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Terence Chi-Shen Tao FAA FRS (Chinese: 陶哲軒; born 17 July 1975) is an Australian-American mathematician, Fields medalist, and professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins Chair in the College of Letters and Sciences.
In mathematical analysis, Strichartz estimates are a family of inequalities for linear dispersive partial differential equations. These inequalities establish size and decay of solutions in mixed norm Lebesgue spaces. They were first noted by Robert Strichartz and arose out of connections to the Fourier restriction problem. [1]
Tao, Terence. Nonlinear Dispersive Equations: Local and Global Analysis. Nonlinear Dispersive Equations: Local and Global Analysis. CBMS regional series in mathematics, 2006.
She became a student of Terence Tao at the University of California, Los Angeles (UCLA), where she completed her doctorate in 2006. Her dissertation was The Defocusing Energy-Critical Nonlinear Schrödinger Equation in Dimensions Five and Higher. [1] [2]
Strichartz estimates are named after him due to his application of such estimates to harmonic analysis on homogeneous and nonhomogeneous linear dispersive and wave equations; his work was subsequently generalized to nonlinear wave equations by Terence Tao and others.
2020 - Terence Tao for his Nonlinear Dispersive Equations: Local and Global Analysis, American Mathematical Society, 2006. ISBN ...
Colliander's research mostly addresses dynamical aspects of solutions of Hamiltonian partial differential equations, especially non-linear Schrödinger equation. [2] Colliander is a collaborator with Markus Keel, Gigliola Staffilani, Hideo Takaoka, and Terence Tao, forming a group known as the "I-team".
Around 2004, Emmanuel Candès, Justin Romberg, Terence Tao, and David Donoho proved that given knowledge about a signal's sparsity, the signal may be reconstructed with even fewer samples than the sampling theorem requires. [4] [5] This idea is the basis of compressed sensing.