|Terence Tao의 정보
||University of California
 Terence Tao, Van Vu, Additive Combinatorics, Cambridge University Press
 Terence Tao, Nonlinear dispersive equations: local and global analysis, CBMS regional conference series in mathematics, July 2006
Restriction, and Bochner-Riesz 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, Bochner-Riesz,
local smoothing, and L^p null form estimate problems.
Generally, these are areas of harmonic analysis with a
strong geometric and combinatorial flavor.
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.
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.
Differential Equations. This is mostly work
on non-linear 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 co-authors Ioan Bejenaru, Michael Christ, Jim Colliander, Phillipe LeFloch,
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.
Harmonic Analysis. This is my catch-all
page for harmonic analysis, wavelet, or functional analysis papers
which are not directly related to multilinear operators, to the
Kakeya/Restriction/Bochner-Riesz family of conjectures, or to sparse
recovery. This includes my work with Pascal Auscher,
Jon Bennet, Tony
Cowling, Steve Hofman,
Katz, Camil Muscalu,
Christoph Thiele, Andreas Seeger, Brani Vidakovic, and Jim Wright.
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
Katz, Van Vu, and
Miscellaneous. This is anything not in the
above seven categories; this includes my work with Andrew Millard and Peter Hall.