Terence Tao의 정보 

수상나이 
31 
출생년도 
1975 
사망년도 

출생지 
Australia 
현재소속 
University of California 
관련출판물 

시상내역 

Other Award 

연구단행본 
[1] Terence Tao, Van Vu, Additive Combinatorics, Cambridge University Press
[2] Terence Tao, Nonlinear dispersive equations: local and global analysis, CBMS regional conference series in mathematics, July 2006

연구실적 
[자세히 보기] 
연구논문 


 Kakeya,
Restriction, and BochnerRiesz problems.
This includes my work with Nets Katz, Izabella Laba, Gerd Mockenhaupt, Adam Sikora, Ana
Vargas, and Luis Vega
on the various variants of the Kakeya, Restriction, BochnerRiesz,
local smoothing, and L^p null form estimate problems.
Generally, these are areas of harmonic analysis with a
strong geometric and combinatorial flavor.
 Honeycombs
and Puzzles. This is joint work with Allen Knutson and Chris Woodward on the
honeycomb and puzzle combinatorial models for computing sums of
Hermitian matrices, tensor product multiplicities, and Schubert
calculus intersection numbers.
 Multilinear
operators. This is joint work with Michael Christ, Ciprian Demeter, Loukas Grafakos, Xiaochun Li, Camil Muscalu, Jill Pipher, Erin Terwilleger, and Christoph Thiele dealing
with multilinear operators such as the bilinear Hilbert transform and
Carleson's maximal operator, and their generalizations; a
characteristic feature of such operators is that one is forced to
decompose the phase plane in rather adaptive ways.
 Partial
Differential Equations. This is mostly work
on nonlinear dispersive and wave equations (and their associated
linear and multilinear estimates), but also includes some work on
elliptic theory and inverse scattering. Most of these papers are
joint work with one or more of my coauthors Ioan Bejenaru, Michael Christ, Jim Colliander, Phillipe LeFloch,
Andrew Hassell,
Mark Keel,
Sergiu Klainerman,
Igor
Rodnianski, Gigliola
Staffilani, Eitan Tadmor,
Hideo Takaoka, Gang Tian,
Jared Wunsch, Monica
Visan, and Xiaoyi Zhang.
 Sparse recovery. This is work in applied harmonic analysis,
signal processing, coding theory, and statistics, all centered around
the issue of how to recover a sparse or compressible signal as best as
possible if only a small number of (possibly noisy) measurements are
made. It turns out that an l^1
minimization (or “basis pursuit”) approach works remarkably well, as
long as the measurements obey suitable “uniform uncertainty principles”. This is joint work with Emmanuel Candes, Justin Romberg, Mark Rudelson,
and Roman Vershynin.
 Miscellaneous
Harmonic Analysis. This is my catchall
page for harmonic analysis, wavelet, or functional analysis papers
which are not directly related to multilinear operators, to the
Kakeya/Restriction/BochnerRiesz family of conjectures, or to sparse
recovery. This includes my work with Pascal Auscher,
Jon Bennet, Tony
Carbery, Michael
Christ, Michael
Cowling, Steve Hofman,
Alex
Iosevich, Nets
Katz, Camil Muscalu,
Christoph Thiele, Andreas Seeger, Brani Vidakovic, and Jim Wright.
 Arithmetic
Combinatorics and Number theory. This is my
work on the combinatorics of addition, multiplication, and arithmetic
progressions, and connections with number theory (for instance, in the
distribution of the primes) and ergodic theory (via Szemeredi’s
theorem), or with random matrices. This
includes my work with Jean Bourgain,
Kevin Costello, Ben
Green, Nets
Katz, Van Vu, and
Tamar Ziegler.
 Totally
Miscellaneous. This is anything not in the
above seven categories; this includes my work with Andrew Millard and Peter Hall.
 
