	2003-

Miscellaneous Duties

1998-	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-	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-	Journal of Partial Differential Equations and Dynamical Systems	Associate Editor

Articles published, submitted, or in preparation

Title	With	Status
Weak-type endpoint bounds for Riesz means		Proc. Amer. Math. Soc. 124 (1996), 2797-2805
On the almost-everywhere convergence of wavelet summation methods		ACHA 3 (1996), 384-387
Harmonic convolution operators on Lipschitz graphs		Adv. Appl. Clifford Alg. 6 (1996), 207-218
On the Structure of Projective Group Representations in Quaternionic Hilbert Space	Andrew Millard	J. Math. Phys. 37 (1996), 5848-5857
The Bochner-Riesz conjecture implies the restriction conjecture		Duke Math. J. 96 (1999), 363-376
Endpoint Strichartz Estimates	Mark Keel	Amer. J. Math., 120 (1998), 955-980
The weak-type endpoint Bochner-Riesz conjecture and related topics		Indiana U. Math. J. 47 (1998), 1097-1124
Low regularity semi-linear wave equations		Comm. PDE 24 (1999), 599—630
Small data blowup for semilinear Klein-Gordon equations	Mark Keel	Amer. J. Math. 121 (1999), 629-669
A bilinear approach to the restriction and Kakeya conjectures	Ana Vargas  Luis Vega	J. Amer. Math. Soc. 11 (1998), 967-1000
On the Maximal Bochner-Riesz conjecture in the plane, for p<2		Trans. Amer. Math. Soc. 354 (2002), 1947-1959
Almost everywhere convergence of general wavelet shrinkage estimators	Brani Vidakovic	ACHA 9 (2000), 72-82
Local and global well-posedness of wave maps in R^{1+1} for rough data	Mark Keel	IMRN 21 (1998), 1117-1156
A bilinear approach to cone multipliers I. Restriction theorems	Ana Vargas	GAFA 10 (2000), 185-215
A bilinear approach to cone multipliers II. Applications	Ana Vargas	GAFA 10 (2000), 216-258
The honeycomb model of GL_n(C) tensor products I. Proof of the saturation conjecture	Allen Knutson	J. Amer. Math. Soc.12 (1999), 1055--1090
Spherically averaged endpoint Strichartz estimates for the two-dimensional Schrödinger equation		Comm. PDE 25 (2000), 1471-1485
Ill-posedness for one-dimensional wave maps at the critical regularity		Amer. J. Math., 122 (2000), 451-463
An improved bound on the Minkowski dimension of Besicovitch sets in R^3	Nets Katz Izabella Laba	Annals of Math. 152 (2000),  383-446
Weak-type endpoint bounds for homogeneous convolution operators		Indiana U. Math. J., 48 (1999), 1547-1584
The honeycomb model of GL_n(C) tensor products II. Facets of the Littlewood-Richardson cone	Allen Knutson Chris Woodward	to appear, J. Amer. Math. Soc.
Global well-posedness for large data for the Maxwell-Klein-Gordon equation below the energy norm	Mark Keel	in preparation
Endpoint bilinear restriction theorems for the cone, and some sharp null form estimates		Math. Z. 238 (2001), 215-268
Bounds on arithmetic projections, and applications to the Kakeya conjecture	Nets Katz	Math Res. Letters 6 (1999), 625-630
An x-ray transform estimate in R^n	Izabella Laba	Revista Mat. Iber. 17 (2001), 375-408
Multilinear operators with singular multipliers	Camil Muscalu  Christoph Thiele	J. Amer. Math. Soc. 15 (2002), 469-496
Convex bodies with a point of curvature do not admit exponential bases	Alex Iosevich  Nets Katz	Amer. J. Math. 123 (2001), 115-120
Endpoint multiplier theorems of Marcinkiewicz type	Jim Wright	Revista Mat. Iber. 17 (2001), 521-558
Some connections between the Falconer and Furstenburg conjectures	Nets Katz	New York J. Math. 7 (2001), 148-187
Sharp Lorentz space estimates for rough operators	Andreas Seeger	Math. Annalen 320 (2001) 2, 381-415
L^p improving estimates for averages along curves	Jim Wright	J. Amer. Math. Soc. 16 (2003), 605-638
A converse extrapolation theorem for translation-invariant operators		J. Funct. Anal. 180 (2001), 1-10
Kakeya and restriction phenomena for finite fields	Gerd Mockenhaupt	to appear, Duke Math. J.
Fuglede's conjecture for convex bodies in the plane	Alex Iosevich  Nets Katz	to appear, Math. Res. Letters
Some light on Littlewood-Paley theory	Michael Cowling	Math. Annalen 321 (2001) 4, 885-888
On the Minkowski dimension of Besicovitch sets in medium dimension	Izabella Laba	GAFA 11 (2001), 773-806
Local well-posedness for the Yang-Mills equation below the energy norm		JDE 189 (2003), 366-382
Uniform estimates for paraproducts	Camil Muscalu  Christoph Thiele	Journal d'Analyse de Jerusalem 87 (2002), 369-384
Uniform estimates for multi-linear operators with modulation symmetry	Camil Muscalu  Christoph Thiele	Journal d'Analyse de Jerusalem 88 (2002), 255-309
Almost conservation laws and global rough solutions to a nonlinear Schrodinger equation	Jim Colliander Mark Keel Gigliola Staffilani  Hideo Takaoka	to appear, Math. Res. Letters
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	submitted, Math. Annalen
L^p estimates for the "biest" II.  The Fourier model.	Camil Muscalu Christoph Thiele	submitted, Math. Annalen
Estimates for iterated Bilinear Hilbert Transforms in the Walsh model	Camil Muscalu Christoph Thiele	in preparation
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	to appear,  J. Funct. Anal.
Global well-posedness for the Schrodinger equations with derivative	Jim Colliander Mark Keel Gigliola Staffilani  Hideo Takaoka	to appear, Siam J. Math.
Endpoint mapping properties of spherical maximal functions	Andreas Seeger Jim Wright	J. Institut Math. Jussieu 2 (2001) 1, 109-144
Pointwise convergence of lacunary spherical means	Andreas Seeger Jim Wright	Mt. Holyoke Proceedings (2001), 341-352
Singular maximal functions and Radon transforms near L^1	Andreas Seeger Jim Wright	to appear, Amer. J. Math.
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	to appear, Duke Math. J.
Puzzles and explicit solutions to Schubert intersection problems	Allen Knutson	in preparation
A refined global well-posedness for the Schrodinger equations with derivative	Jim Colliander Mark Keel Gigliola Staffilani  Hideo Takaoka	to appear, Siam J. Math.
Improved low-regularity global well-posedness results for NLS	Jim Colliander Mark Keel Gigliola Staffilani  Hideo Takaoka	in preparation
Polynomial upper bounds for the orbital instability of the 1D cubic NLS below the energy norm	Jim Colliander Mark Keel Gigliola Staffilani  Hideo Takaoka	to appear, Discrete Cont. Dynam. Systems
Polynomial growth and orbital instability bounds for $L^2$-subcritical NLS below the energy norm	Jim Colliander Mark Keel Gigliola Staffilani Hideo Takaoka	to appear, Comm. Pure Appl. Anal.
Scattering below the energy norm for 3D NLS	Jim Colliander Mark Keel Gigliola Staffilani  Hideo Takaoka	submitted, CPAM
A geometric optics approach to bilinear wave estimates	Sergiu Klainerman Igor Rodnianski	to appear, Journal d'Analyse de Jerusalem
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	submitted, Comm. Anal. Geom.
A new bound for finite field Besicovitch sets in four dimensions		to appear, Pacific J. Math
A discrete model for the bi-carleson operator	Camil Muscalu Christoph Thiele	GAFA 12 (2002), 1324-1364
A counterexample to a multilinear endpoint question of Christ and Kiselev	Camil Muscalu Christoph Thiele	to appear, Math. Res. Letters
Multilinear interpolation between adjoint operators	Loukas Grafakos	to appear, J. Funct. Anal.
Carleson measures, trees, extrapolation, and T(b) theorems	Pascal Auscher Steve Hofman Camil Muscalu Christoph Thiele	to appear, Publications Matematiques Barcelona
Weak-type (1,1) bounds for Fourier integral operators		to appear, J. Aust. Math. Soc.
Sharp constants for Hardy's inequality for fractals	Boris Pavlov	in preparation
Removing singularities in gauge fields in higher dimensions	Gang Tian	submitted, J. Amer. Math. Soc.
Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocussing equations	Michael Christ Jim Colliander	submitted, Amer. J. Math.
Global regularity for the Maxwell-Klein-Gordon equation in high dimensions	Sergiu Klainerman Igor Rodnianski	in preparation
Symplectic non-squeezing for periodic KdV	Jim Colliander Mark Keel Gigliola Staffilani Hideo Takaoka	in preparation
Upper and lower bounds for Dirichlet eigenfunctions	Andrew Hassell	Math. Res. Letters 9 (2002), 289-305
Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocussing equations II.	Michael Christ Jim Colliander	in preparation
Relative efficiencies of kernel and local likelihood density estimators	Peter Hall	to appear, J. Royal Statistical Society B
A sharp bilinear restriction estimate for paraboloids		to appear, GAFA
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		to appear,  CMA proceedings 40
Existence globale et diffusion pour l'équation de Schrödinger nonlinéaire répulsive cubique sur R^3 en dessous l'espace d'énergie	Jim Colliander Mark Keel Gigliola Staffilani Hideo Takaoka	submitted, Forges les Eaux proceedings
A sum-product estimate for finite fields, and applications	Jean Bourgain Nets Katz	to appear, GAFA
Some recent progress on the Restriction conjecture		submitted, Proceedings, Fourier Analysis and Convexity Workshop
L^p bounds for a maximal dyadic sum operator	Loukas Grafakos Erin Terwilleger	submitted, Math. Z.
An extension of the Coifman-Meyer theorem on product domains	Camil Muscalu Jill Pipher Christoph Thiele	in preparation
On multilinear oscillatory singular integrals	Michael Christ Xiaochun Li Christoph Thiele	in preparation
Randomized Beltrami coefficients	Steffen Rohde	in preparation
Long-time decay estimates for Schrodinger equations on manifolds	Igor Rodnianski	in preparation
Interaction Morawetz estimates of Strichartz type for Schrodinger equations on manifolds	Andrew Hassell Jared Wunsch	in preparation
A positive proof of the Littlewood-Richardson rule using the octahedron recurrence	Allen Knutson Chris Woodward	submitted, Electron. J. Combin.
Global well-posedness of the Benjamin-Ono equation in H^1(R)		submitted, J. Hyperbolic Diff. Eq.
Fuglede's conjecture is false in 5 and higher dimensions		submitted, Math. Res. Letters

Books published

• "Solving Mathematical Problems: A Personal Perspective", Deakin University Press, 1992.