Belgian mathematician (1954–2018)
Jean Louis, baron Bourgain (French: [buʁɡɛ̃] (1954-02-28 ) 28 February 1954 –(2018-12-22 ) 22 December 2018) was a Belgian mathematician. He was awarded theFields Medal in 1994 in recognition of his work on several core topics ofmathematical analysis such as the geometry ofBanach spaces ,harmonic analysis ,ergodic theory andnonlinear partial differential equations frommathematical physics .[ 3]
Bourgain received his PhD from theVrije Universiteit Brussel in 1977. He was a faculty member at theUniversity of Illinois Urbana-Champaign and, from 1985 until 1995, professor atInstitut des Hautes Études Scientifiques atBures-sur-Yvette in France, at theInstitute for Advanced Study inPrinceton, New Jersey from 1994 until 2018.[ 4] Annals of Mathematics UC Berkeley .[ 5]
His research work included several areas ofmathematical analysis such as thegeometry ofBanach spaces ,harmonic analysis ,analytic number theory ,combinatorics ,ergodic theory ,partial differential equations andspectral theory , and later alsogroup theory . He proved the uniqueness of the solutions for the initial value problem of theKorteweg–De Vries equation . He formulated what became known as the Bourgain slicing problem in high-dimensional convex geometry. In 1985, he proved Bourgain's embedding theorem in metric dimension reduction, which states that every metric space can be embedded into anl p {\displaystyle l_{p}} O ( log 2 ( n ) ) {\displaystyle O(\log ^{2}(n))} O ( log ( n ) ) {\displaystyle O(\log(n))} Vitali Milman , he contributed to progress onMahler’s conjecture in 1987. In 2000, he connected theKakeya problem toarithmetic combinatorics .[ 6] [ 7] [ 8]
Together with Ciprian Demeter andLarry Guth , he provedVinogradov's mean-value theorem in 2015.
Bourgain was diagnosed withpancreatic cancer in late 2014. He died of it on 22 December 2018 at a hospital in Bonheiden, Belgium.[ 9]
Awards and recognition [ edit ] Bourgain received several awards during his career, the most notable being theFields Medal in 1994.
In 2009 Bourgain was elected a foreign member of theRoyal Swedish Academy of Sciences .[ 10]
In 2010, he received theShaw Prize in Mathematics.[ 11]
In 2012, he andTerence Tao received theCrafoord Prize in Mathematics from theRoyal Swedish Academy of Sciences .[ 12]
In 2015, he was made a baron by KingPhilippe of Belgium .[ 13]
In 2017, he received theBreakthrough Prize in Mathematics .[ 14]
In 2018, he received theSteele Prize for Lifetime Achievement .[ 15]
Selected publications [ edit ] Bourgain, Jean (1983)."Some remarks on Banach spaces in which martingale difference sequences are unconditional" (PDF) .Arkiv för Matematik .21 (1):163– 168.Bibcode :1983ArM....21..163B .doi :10.1007/BF02384306 S2CID 121419327 . Banach space andmartingale .)Bourgain, J. (1985). "On lipschitz embedding of finite metric spaces in Hilbert space".Israel Journal of Mathematics 52 (1– 2):46– 52.doi :10.1007/BF02776078 .S2CID 121649019 . Bourgain, J. (1986). "Averages in the plane over convex curves and maximal operators".Journal d'Analyse Mathématique 47 :69– 85.doi :10.1007/BF02792533 .S2CID 120149032 . Bourgain, J.; Milman, V. D. (1987). "New volume ratio properties for convex symmetric bodies inR n , {\displaystyle \mathbb {R} ^{n},} Inventiones Mathematicae .88 (2):319– 340.Bibcode :1987InMat..88..319B .doi :10.1007/BF01388911 .S2CID 123312114 . Bourgain, Jean (1989)."Pointwise ergodic theorems for arithmetic sets" Publications Mathématiques de l'IHÉS .69 :5– 41.doi :10.1007/BF02698838 .S2CID 55288816 . Bourgain, J. (1993). "Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations".Geometric and Functional Analysis .3 (3):209– 262.doi :10.1007/BF01895688 .S2CID 124191732 . Bourgain, J. (1994)."Periodic nonlinear Schrödinger equation and invariant measures" .Communications in Mathematical Physics .166 (1):1– 26.Bibcode :1994CMaPh.166....1B .doi :10.1007/BF02099299 .S2CID 53447933 . Bourgain, J. (1998)."Quasi-Periodic Solutions of Hamiltonian Perturbations of 2D Linear Schrödinger Equations" .Annals of Mathematics .148 (2):363– 439.doi :10.2307/121001 .JSTOR 121001 . Friedgut, Ehud; Jean Bourgain, Appendix by (1999)."Sharp thresholds of graph properties, and thek {\displaystyle k} .Journal of the American Mathematical Society .12 (4):1017– 1054.doi :10.1090/s0894-0347-99-00305-7 Bourgain, J. (1999)."Global Wellposedness of Defocusing Critical Nonlinear Schrödinger Equation in the Radial Case" .Journal of the American Mathematical Society .12 (1):145– 171.doi :10.1090/S0894-0347-99-00283-0 JSTOR 2646233 . Bourgain, Jean; Brezis, Haim; Mironescu, Petru (2001)."Another look at Sobolev spaces" . pp. 439– 455. Sobolev space .)Bourgain, J. (2002)."Nonlinear partial differential equations and applications: On the global Cauchy problem for the nonlinear Schrödinger equation" .Proceedings of the National Academy of Sciences .99 (24):15262– 15268.doi :10.1073/pnas.222494399 ISSN 0027-8424 .PMC 137704 PMID 12432098 . Bourgain, Jean; Katz, Nets; Tao, Terence (2004). "A sum-product estimate in finite fields, and applications".Geometric and Functional Analysis .14 :27– 57.arXiv :math/0301343 doi :10.1007/s00039-004-0451-1 .S2CID 14097626 . Bourgain, J. (2005). "More on the Sum-Product Phenomenon in Prime Fields and its Applications".International Journal of Number Theory .01 :1– 32.doi :10.1142/s1793042105000108 . Bourgain, Jean (2017), "Decoupling, exponential sums and the Riemann zeta function",Journal of the American Mathematical Society 30 (1):205– 224,arXiv :1408.5794 doi :10.1090/jams/860 ,MR 3556291 ,S2CID 118064221 Lindelöf hypothesis .)J. Bourgain (1 October 1981).New Classes of Lp -Spaces ISBN 978-3-540-11156-6 Bourgain, Jean; Casazza, Peter G.; Lindenstrauss, J.; Tzafriri, Lior (1985).Banach Spaces with a Unique Unconditional Basis, up to Permutation ISBN 978-0-8218-2323-1 Bourgain, Jean (1999).Global Solutions of Nonlinear Schrödinger Equations ISBN 9780821819197 [ 16] [ 17] Bourgain, Jean (November 2004).Green's Function Estimates for Lattice Schrödinger Operators and Applications. (AM-158) ISBN 9781400837144 Bourgain, Jean; Kening, Carlos E.; Klainerman, Sergiu, eds. (10 January 2009).Mathematical Aspects of Nonlinear Dispersive Equations (AM-163) ISBN 978-1-4008-2779-4 ^ Jean Bourgain at theMathematics Genealogy Project ^ "Death of mathematician Jean Bourgain" .The Brussels Times . Retrieved30 December 2018 .^ "Fields Medals and Nevanlinna Prize 1994" .www.mathunion.org . Retrieved31 August 2019 .^ O'Connor, John J.;Robertson, Edmund F. ,"Jean Bourgain" ,MacTutor History of Mathematics Archive University of St Andrews ^ "Jean Bourgain | Department of Mathematics at University of California Berkeley" .math.berkeley.edu . Retrieved23 April 2016 .^ Bourgain, J. (2000). "Harmonic analysis and combinatorics: How much may they contribute to each other?".Mathematics: Frontiers and Perspectives . IMU/Amer. Math. Soc. pp. 13– 32. ^ Tao, Terence (March 2001)."From Rotating Needles to Stability of Waves: Emerging Connections between Combinatorics, Analysis and PDE" (PDF) .Notices of the American Mathematical Society 48 (3):297– 303.arXiv :math/0008098 Bibcode :2000math......8098T .^ Tao, Terence Chi-Shen (2019)."Jean Bourgain, problem solver" .Proceedings of the National Academy of Sciences .116 (28):13717– 13718.Bibcode :2019PNAS..11613717T .doi :10.1073/pnas.1901965116 ISSN 0027-8424 .PMC 6628665 PMID 31209024 . ^ Kenneth Chang (16 January 2019),"Jean Bourgain, Problem-Conquering Mathematician, Is Dead at 64" ,New York Times ^ Royal Swedish Academy of Sciences: Many new members elected to the Academy , press release on 12 February 2009^ "Shaw Prize Press Release" . Archived fromthe original on 4 July 2010. Retrieved28 May 2010 .^ Crafoord Press Release Archived 27 December 2012 at theWayback Machine on 19 January 2012^ Jean Bourgain’s Coat of Arms —Institute for Advanced Study^ Breakthrough Prize Press Release ^ Jean Bourgain to Receive 2018 Steele Prize for Lifetime Achievement ^ Staffilani, Gigliola (2003)."Review ofGlobal Solutions of Nonlinear Schrödinger Equations by Jean Bourgain" .Bull. Amer. Math. Soc .40 :99– 107.doi :10.1090/S0273-0979-02-00956-4 ^ Kenig, Carlos E. (2020)."On the work of Jean Bourgain in nonlinear dispersive equations" .Bulletin of the American Mathematical Society .58 (2):173– 189.doi :10.1090/bull/1718 ISSN 0273-0979 . O'Connor, John J.;Robertson, Edmund F. ,"Jean Bourgain" ,MacTutor History of Mathematics Archive University of St Andrews Daubechies, Ingrid; Delbaen, Freddy; Guth, Larry; Jitomirskaya, Svetlana; Kontorovich, Alex; Lindenstrauss, Elon; Milman, Vitali; Pisier, Gilles; Rudnick, Zeev; Sarnak, Peter; Schlag, Wilhelm; Staffilani, Gigliola; Tao, Terence; Varjú, Péter (June 2021)."Remembering Jean Bourgain (1954–2018)" (PDF) .Notices of the American Mathematical Society 68 (6):942– 957.doi :10.1090/noti2290 "The Search for Randomness | Jean Bourgain" .YouTube . Institute for Advanced Study. 25 April 2012."Jean Bourgain - 1/2 The orbital circle method and applications..." YouTube . Institut des Hautes Études Scientifiques (IHÉS). 14 July 2014."Expansion in Linear Groups and Applications - Jean Bourgain" .YouTube . Institute for Advanced Study. 8 March 2016."Diphantine properties of Markoff numbers - Jean Bourgain" .YouTube . Institute for Advanced Study. 4 April 2016."Working with Bourgain - Enrico Bombieri" .YouTube . Institute for Advanced Study. 26 May 2016."Decoupling in harmonic analysis and applications to number theory - Jean Bourgain" .YouTube . Institute for Advanced Study. 27 July 2016."On Zaremba's Conjecture on Continued Fractions - Jean Bourgain" .YouTube . Institute for Advanced Study. 19 August 2016."Jean Bourgain's Impact on Asymptotic Geometric Analysis; Selected Topics - Vital Milman" .YouTube . Institute for Advanced Study. 4 June 2019.
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