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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.
142 Higher Order Fourier Analysis, Terence Tao (2012, ISBN 978-0-8218-8986-2) 143 Lecture Notes on Functional Analysis: With Applications to Linear Partial Differential Equations, Alberto Bressan (2013, ISBN 978-0-8218-8771-4) 144 Dualities and Representations of Lie Superalgebras, Shun-Jen Cheng, Weiqiang Wang (2012, ISBN 978-0-8218-9118-6)
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.
Terence Tao, 254A, Notes 5: Free probability (10 February, 2010), course notes for graduate course on "Topics in random matrix ... recorded lectures on free probability
Why global regularity for Navier–Stokes is hard — Possible routes to resolution are scrutinized by Terence Tao. Navier–Stokes existence and smoothness (Millennium Prize Problem) A lecture on the problem by Luis Caffarelli. "Navier Stokes Equation – A Million-Dollar Question in Fluid Mechanics". Aleph Zero. June 3, 2020.
Tao, Terence (2014). Hilbert’s fifth problem and related topics. Graduate Studies in Mathematics. American Mathematical Society. pp. xiii+338. ISBN 978-1-4704-1564-8. Zbl 1298.22001. Montgomery, Deane; Zippin, Leo (1955). Topological Transformation Groups. Interscience Tracts in Pure and Applied Mathematics. Interscience Publishers. p. 281.
The Green–Tao theorem, proved by Ben Green and Terence Tao in 2004, [3] states that the sequence of prime numbers contains arbitrarily long arithmetic progressions. In other words, there exist arithmetic progressions of primes, with k terms, where k can be any natural number. The proof is an extension of Szemerédi's theorem.
One can find more efficient non-deterministic algorithms, as formally detailed in Terence Tao's blog [26] and implicitly mentioned in various papers. [27] [28] [29] An inequality of Terence Tao extends the Szemerédi regularity lemma, by revisiting it from the perspective of probability theory and information theory instead of graph theory. [30]