Jean Bourgain: Difference between revisions

Jean Bourgain
Jean Bourgain
Born	28 February 1954; Ostend, Belgium
Died	22 December 2018 (aged 64); Bonheiden, Belgium
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	Mathematical analysis
Institutions	Institute for Advanced Study; University of Illinois Urbana-Champaign; University of California, Berkeley
Doctoral advisor	Freddy Delbaen
Doctoral students	James Colliander; Péter Varjú

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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 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. He proved the uniqueness of the solutions for the initial value problem of the Korteweg–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 an $l_{p}$ space of dimension $O(\log ^{2}(n))$ with distortion $O(\log(n))$ . Together with Vitali Milman, he contributed to progress on Mahler’s conjecture in 1987. 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]

Together with Ciprian Demeter and Larry Guth, he proved Vinogradov's mean-value theorem in 2015.

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. Bibcode:1983ArM....21..163B. doi:10.1007/BF02384306. S2CID 121419327. (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 $\mathbb {R} ^{n},$ ". 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 the $k$ -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". pp. 439–455. (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. 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 (See Lindelöf hypothesis.)

Books

J. Bourgain (1 October 1981). New Classes of L^p-Spaces. Springer Berlin Heidelberg. 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. American Mathematical Soc. ISBN 978-0-8218-2323-1.
Bourgain, Jean (1999). Global Solutions of Nonlinear Schrödinger Equations. American Mathematical Soc. ISBN 9780821819197.^[16] (Bourgain's research on nonlinear dispersive equations was, according to Carlos Kenig, "deep and influential".^[17])
Bourgain, Jean (November 2004). Green's Function Estimates for Lattice Schrödinger Operators and Applications. (AM-158). Princeton University Press. ISBN 9781400837144.
Bourgain, Jean; Kening, Carlos E.; Klainerman, Sergiu, eds. (10 January 2009). Mathematical Aspects of Nonlinear Dispersive Equations (AM-163). Princeton University Press. ISBN 978-1-4008-2779-4.

References

^ Jean Bourgain at the Mathematics Genealogy Project
^ "Death of mathematician Jean Bourgain". The Brussels Times. 30 December 2018. Retrieved 30 December 2018.
^ "Fields Medals and Nevanlinna Prize 1994". www.mathunion.org. Retrieved 31 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. Retrieved 23 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 from the original on 4 July 2010. Retrieved 28 May 2010.
^ Crafoord Press Release Archived 27 December 2012 at the Wayback 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 of Global 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.

External links

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.

[1] Jean Bourgain at the Mathematics Genealogy Project

[Death-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.

[Tao2019-8] 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.

[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, press release on 12 February 2009

[11] "Shaw Prize Press Release". Archived from the original on 4 July 2010. Retrieved 28 May 2010.

[12] Crafoord Press Release Archived 27 December 2012 at the Wayback Machine 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] Staffilani, Gigliola (2003). "Review of Global Solutions of Nonlinear Schrödinger Equations by Jean Bourgain". Bull. Amer. Math. Soc. 40: 99–107. doi:10.1090/S0273-0979-02-00956-4.

[Kenig2020-17] 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.

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@@ Line 1: / Line 1: @@
-{{short description|Belgian mathematician}}
+{{Short description|Belgian mathematician (1954–2018)}}
 {{Use dmy dates|date=September 2020}}
 {{Infobox scientist
-|name              = Jean Bourgain
+| name              = Jean Bourgain
-|image             = Jean Bourgain (vertical crop).jpg
+| image             = Jean Bourgain (vertical crop).jpg
-|caption           =
+| caption           =
-|birth_date        = {{Birth date|df=yes|1954|02|28}}
+| birth_date        = {{Birth date|df=yes|1954|02|28}}
-|birth_place       = [[Ostend]], [[Belgium]]
+| birth_place       = [[Ostend]], Belgium
-|death_date        = {{death date and age|2018|12|22|1954|2|28|df=yes}}<ref name="Death">{{cite news |author=<!--Staff writer(s); no by-line.--> |title=Death of mathematician Jean Bourgain |url=http://www.brusselstimes.com/belgium/13594/death-of-mathematician-jean-bourgain |newspaper=[[The Brussels Times]] |date=30 December 2018 |access-date=30 December 2018 }}</ref>
+| death_date        = {{death date and age|2018|12|22|1954|2|28|df=yes}}<ref name="Death">{{cite news |author=<!--Staff writer(s); no by-line.--> |title=Death of mathematician Jean Bourgain |url=http://www.brusselstimes.com/belgium/13594/death-of-mathematician-jean-bourgain |newspaper=[[The Brussels Times]] |date=30 December 2018 |access-date=30 December 2018 }}</ref>
-|death_place       = [[Bonheiden]], Belgium
+| death_place       = [[Bonheiden]], Belgium
-|nationality       = [[Belgian]]
+| alma_mater        = [[Vrije Universiteit Brussel]]
+| doctoral_advisor  = [[Freddy Delbaen]]
-|alma_mater        = [[Vrije Universiteit Brussel]]
+| doctoral_students = [[James Colliander]]<br>[[Péter Varjú]]<ref>{{MathGenealogy|id=63054}}</ref>
-|doctoral_advisor  = [[Freddy Delbaen]]
+| known_for         = [[Analytic number theory]]<br>[[Harmonic analysis]]<br>[[Ergodic theory]]<br>[[Banach space]]s<br>[[Partial differential equation]]s
-|doctoral_students = [[James Colliander]]<br>[[Péter Varjú]]<ref>{{MathGenealogy|id=63054}}</ref>
+| field             = [[Mathematical analysis]]
-|known_for         = [[Analytic number theory]]<br>[[Harmonic analysis]]<br>[[Ergodic theory]]<br>[[Banach space]]s<br>[[Partial differential equations]]
+| work_institutions = [[Institute for Advanced Study]]<br>[[University of Illinois Urbana-Champaign]]<br>[[University of California, Berkeley]]
-|influences        = [[Laurent Schwartz]]<br>[[Bernard Maurey]]<br>[[Gilles Pisier]]<br>[[Vitali Milman]]
+| prizes            = [[Salem Prize]] (1983)<br>[[Ostrowski Prize]] (1991)<br>[[Fields Medal]] (1994)<br>[[Shaw Prize]] (2010)<br>[[Crafoord Prize]] (2012)<br>[[Breakthrough Prize in Mathematics]] (2017)<br>[[Steele Prize]] (2018)
-|influenced        = [[Terence Tao]]
-|field             = [[Mathematics]]
-|work_institutions = [[Institute for Advanced Study]]<br>[[University of Illinois, Urbana-Champaign]]<br>[[University of California, Berkeley]]
-|prizes            = [[Salem Prize]] (1983)<br>[[Ostrowski Prize]] (1991)<br>[[Fields Medal]] (1994)<br>[[Shaw Prize]] (2010)<br>[[Crafoord Prize]] (2012)<br>[[Breakthrough Prize in Mathematics]] (2017)<br>[[Steele Prize]] (2018)
 }}
-'''Jean, Baron Bourgain''' ({{IPA-fr|buʁɡɛ̃|lang}}; {{birth date|df=yes|1954|02|28}} – {{death date|df=yes|2018|12|22}}) 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 space]]s, [[harmonic analysis]], [[ergodic theory]] and [[nonlinear partial differential equation]]s from [[mathematical physics]].<ref>{{Cite web|url=https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/1994/index.html|title=Fields Medals and Nevanlinna Prize 1994|website=www.mathunion.org|access-date=2019-08-31}}</ref>
+'''Jean Louis, baron  Bourgain''' ({{IPA|fr|buʁɡɛ̃|lang}}; {{birth date|df=yes|1954|02|28}} – {{death date|df=yes|2018|12|22}}) 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 space]]s, [[harmonic analysis]], [[ergodic theory]] and [[nonlinear partial differential equation]]s from [[mathematical physics]].<ref>{{Cite web|url=https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/1994/index.html|title=Fields Medals and Nevanlinna Prize 1994|website=www.mathunion.org|access-date=2019-08-31}}</ref>
 ==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.<ref>{{MacTutor|id=Bourgain|title=Jean Bourgain}}</ref> He was an editor for the ''[[Annals of Mathematics]]''. From 2012 to 2014, he was a visiting scholar at [[University of California, Berkeley|UC Berkeley]].<ref>{{Cite web|url=https://math.berkeley.edu/people/faculty/jean-bourgain|title=Jean Bourgain {{!}} Department of Mathematics at University of California Berkeley|website=math.berkeley.edu|access-date=2016-04-23}}</ref>
+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.<ref>{{MacTutor|id=Bourgain|title=Jean Bourgain}}</ref> He was an editor for the ''[[Annals of Mathematics]]''. From 2012 to 2014, he was a visiting scholar at [[University of California, Berkeley|UC Berkeley]].<ref>{{Cite web|url=https://math.berkeley.edu/people/faculty/jean-bourgain|title=Jean Bourgain {{!}} Department of Mathematics at University of California Berkeley|website=math.berkeley.edu|access-date=2016-04-23}}</ref>
-His research work included several areas of [[mathematical analysis]] such as the [[geometry]] of [[Banach space]]s, [[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 set|Kakeya problem]] to [[arithmetic combinatorics]].<ref>{{cite book|title=Mathematics: Frontiers and Perspectives|last=Bourgain|first=J.|publisher=IMU/Amer. Math. Soc.|year=2000|pages=13–32|chapter=Harmonic analysis and combinatorics: How much may they contribute to each other?}}</ref><ref>{{cite journal|last=Tao|first=Terence|author-link=Terence Tao|date=March 2001|title=From Rotating Needles to Stability of Waves: Emerging Connections between Combinatorics, Analysis and PDE|url=http://www.ams.org/notices/200103/fea-tao.pdf|journal=[[Notices of the American Mathematical Society]]|volume=48|issue=3|pages=297–303|bibcode=2000math......8098T|arxiv=math/0008098}}</ref> As a researcher, he was the author or coauthor of more than 500 articles.<ref name="Tao2019">{{cite journal|last1=Tao|first1=Terence Chi-Shen|title=Jean Bourgain, problem solver|journal=Proceedings of the National Academy of Sciences|volume=116|issue=28|year=2019|pages=13717–13718|issn=0027-8424|doi=10.1073/pnas.1901965116|pmid=31209024|pmc=6628665|doi-access=free}}</ref>
+His research work included several areas of [[mathematical analysis]] such as the [[geometry]] of [[Banach space]]s, [[harmonic analysis]], [[analytic number theory]], [[combinatorics]], [[ergodic theory]], [[partial differential equation]]s and [[spectral theory]], and later also [[group theory]]. He proved the uniqueness of the solutions for the initial value problem of the [[Korteweg–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 an <math>l_p</math> space of dimension <math>O(\log^2 (n))</math> with distortion <math>O(\log(n))</math>. Together with [[Vitali Milman]], he contributed to progress on [[Mahler volume|Mahler’s conjecture]] in 1987. In 2000, Bourgain connected the [[Kakeya set|Kakeya problem]] to [[arithmetic combinatorics]].<ref>{{cite book|title=Mathematics: Frontiers and Perspectives|last=Bourgain|first=J.|publisher=IMU/Amer. Math. Soc.|year=2000|pages=13–32|chapter=Harmonic analysis and combinatorics: How much may they contribute to each other?}}</ref><ref>{{cite journal|last=Tao|first=Terence|author-link=Terence Tao|date=March 2001|title=From Rotating Needles to Stability of Waves: Emerging Connections between Combinatorics, Analysis and PDE|url=https://www.ams.org/notices/200103/fea-tao.pdf|journal=[[Notices of the American Mathematical Society]]|volume=48|issue=3|pages=297–303|bibcode=2000math......8098T|arxiv=math/0008098}}</ref> As a researcher, he was the author or coauthor of more than 500 articles.<ref name="Tao2019">{{cite journal|last1=Tao|first1=Terence Chi-Shen|title=Jean Bourgain, problem solver|journal=Proceedings of the National Academy of Sciences|volume=116|issue=28|year=2019|pages=13717–13718|issn=0027-8424|doi=10.1073/pnas.1901965116|pmid=31209024|pmc=6628665|bibcode=2019PNAS..11613717T |doi-access=free}}</ref>
+Together with Ciprian Demeter and [[Larry Guth]], he proved [[Vinogradov's mean-value theorem]] in 2015.
 Bourgain was diagnosed with [[pancreatic cancer]] in late 2014.  He died of it on 22 December 2018 at a hospital in Bonheiden, Belgium.<ref>{{citation|url=https://www.nytimes.com/2019/01/16/obituaries/jean-bourgain-dead.html|author=Kenneth Chang|title=Jean Bourgain, Problem-Conquering Mathematician, Is Dead at 64|work=New York Times|date=16 January 2019}}</ref>
@@ Line 32: / Line 31: @@
 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]].<ref>[http://www.kva.se/KVA_Root/eng/_press/detail.asp?NewsId=1134 Royal Swedish Academy of Sciences: Many new members elected to the Academy]{{dead link|date=April 2017 |bot=InternetArchiveBot |fix-attempted=yes }}, press release on 12 February 2009</ref>
+In 2009 Bourgain was elected a foreign member of the [[Royal Swedish Academy of Sciences]].<ref>[https://web.archive.org/web/20180710163709/https://www.kva.se/KVA_Root/eng/_press/detail.asp?NewsId=1134 Royal Swedish Academy of Sciences: Many new members elected to the Academy], press release on 12 February 2009</ref>
-In 2010, he received the [[Shaw Prize]] in Mathematics.<ref>[http://www.shawprize.org/en/laureates/2010/mathematical/Bourgain/release.html Shaw Prize Press Release]</ref>
+In 2010, he received the [[Shaw Prize]] in Mathematics.<ref>{{Cite web |url=http://www.shawprize.org/en/laureates/2010/mathematical/Bourgain/release.html |title=Shaw Prize Press Release |access-date=28 May 2010 |archive-date=4 July 2010 |archive-url=https://web.archive.org/web/20100704143920/http://www.shawprize.org/en/laureates/2010/mathematical/Bourgain/release.html |url-status=dead }}</ref>
-In 2012, he and [[Terence Tao]] received the [[Crafoord Prize]] in Mathematics from the [[Royal Swedish Academy of Sciences]].<ref>[http://www.crafoordprize.se/press/arkivpressreleases/thecrafoordprizeinmathematics2012andthecrafoordprizeinastronomy2012.5.6018c17913483dc064280001363.html Crafoord Press Release] on 19 January 2012</ref>
+In 2012, he and [[Terence Tao]] received the [[Crafoord Prize]] in Mathematics from the [[Royal Swedish Academy of Sciences]].<ref>[http://www.crafoordprize.se/press/arkivpressreleases/thecrafoordprizeinmathematics2012andthecrafoordprizeinastronomy2012.5.6018c17913483dc064280001363.html Crafoord Press Release] {{Webarchive|url=https://web.archive.org/web/20121227011055/http://www.crafoordprize.se/press/arkivpressreleases/thecrafoordprizeinmathematics2012andthecrafoordprizeinastronomy2012.5.6018c17913483dc064280001363.html |date=27 December 2012 }} on 19 January 2012</ref>
 In 2015, he was made a baron by king [[Philippe of Belgium]].<ref>[https://www.ias.edu/ideas/jean-bourgains-coat-arms Jean Bourgain’s Coat of Arms] &nbsp;—Institute for Advanced Study</ref>
@@ Line 46: / Line 45: @@
 ==Selected publications==
 ===Articles===
-* {{cite journal|author=Bourgain, Jean|title=Some remarks on Banach spaces in which martingale difference sequences are unconditional|journal=Arkiv för Matematik|volume=21|issue=1|year=1983|pages=163–168|doi=10.1007/BF02384306|bibcode=1983ArM....21..163B|s2cid=121419327|url=http://archive.ymsc.tsinghua.edu.cn/pacm_download/116/7390-11512_2006_Article_BF02384306.pdf}} (See [[Banach space]] and [[Martingale (probability theory)|martingale]].)
+* {{cite journal|author=Bourgain, Jean|title=Some remarks on Banach spaces in which martingale difference sequences are unconditional|journal=Arkiv för Matematik|volume=21|issue=1|year=1983|pages=163–168|doi=10.1007/BF02384306|bibcode=1983ArM....21..163B|s2cid=121419327|url=http://archive.ymsc.tsinghua.edu.cn/pacm_download/116/7390-11512_2006_Article_BF02384306.pdf|doi-access=free}} (See [[Banach space]] and [[Martingale (probability theory)|martingale]].)
-* {{cite journal|doi=10.1007/BF02776078|title=On lipschitz embedding of finite metric spaces in Hilbert space|year=1985|last1=Bourgain|first1=J.|journal=Israel Journal of Mathematics|volume=52|issue=1–2|pages=46–52|s2cid=121649019}}
+* {{cite journal|doi=10.1007/BF02776078|doi-access=|title=On lipschitz embedding of finite metric spaces in Hilbert space|year=1985|last1=Bourgain|first1=J.|journal=[[Israel Journal of Mathematics]]|volume=52|issue=1–2|pages=46–52|s2cid=121649019}}
-* {{cite journal|doi=10.1007/BF02792533|title=Averages in the plane over convex curves and maximal operators|year=1986|last1=Bourgain|first1=J.|journal=Journal d'Analyse Mathématique|volume=47|pages=69–85|s2cid=120149032}}
+* {{cite journal|doi=10.1007/BF02792533|doi-access=|title=Averages in the plane over convex curves and maximal operators|year=1986|last1=Bourgain|first1=J.|journal=[[Journal d'Analyse Mathématique]]|volume=47|pages=69–85|s2cid=120149032}}
 * {{cite journal|doi=10.1007/BF01388911|title=New volume ratio properties for convex symmetric bodies in <math>\mathbb R^n,</math>|year=1987|last1=Bourgain|first1=J.|last2=Milman|first2=V. D.|journal=Inventiones Mathematicae|volume=88|issue=2|pages=319–340|bibcode=1987InMat..88..319B|s2cid=123312114}}
 * {{cite journal|doi=10.1007/BF02698838|title=Pointwise ergodic theorems for arithmetic sets|year=1989|last1=Bourgain|first1=Jean|journal=Publications Mathématiques de l'IHÉS|volume=69|pages=5–41|s2cid=55288816|url=http://www.numdam.org/item/PMIHES_1989__69__5_0/}}
 * {{cite journal|doi=10.1007/BF01895688|title=Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations|year=1993|last1=Bourgain|first1=J.|journal=Geometric and Functional Analysis|volume=3|issue=3|pages=209–262|s2cid=124191732}}
 * {{cite journal|doi=10.1007/BF02099299|title=Periodic nonlinear Schrödinger equation and invariant measures|year=1994|last1=Bourgain|first1=J.|journal=Communications in Mathematical Physics|volume=166|issue=1|pages=1–26|bibcode=1994CMaPh.166....1B|s2cid=53447933|url=http://projecteuclid.org/euclid.cmp/1104271501}}
-* {{cite journal|doi=10.2307/121001|jstor=121001|last1=Bourgain|first1=J.|title=Quasi-Periodic Solutions of Hamiltonian Perturbations of 2D Linear Schrödinger Equations|journal=Annals of Mathematics|year=1998|volume=148|issue=2|pages=363–439|url=http://cds.cern.ch/record/277189}}
+* {{cite journal|doi=10.2307/121001|jstor=121001|last1=Bourgain|first1=J.|title=Quasi-Periodic Solutions of Hamiltonian Perturbations of 2D Linear Schrödinger Equations|journal=Annals of Mathematics|year=1998|volume=148|issue=2|pages=363–439|url=https://cds.cern.ch/record/277189}}
 * {{cite journal|doi=10.1090/s0894-0347-99-00305-7|title=Sharp thresholds of graph properties, and the <math>k</math>-sat problem|year=1999|last1=Friedgut|first1=Ehud|last2=Jean Bourgain|first2=Appendix by|journal=Journal of the American Mathematical Society|volume=12|issue=4|pages=1017–1054|doi-access=free}}
 * {{cite journal|jstor=2646233|last1=Bourgain|first1=J.|title=Global Wellposedness of Defocusing Critical Nonlinear Schrödinger Equation in the Radial Case|journal=Journal of the American Mathematical Society|year=1999|volume=12|issue=1|pages=145–171|doi=10.1090/S0894-0347-99-00283-0|doi-access=free}}
-* {{cite journal|author=Bourgain, Jean|author2=Brezis, Haim|author3=Mironescu, Petru|title=Another look at Sobolev spaces|year=2001|pages=439–455|url=https://hal.archives-ouvertes.fr/hal-00747692/}} (See [[Sobolev space]].)
+* {{cite web|author=Bourgain, Jean|author2=Brezis, Haim|author3=Mironescu, Petru|title=Another look at Sobolev spaces|year=2001|pages=439–455|url=https://hal.archives-ouvertes.fr/hal-00747692/}} (See [[Sobolev space]].)
 * {{cite journal|last1=Bourgain|first1=J.|title=Nonlinear partial differential equations and applications: On the global Cauchy problem for the nonlinear Schrödinger equation|journal=Proceedings of the National Academy of Sciences|volume=99|issue=24|year=2002|pages=15262–15268|issn=0027-8424|doi=10.1073/pnas.222494399|pmid=12432098|pmc=137704|doi-access=free}}
 * {{cite journal|doi=10.1007/s00039-004-0451-1|title=A sum-product estimate in finite fields, and applications|year=2004|last1=Bourgain|first1=Jean|last2=Katz|first2=Nets|last3=Tao|first3=Terence|journal=Geometric and Functional Analysis|volume=14|pages=27–57|arxiv=math/0301343|s2cid=14097626}}
@@ Line 65: / Line 64: @@
 * {{cite book|author=J. Bourgain|title=New Classes of L<sup>p</sup>-Spaces|url=https://books.google.com/books?id=l7gZAQAAIAAJ|date=1 October 1981|publisher=Springer Berlin Heidelberg|isbn=978-3-540-11156-6}}
 * {{cite book|author1=Bourgain, Jean|author2=Casazza, Peter G.|author3=Lindenstrauss, J.|author4=Tzafriri, Lior|title=Banach Spaces with a Unique Unconditional Basis, up to Permutation|url=https://books.google.com/books?id=hznUCQAAQBAJ|year=1985|publisher=American Mathematical Soc.|isbn=978-0-8218-2323-1}}
-* {{cite book|url=https://books.google.com/books?id=jr8jDwAAQBAJ|title = Global Solutions of Nonlinear Schrödinger Equations|isbn = 9780821819197|last1 = Bourgain|first1 = Jean|year = 1999}}<ref>{{cite journal|author=Staffilani, Gigliola|title=Review of ''Global Solutions of Nonlinear Schrödinger Equations'' by Jean Bourgain|journal=Bull. Amer. Math. Soc.|volume=40|year=2003|pages=99–107|doi=10.1090/S0273-0979-02-00956-4|url=https://www.ams.org/journals/bull/2003-40-01/S0273-0979-02-00956-4/}}</ref> (Bourgain's research on nonlinear dispersive equations was, according to Carlos Kenig, "deep and influential".<ref name="Kenig2020">{{cite journal|last1=Kenig|first1=Carlos E.|title=On the work of Jean Bourgain in nonlinear dispersive equations|journal=Bulletin of the American Mathematical Society|year=2020|volume=58|issue=2|pages=173–189|issn=0273-0979|doi=10.1090/bull/1718|doi-access=free}}</ref>)
+* {{cite book|url=https://books.google.com/books?id=jr8jDwAAQBAJ|title = Global Solutions of Nonlinear Schrödinger Equations|isbn = 9780821819197|last1 = Bourgain|first1 = Jean|year = 1999| publisher=American Mathematical Soc. }}<ref>{{cite journal|author=Staffilani, Gigliola|title=Review of ''Global Solutions of Nonlinear Schrödinger Equations'' by Jean Bourgain|journal=Bull. Amer. Math. Soc.|volume=40|year=2003|pages=99–107|doi=10.1090/S0273-0979-02-00956-4|url=https://www.ams.org/journals/bull/2003-40-01/S0273-0979-02-00956-4/|doi-access=free}}</ref> (Bourgain's research on nonlinear dispersive equations was, according to Carlos Kenig, "deep and influential".<ref name="Kenig2020">{{cite journal|last1=Kenig|first1=Carlos E.|title=On the work of Jean Bourgain in nonlinear dispersive equations|journal=Bulletin of the American Mathematical Society|year=2020|volume=58|issue=2|pages=173–189|issn=0273-0979|doi=10.1090/bull/1718|doi-access=free}}</ref>)
-* {{cite book|url=https://books.google.com/books?id=cGxVBAAAQBAJ|title = Green's Function Estimates for Lattice Schrödinger Operators and Applications. (AM-158)|isbn = 9781400837144|last1 = Bourgain|first1 = Jean|date = November 2004}}
+* {{cite book|url=https://books.google.com/books?id=cGxVBAAAQBAJ|title = Green's Function Estimates for Lattice Schrödinger Operators and Applications. (AM-158)|isbn = 9781400837144|last1 = Bourgain|first1 = Jean|date = November 2004| publisher=Princeton University Press }}
 * {{cite book|editor1=Bourgain, Jean|editor2=Kening, Carlos E.|editor3=Klainerman, Sergiu|title=Mathematical Aspects of Nonlinear Dispersive Equations (AM-163)|url=https://books.google.com/books?id=SVcY3L_SZYEC|date=10 January 2009|publisher=Princeton University Press|isbn=978-1-4008-2779-4}}
@@ Line 73: / Line 72: @@
 ==External links==
-*[http://ams.org/mathscinet/search/publications.html?extend=1&pg1=IID&r=1&s1=40280 MathSciNet: "Items authored by Bourgain, Jean."]{{dead link|date=November 2017 |bot=InternetArchiveBot |fix-attempted=yes }}
 *{{MacTutor Biography|id=Bourgain}}
+*{{cite journal |date=June 2021 | title = Remembering Jean Bourgain (1954–2018) | journal = [[Notices of the American Mathematical Society]] | volume = 68 | issue = 6| pages = 942–957 | doi = 10.1090/noti2290 | url = https://www.ams.org/journals/notices/202106/rnoti-p942.pdf?_zs=kq3BH1&_zl=Bs5L6 | doi-access = free | last1 = Daubechies | first1 = Ingrid | last2 = Delbaen | first2 = Freddy | last3 = Guth | first3 = Larry | last4 = Jitomirskaya | first4 = Svetlana | last5 = Kontorovich | first5 = Alex | last6 = Lindenstrauss | first6 = Elon | last7 = Milman | first7 = Vitali | last8 = Pisier | first8 = Gilles | last9 = Rudnick | first9 = Zeev | last10 = Sarnak | first10 = Peter | last11 = Schlag | first11 = Wilhelm | last12 = Staffilani | first12 = Gigliola | last13 = Tao | first13 = Terence | last14 = Varjú | first14 = Péter }}
 * {{cite web|title=The Search for Randomness {{!}} Jean Bourgain|date=April 25, 2012|publisher=Institute for Advanced Study|website=YouTube|url=https://www.youtube.com/watch?v=xMWlv_1DqyM&t=232s}}
 * {{cite web|title=Jean Bourgain - 1/2 The orbital circle method and applications...|date=July 14, 2014|publisher=Institut des Hautes Études Scientifiques (IHÉS)|website=YouTube|url=https://www.youtube.com/watch?v=1Yk09qtwrrU}}
@@ Line 97: / Line 96: @@
 [[Category:Members of the Royal Swedish Academy of Sciences]]
 [[Category:Foreign associates of the National Academy of Sciences]]
-[[Category:Highly Cited Researchers]]
 [[Category:Functional analysts]]
 [[Category:Mathematical analysts]]
 [[Category:Institute for Advanced Study faculty]]
-[[Category:University of Illinois at Urbana–Champaign faculty]]
+[[Category:University of Illinois Urbana-Champaign faculty]]
 [[Category:20th-century Belgian mathematicians]]
 [[Category:Belgian mathematicians]]
-[[Category:Free University of Brussels alumni]]
+[[Category:Vrije Universiteit Brussel alumni]]

v t e Shaw Prize laureates
Astronomy	Jim Peebles (2004) Geoffrey Marcy and Michel Mayor (2005) Saul Perlmutter, Adam Riess and Brian Schmidt (2006) Peter Goldreich (2007) Reinhard Genzel (2008) Frank Shu (2009) Charles Bennett, Lyman Page and David Spergel (2010) Enrico Costa and Gerald Fishman (2011) David C. Jewitt and Jane Luu (2012) Steven Balbus and John F. Hawley (2013) Daniel Eisenstein, Shaun Cole and John A. Peacock (2014) William J. Borucki (2015) Ronald Drever, Kip Thorne and Rainer Weiss (2016) Simon White (2017) Jean-Loup Puget (2018) Edward C. Stone (2019) Roger Blandford (2020) Victoria Kaspi and Chryssa Kouveliotou (2021) Lennart Lindegren and Michael Perryman (2022) Matthew Bailes, Duncan Lorimer and Maura McLaughlin (2023) Shrinivas R. Kulkarni (2024)
Life science and medicine	Stanley Norman Cohen, Herbert Boyer, Yuet-Wai Kan and Richard Doll (2004) Michael Berridge (2005) Xiaodong Wang (2006) Robert Lefkowitz (2007) Ian Wilmut, Keith H. S. Campbell and Shinya Yamanaka (2008) Douglas Coleman and Jeffrey Friedman (2009) David Julius (2010) Jules Hoffmann, Ruslan Medzhitov and Bruce Beutler (2011) Franz-Ulrich Hartl and Arthur L. Horwich (2012) Jeffrey C. Hall, Michael Rosbash and Michael W. Young (2013) Kazutoshi Mori and Peter Walter (2014) Bonnie Bassler and Everett Peter Greenberg (2015) Adrian Bird and Huda Zoghbi (2016) Ian R. Gibbons and Ronald Vale (2017) Mary-Claire King (2018) Maria Jasin (2019) Gero Miesenböck, Peter Hegemann and Georg Nagel (2020) Scott D. Emr (2021) Paul A. Negulescu and Michael J. Welsh (2022) Patrick Cramer and Eva Nogales (2023) Stuart H. Orkin and Swee Lay Thein (2024)
Mathematical science	Shiing-Shen Chern (2004) Andrew Wiles (2005) David Mumford and Wentsun Wu (2006) Robert Langlands and Richard Taylor (2007) Vladimir Arnold and Ludwig Faddeev (2008) Simon Donaldson and Clifford Taubes (2009) Jean Bourgain (2010) Demetrios Christodoulou and Richard S. Hamilton (2011) Maxim Kontsevich (2012) David Donoho (2013) George Lusztig (2014) Gerd Faltings and Henryk Iwaniec (2015) Nigel Hitchin (2016) János Kollár and Claire Voisin (2017) Luis Caffarelli (2018) Michel Talagrand (2019) Alexander Beilinson and David Kazhdan (2020) Jean-Michel Bismut and Jeff Cheeger (2021) Noga Alon and Ehud Hrushovski (2022) Vladimir Drinfeld and Shing-Tung Yau (2023) Peter Sarnak (2024)

v t e Breakthrough Prize laureates
Mathematics	Simon Donaldson, Maxim Kontsevich, Jacob Lurie, Terence Tao and Richard Taylor (2015) Ian Agol (2016) Jean Bourgain (2017) Christopher Hacon, James McKernan (2018) Vincent Lafforgue (2019) Alex Eskin (2020) Martin Hairer (2021) Takuro Mochizuki (2022) Daniel A. Spielman (2023) Simon Brendle (2024)
Fundamental physics	Nima Arkani-Hamed, Alan Guth, Alexei Kitaev, Maxim Kontsevich, Andrei Linde, Juan Maldacena, Nathan Seiberg, Ashoke Sen, Edward Witten (2012) Special: Stephen Hawking, Peter Jenni, Fabiola Gianotti (ATLAS), Michel Della Negra, Tejinder Virdee, Guido Tonelli, Joseph Incandela (CMS) and Lyn Evans (LHC) (2013) Alexander Polyakov (2013) Michael Green and John Henry Schwarz (2014) Saul Perlmutter and members of the Supernova Cosmology Project; Brian Schmidt, Adam Riess and members of the High-Z Supernova Team (2015) Special: Ronald Drever, Kip Thorne, Rainer Weiss and contributors to LIGO project (2016) Yifang Wang, Kam-Biu Luk and the Daya Bay team, Atsuto Suzuki and the KamLAND team, Kōichirō Nishikawa and the K2K / T2K team, Arthur B. McDonald and the Sudbury Neutrino Observatory team, Takaaki Kajita and Yōichirō Suzuki and the Super-Kamiokande team (2016) Joseph Polchinski, Andrew Strominger, Cumrun Vafa (2017) Charles L. Bennett, Gary Hinshaw, Norman Jarosik, Lyman Page Jr., David Spergel (2018) Special: Jocelyn Bell Burnell (2018) Charles Kane and Eugene Mele (2019) Special: Sergio Ferrara, Daniel Z. Freedman, Peter van Nieuwenhuizen (2019) The Event Horizon Telescope Collaboration (2020) Eric Adelberger, Jens H. Gundlach and Blayne Heckel (2021) Special: Steven Weinberg (2021) Hidetoshi Katori and Jun Ye (2022) Charles H. Bennett, Gilles Brassard, David Deutsch, Peter W. Shor (2023) John Cardy and Alexander Zamolodchikov (2024)
Life sciences	Cornelia Bargmann, David Botstein, Lewis C. Cantley, Hans Clevers, Titia de Lange, Napoleone Ferrara, Eric Lander, Charles Sawyers, Robert Weinberg, Shinya Yamanaka and Bert Vogelstein (2013) James P. Allison, Mahlon DeLong, Michael N. Hall, Robert S. Langer, Richard P. Lifton and Alexander Varshavsky (2014) Alim Louis Benabid, Charles David Allis, Victor Ambros, Gary Ruvkun, Jennifer Doudna and Emmanuelle Charpentier (2015) Edward Boyden, Karl Deisseroth, John Hardy, Helen Hobbs and Svante Pääbo (2016) Stephen J. Elledge, Harry F. Noller, Roeland Nusse, Yoshinori Ohsumi, Huda Zoghbi (2017) Joanne Chory, Peter Walter, Kazutoshi Mori, Kim Nasmyth, Don W. Cleveland (2018) C. Frank Bennett and Adrian R. Krainer, Angelika Amon, Xiaowei Zhuang, Zhijian Chen (2019) Jeffrey M. Friedman, Franz-Ulrich Hartl, Arthur L. Horwich, David Julius, Virginia Man-Yee Lee (2020) David Baker, Catherine Dulac, Dennis Lo, Richard J. Youle [de] (2021) Jeffery W. Kelly, Katalin Karikó, Drew Weissman, Shankar Balasubramanian, David Klenerman and Pascal Mayer (2022) Clifford P. Brangwynne, Anthony A. Hyman, Demis Hassabis, John Jumper, Emmanuel Mignot, Masashi Yanagisawa (2023) Carl June, Michel Sadelain, Sabine Hadida, Paul Negulescu, Fredrick Van Goor, Thomas Gasser, Ellen Sidransky and Andrew Singleton (2024)

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