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Jean Bourgain



Born  Ostend, Belgium

28 February 1954
Died  22 December 2018 Bonheiden, Belgium

(aged 64)
Alma mater  Vrije Universiteit Brussel 
Known for  Analytic number theory Harmonic analysis Ergodic theory Banach spaces Partial differential equations 
Awards  Salem Prize (1983) Ostrowski Prize (1991) Fields Medal (1994) Shaw Prize (2010) Crafoord Prize (2012) Breakthrough Prize in Mathematics (2017) Steele Prize (2018) 
Scientific career  
Fields  Mathematics 
Institutions  Institute for Advanced Study University of Illinois, UrbanaChampaign University of California, Berkeley 
Doctoral advisor  Freddy Delbaen 
Doctoral students  James Colliander Péter Varjú 
Influences  Laurent Schwartz Bernard Maurey Gilles Pisier Vitali Milman 
Influenced  Terence Tao 
Jean, Baron Bourgain (French: [buʁɡɛ̃]; 28 February 1954 – 22 December 2018 ) was a Belgian mathematician. He was awarded the Fields Medal in 1994 in recognition of his work on several core topics of mathematical analysis such as the geometry of Banach spaces, harmonic analysis, ergodic theory and nonlinear partial differential equations from mathematical physics.
Biography
Bourgain received his PhD from the Vrije Universiteit Brussel in 1977. He was a faculty member at the University of Illinois, UrbanaChampaign and, from 1985 until 1995, professor at Institut des Hautes Études Scientifiques at BuressurYvette in France, at the Institute for Advanced Study in Princeton, New Jersey from 1994 until 2018. He was an editor for the Annals of Mathematics. From 2012 to 2014, he was a visiting scholar at UC Berkeley.
His research work included several areas of mathematical analysis such as the geometry of Banach spaces, harmonic analysis, analytic number theory, combinatorics, ergodic theory, partial differential equations and spectral theory, and later also group theory. In 2000, Bourgain connected the Kakeya problem to arithmetic combinatorics. As a researcher, he was the author or coauthor of more than 500 articles.
Bourgain was diagnosed with pancreatic cancer in late 2014. He died of it on 22 December 2018 at a hospital in Bonheiden, Belgium.
Awards and recognition
Bourgain received several awards during his career, the most notable being the Fields Medal in 1994.
In 2009 Bourgain was elected a foreign member of the Royal Swedish Academy of Sciences.
In 2010, he received the Shaw Prize in Mathematics.
In 2012, he and Terence Tao received the Crafoord Prize in Mathematics from the Royal Swedish Academy of Sciences.
In 2015, he was made a baron by king Philippe of Belgium.
In 2016, he received the 2017 Breakthrough Prize in Mathematics.
In 2017, he received the 2018 Leroy P. Steele Prizes.
Selected publications
Articles
 Bourgain, Jean (1983). "Some remarks on Banach spaces in which martingale difference sequences are unconditional". Arkiv för Matematik 21 (1): 163–168. doi:10.1007/BF02384306. http://archive.ymsc.tsinghua.edu.cn/pacm_download/116/739011512_2006_Article_BF02384306.pdf. (See Banach space and martingale.)
 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.
 Bourgain, J. (1986). "Averages in the plane over convex curves and maximal operators". Journal d'Analyse Mathématique 47: 69–85. doi:10.1007/BF02792533.
 Bourgain, J.; Milman, V. D. (1987). "New volume ratio properties for convex symmetric bodies in ". Inventiones Mathematicae 88 (2): 319–340. doi:10.1007/BF01388911.
 Bourgain, Jean (1989). "Pointwise ergodic theorems for arithmetic sets". Publications Mathématiques de l'IHÉS 69: 5–41. doi:10.1007/BF02698838. http://www.numdam.org/item/PMIHES_1989__69__5_0/.
 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.
 Bourgain, J. (1994). "Periodic nonlinear Schrödinger equation and invariant measures". Communications in Mathematical Physics 166 (1): 1–26. doi:10.1007/BF02099299. http://projecteuclid.org/euclid.cmp/1104271501.
 Bourgain, J. (1998). "QuasiPeriodic Solutions of Hamiltonian Perturbations of 2D Linear Schrödinger Equations". Annals of Mathematics 148 (2): 363–439. doi:10.2307/121001. http://cds.cern.ch/record/277189.
 Friedgut, Ehud; Jean Bourgain, Appendix by (1999). "Sharp thresholds of graph properties, and the sat problem". Journal of the American Mathematical Society 12 (4): 1017–1054. doi:10.1090/s0894034799003057.
 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/S0894034799002830.
 Bourgain, Jean; Brezis, Haim; Mironescu, Petru (2001). Another look at Sobolev spaces. pp. 439–455. https://hal.archivesouvertes.fr/hal00747692/. (See 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 00278424. PMC 137704. PMID 12432098.
 Bourgain, Jean; Katz, Nets; Tao, Terence (2004). "A sumproduct estimate in finite fields, and applications". Geometric and Functional Analysis 14: 27–57. doi:10.1007/s0003900404511.
 Bourgain, J. (2005). "More on the SumProduct Phenomenon in Prime Fields and its Applications". International Journal of Number Theory 01: 1–32. doi:10.1142/s1793042105000108.
 (See Lindelöf hypothesis.)
Books
 J. Bourgain (1 October 1981). New Classes of L^{p}Spaces. Springer Berlin Heidelberg. ISBN 9783540111566. https://books.google.com/books?id=l7gZAQAAIAAJ.
 Bourgain, Jean; Casazza, Peter G.; Lindenstrauss, J.; Tzafriri, Lior (1985). Banach Spaces with a Unique Unconditional Basis, up to Permutation. American Mathematical Soc.. ISBN 9780821823231. https://books.google.com/books?id=hznUCQAAQBAJ.
 Bourgain, Jean (1999). Global Solutions of Nonlinear Schrödinger Equations. ISBN 9780821819197. https://books.google.com/books?id=jr8jDwAAQBAJ. (Bourgain's research on nonlinear dispersive equations was, according to Carlos Kenig, "deep and influential".)
 Bourgain, Jean (November 2004). Green's Function Estimates for Lattice Schrödinger Operators and Applications. (AM158). ISBN 9781400837144. https://books.google.com/books?id=cGxVBAAAQBAJ.
 Mathematical Aspects of Nonlinear Dispersive Equations (AM163). Princeton University Press. 10 January 2009. ISBN 9781400827794. https://books.google.com/books?id=SVcY3L_SZYEC.
Hypatia 
Agnodice 
Aglaonice 
Mary the Jewess 