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Jean Bourgain

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Jean Bourgain
Born(1954-02-28)28 February 1954
Ostend, Belgium
Died22 December 2018(2018-12-22) (aged 64)[2]
Bonheiden, Belgium
NationalityBelgian
Alma materVrije Universiteit Brussel
Known forAnalytic number theory
Harmonic analysis
Ergodic theory
Banach spaces
Partial differential equations
AwardsSalem Prize (1983)
Ostrowski Prize (1991)
Fields Medal (1994)
Shaw Prize (2010)
Crafoord Prize (2012)
Breakthrough Prize in Mathematics (2017)
Steele Prize (2018)
Scientific career
FieldsMathematics
InstitutionsInstitute for Advanced Study
University of Illinois, Urbana-Champaign
University of California, Berkeley
Doctoral advisorFreddy Delbaen
Doctoral studentsJames Colliander
Péter Varjú[1]

Jean, Baron Bourgain (French: [buʁɡɛ̃]; (1954-02-28)28 February 1954 – (2018-12-22)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.[3]

Biography

Bourgain received his PhD from the Vrije Universiteit Brussel in 1977. He was a faculty member at the University of Illinois, Urbana-Champaign and, from 1985 until 1995, professor at Institut des Hautes Études Scientifiques at Bures-sur-Yvette in France, at the Institute for Advanced Study in Princeton, New Jersey from 1994 until 2018.[4] He was an editor for the Annals of Mathematics. From 2012 to 2014, he was a visiting scholar at UC Berkeley.[5]

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.[6][7] As a researcher, he was the author or coauthor of more than 500 articles.[8]

Bourgain was diagnosed with pancreatic cancer in late 2014. He died of it on 22 December 2018 at a hospital in Bonheiden, Belgium.[9]

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.[10]

In 2010, he received the Shaw Prize in Mathematics.[11]

In 2012, he and Terence Tao received the Crafoord Prize in Mathematics from the Royal Swedish Academy of Sciences.[12]

In 2015, he was made a baron by king Philippe of Belgium.[13]

In 2016, he received the 2017 Breakthrough Prize in Mathematics.[14]

In 2017, he received the 2018 Leroy P. Steele Prizes.[15]

Selected publications

Articles

  • Bourgain, Jean (1983). "Some remarks on Banach spaces in which martingale difference sequences are unconditional" (PDF). Arkiv för Matematik. 21 (1): 163–168. (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. 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 in ". 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 the -sat problem". 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": 439–455. {{cite journal}}: Cite journal requires |journal= (help) (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 0027-8424.
  • 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 (See Lindelöf hypothesis.)

Books

References

  1. ^ Jean Bourgain at the Mathematics Genealogy Project
  2. ^ "Death of mathematician Jean Bourgain". The Brussels Times. 30 December 2018. Retrieved 30 December 2018.
  3. ^ "Fields Medals and Nevanlinna Prize 1994". www.mathunion.org. Retrieved 31 August 2019.
  4. ^ O'Connor, John J.; Robertson, Edmund F., "Jean Bourgain", MacTutor History of Mathematics Archive, University of St Andrews
  5. ^ "Jean Bourgain | Department of Mathematics at University of California Berkeley". math.berkeley.edu. Retrieved 23 April 2016.
  6. ^ 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.
  7. ^ 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.
  8. ^ Tao, Terence Chi-Shen (2019). "Jean Bourgain, problem solver". Proceedings of the National Academy of Sciences. 116 (28): 13717–13718. doi:10.1073/pnas.1901965116. ISSN 0027-8424.
  9. ^ Kenneth Chang (16 January 2019), Jean Bourgain, Problem-Conquering Mathematician, Is Dead at 64, New York Times
  10. ^ Royal Swedish Academy of Sciences: Many new members elected to the Academy[permanent dead link‍], press release on 12 February 2009
  11. ^ Shaw Prize Press Release
  12. ^ Crafoord Press Release on 19 January 2012
  13. ^ Jean Bourgain’s Coat of Arms  —Institute for Advanced Study
  14. ^ Breakthrough Prize Press Release
  15. ^ Jean Bourgain to Receive 2018 Steele Prize for Lifetime Achievement
  16. ^ Kenig, Carlos E. (2020). "On the work of Jean Bourgain in nonlinear dispersive equations". Bulletin of the American Mathematical Society: 1. doi:10.1090/bull/1718. ISSN 0273-0979.
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