Terence Tao's research interests

Research interests

Bochner-Riesz, Restriction, and Kakeya estimates
Linear and bilinear dispersive equation estimates, and well-posedness of dispersive equations for rough data
The symplectic and representation theory of U(n) and similar groups, and the honeycomb model
L^p properties of multilinear singular integrals and multipliers, and applications to Schrodinger eigenfunctions
Analysis of dispersive PDE (KdV, NLS, NLW, Wave maps, beyond the reach of iterative (or Fourier) methods
Spectral sets and Fuglede's conjecture
Endpoint estimates for rough operators

NB: the above links have not been updated since 1998.

Active projects (not close to completion)

The averaging lemma in dissipative transport equations	Eitan Tadmor
Boundedness of 1D Schrodinger eigenfunctions with L^2 potential	Camil Muscalu Christoph Thiele
Well-posedness of Einstein's equations with L^2 curvature	Sergiu Klainerman Igor Rodnianski
Exact sequences of torsion modules	Bill Fulton
Global regularity for wave maps III. Large data in two dimensions	Mark Keel
The Schubert calculus for flag manifolds	Allen Knutson
The two-weight weak-type problem for the Hilbert transform	Carlos Perez
On sections of convex bodies by hyperplanes at a fixed distance from the origin	Alexander Koldobsky