276 citations · 4.5k across the 293 of their papers we have counts for
15 papers · 1 filter
The inverse conjecture for the Gowers norm over finite fields via the correspondence principle
Terence Tao, Tamar Ziegler
The inverse conjecture for the Gowers norms for finite-dimensional vector spaces over a finite field $\F$ asserts, roughly speaking, that a bounded function has la…
From the Littlewood-Offord problem to the Circular Law: universality of the spectral distribution of random matrices
Terence Tao, Van Vu
The famous \emph{circular law} asserts that if is an matrix with iid complex entries of mean zero and unit variance, then the empirical spectral distribution (ES…
Weakly turbulent solutions for the cubic defocusing nonlinear Schrödinger equation
J. Colliander, M. Keel, G. Staffilani +2
We consider the cubic defocusing nonlinear Schrödinger equation on the two dimensional torus. We exhibit smooth solutions for which the support of the conserved energy moves to hig…
Global regularity of wave maps V. Large data local wellposedness and perturbation theory in the energy class
Terence Tao
Using the harmonic map heat flow and the function spaces of Tataru and the author, we establish a large data local well-posedness result in the energy class for wave maps from two-…
Classification of Almost Quarter-Pinched Manifolds
Peter Petersen, Terence Tao
We show that if a simply connected manifold is almost quarter pinched then it is diffeomorphic to a CROSS (a compact rank one symmetric space) or a sphere.
Random matrices: Universality of ESDs and the circular law
Terence Tao, Van Vu, Manjunath Krishnapur
Given an complex matrix , let be the empirical spectral distribution (ESD) of its eige…
Global existence and uniqueness results for weak solutions of the focusing mass-critical non-linear Schrödinger equation
Terence Tao
We consider the focusing mass-critical NLS in high dimensions , with initial data having finite mass $M(u_0) = \int_{\R^d} |u_0(x…
The Mobius function is strongly orthogonal to nilsequences
Ben Green, Terence Tao
We show that the Mobius function mu(n) is strongly asymptotically orthogonal to any polynomial nilsequence n -> F(g(n)L). Here, G is a simply-connected nilpotent Lie group with a d…
Global regularity of wave maps IV. Absence of stationary or self-similar solutions in the energy class
Terence Tao
Using the harmonic map heat flow, we construct an energy class for wave maps from two-dimensional Minkowski space to hyperbolic spaces $\H^m$, and then show (conditi…
The sum-product phenomenon in arbitrary rings
Terence Tao
The \emph{sum-product phenomenon} predicts that a finite set in a ring should have either a large sumset or large product set unless it is in some sense "…
A global compact attractor for high-dimensional defocusing non-linear Schrödinger equations with potential
Terence Tao
We study the asymptotic behavior of large data solutions in the energy space in very high dimension to defocusing Schrödinger equations $i u_t + Δu = |…
Global regularity of wave maps III. Large energy from to hyperbolic spaces
Terence Tao
We show that wave maps from two-dimensional Minkowski space to hyperbolic spaces $\H^m$ are globally smooth in time if the initial data is smooth, conditionally on s…
Smooth analysis of the condition number and the least singular value
Terence Tao, Van Vu
Let $\a$ be a complex random variable with mean zero and bounded variance. Let be the random matrix of size whose entries are iid copies of $\a$ and be a fixed matr…
Why are solitons stable?
Terence Tao
The theory of linear dispersive equations predicts that waves should spread out and disperse over time. However, it is a remarkable phenomenon, observed both in theory and practice…
A remark on primality testing and decimal expansions
Terence Tao
We show that for any fixed base , a positive proportion of primes have the property that they become composite after altering any one of their digits in the base expansion;…