Jelaskan 2020 - Bolyai Prize dari Terence Tao

2021 - IEEE Jack S. Kilby Signal Processing Medal

Solving mathematical problems. A personal perspective. Oxford University Press, Oxford, 2006. xii+103 pp.

Nonlinear dispersive equations. Local and global analysis. CBMS Regional Conference Series in Mathematics, 106. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 2006. xvi+373 pp.

Structure and randomness. Pages from year one of a mathematical blog. American Mathematical Society, Providence, RI, 2008. xii+298 pp.

Poincaré's legacies, pages from year two of a mathematical blog. Part I. American Mathematical Society, Providence, RI, 2009. x+293 pp.

Poincaré's legacies, pages from year two of a mathematical blog. Part II. American Mathematical Society, Providence, RI, 2009. x+292 pp.

An epsilon of room, I: real analysis. Pages from year three of a mathematical blog. Graduate Studies in Mathematics, 117. American Mathematical Society, Providence, RI, 2010. xii+349 pp.

An epsilon of room, II. Pages from year three of a mathematical blog. American Mathematical Society, Providence, RI, 2010. viii+248 pp.

(with Van H. Vu) Additive combinatorics. Cambridge Studies in Advanced Mathematics, 105. Cambridge University Press, Cambridge, 2010. xviii+512 pp.

An introduction to measure theory. Graduate Studies in Mathematics, 126. American Mathematical Society, Providence, RI, 2011. xvi+206 pp.

Topics in random matrix theory. Graduate Studies in Mathematics, 132. American Mathematical Society, Providence, RI, 2012. x+282 pp.

Higher order Fourier analysis. Graduate Studies in Mathematics, 142. American Mathematical Society, Providence, RI, 2012. x+187 pp.

Compactness and contradiction. American Mathematical Society, Providence, RI, 2013. xii+256 pp.

Analysis. I. Third edition. Texts and Readings in Mathematics, 37. Hindustan Book Agency, New Delhi, 2014. xviii+347 pp.

Analysis. II. Third edition. Texts and Readings in Mathematics, 38. Hindustan Book Agency, New Delhi, 2014. xvi+218 pp.

Hilbert's fifth problem and related topics. Graduate Studies in Mathematics, 153. American Mathematical Society, Providence, RI, 2014. xiv+338 pp.

Expansion in finite simple groups of Lie type. Graduate Studies in Mathematics, 164. American Mathematical Society, Providence, RI, 2015. xiv+303 pp.

Artikel penelitian mengenai persamaan diferensial parsial dispersive

Keel, Markus; Tao, Terence. Endpoint Strichartz estimates. Amer. J. Math. 120 (1998), no. 5, 955–980.

Colliander, J.; Keel, M.; Staffilani, G.; Takaoka, H.; Tao, T. Global well-posedness for Schrödinger equations with derivative. SIAM J. Math. Anal. 33 (2001), no. 3, 649–669.

Tao, Terence. Global regularity of wave maps. II. Small energy in two dimensions. Comm. Math. Phys. 224 (2001), no. 2, 443–544.

Colliander, J.; Keel, M.; Staffilani, G.; Takaoka, H.; Tao, T. A refined global well-posedness result for Schrödinger equations with derivative. SIAM J. Math. Anal. 34 (2002), no. 1, 64–86.

Colliander, J.; Keel, M.; Staffilani, G.; Takaoka, H.; Tao, T. Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation. Math. Res. Lett. 9 (2002), no. 5–6, 659–682.

Christ, Michael; Colliander, James; Tao, Terrence. Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations. Amer. J. Math. 125 (2003), no. 6, 1235–1293.

Colliander, J.; Keel, M.; Staffilani, G.; Takaoka, H.; Tao, T. Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋. J. Amer. Math. Soc. 16 (2003), no. 3, 705–749.

Colliander, J.; Keel, M.; Staffilani, G.; Takaoka, H.; Tao, T. Multilinear estimates for periodic KdV equations, and applications. J. Funct. Anal. 211 (2004), no. 1, 173–218.

Colliander, J.; Keel, M.; Staffilani, G.; Takaoka, H.; Tao, T. Global existence and scattering for rough solutions of a nonlinear Schrödinger equation on ℝ3. Comm. Pure Appl. Math. 57 (2004), no. 8, 987–1014.

Tao, Terence. Global well-posedness of the Benjamin-Ono equation in H1(ℝ). J. Hyperbolic Differ. Equ. 1 (2004), no. 1, 27–49.

Bejenaru, Ioan; Tao, Terence. Sharp well-posedness and ill-posedness results for a quadratic non-linear Schrödinger equation. J. Funct. Anal. 233 (2006), no. 1, 228–259.

Tao, Terence; Visan, Monica; Zhang, Xiaoyi. The nonlinear Schrödinger equation with combined power-type nonlinearities. Comm. Partial Differential Equations 32 (2007), no. 7–9, 1281–1343.

Colliander, J.; Keel, M.; Staffilani, G.; Takaoka, H.; Tao, T. Global well-posedness and scattering for the energy-critical nonlinear Schrödinger equation in ℝ3. Ann. of Math. (2) 167 (2008), no. 3, 767–865.

Killip, Rowan; Tao, Terence; Visan, Monica. The cubic nonlinear Schrödinger equation in two dimensions with radial data. J. Eur. Math. Soc. (JEMS) 11 (2009), no. 6, 1203–1258.

Artikel penelitian mengenai compressed sensing

Candes, Emmanuel J.; Tao, Terence. Decoding by linear programming. IEEE Trans. Inform. Theory 51 (2005), no. 12, 4203–4215.

Candes, Emmanuel J.; Tao, Terence. Near-optimal signal recovery from random projections: universal encoding strategies? IEEE Trans. Inform. Theory 52 (2006), no. 12, 5406–5425.

Candès, Emmanuel J.; Romberg, Justin K.; Tao, Terence. Stable signal recovery from incomplete and inaccurate measurements. Comm. Pure Appl. Math. 59 (2006), no. 8, 1207–1223.

Candès, Emmanuel J.; Romberg, Justin; Tao, Terence. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inform. Theory 52 (2006), no. 2, 489–509.

Candes, Emmanuel; Tao, Terence. The Dantzig selector: statistical estimation when p is much larger than n. Ann. Statist. 35 (2007), no. 6, 2313–2351.

Candès, Emmanuel J.; Tao, Terence. The power of convex relaxation: near-optimal matrix completion. IEEE Trans. Inform. Theory 56 (2010), no. 5, 2053–2080.

Artikel penelitian mengenai teori bilangan analitik

Bourgain, J.; Katz, N.; Tao, T. A sum-product estimate in finite fields, and applications. Geom. Funct. Anal. 14 (2004), no. 1, 27–57.

Green, Ben; Tao, Terence. The primes contain arbitrarily long arithmetic progressions. Ann. of Math. (2) 167 (2008), no. 2, 481–547.

Green, Benjamin; Tao, Terence. Linear equations in primes. Ann. of Math. (2) 171 (2010), no. 3, 1753–1850.

Artikel penelitian mengenai matriks acak

Tao, Terence; Vu, Van. Random matrices: universality of ESDs and the circular law. With an appendix by Manjunath Krishnapur. Ann. Probab. 38 (2010), no. 5, 2023–2065.

Tao, Terence; Vu, Van. Random matrices: universality of local eigenvalue statistics. Acta Math. 206 (2011), no. 1, 127–204.

Artikel penelitian mengenai analisis harmonik

Tao, Terence; Vargas, Ana; Vega, Luis. A bilinear approach to the restriction and Kakeya conjectures. J. Amer. Math. Soc. 11 (1998), no. 4, 967–1000.

Tao, Terence. Multilinear weighted convolution of L2-functions, and applications to nonlinear dispersive equations. Amer. J. Math. 123 (2001), no. 5, 839–908.

Muscalu, Camil; Tao, Terence; Thiele, Christoph. Multi-linear operators given by singular multipliers. J. Amer. Math. Soc. 15 (2002), no. 2, 469–496.

Tao, T. A sharp bilinear restrictions estimate for paraboloids. Geom. Funct. Anal. 13 (2003), no. 6, 1359–1384.

Tao, Terence. Fuglede's conjecture is false in 5 and higher dimensions. Math. Res. Lett. 11 (2004), no. 2–3, 251–258.

Bennett, Jonathan; Carbery, Anthony; Tao, Terence. On the multilinear restriction and Kakeya conjectures. Acta Math. 196 (2006), no. 2, 261–302.

Artikel penelitian mengenai kombinatorika aljabar''

Knutson, Allen; Tao, Terence. The honeycomb model of GLn(ℂ) tensor products. I. Proof of the saturation conjecture. J. Amer. Math. Soc. 12 (1999), no. 4, 1055–1090.

Knutson, Allen; Tao, Terence; Woodward, Christopher. The honeycomb model of GLn(ℂ) tensor products. II. Puzzles determine facets of the Littlewood-Richardson cone. J. Amer. Math. Soc. 17 (2004), no. 1, 19–48.