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{{short description|Belgian mathematician}}
{{Short description|Belgian mathematician (1954–2018)}}
{{Use dmy dates|date=September 2020}}
{{Use dmy dates|date=September 2020}}
{{Infobox scientist
{{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
|alma_mater = [[Vrije Universiteit Brussel]]
| alma_mater = [[Vrije Universiteit Brussel]]
|doctoral_advisor = [[Freddy Delbaen]]
| doctoral_advisor = [[Freddy Delbaen]]
|doctoral_students = [[James Colliander]]<br>[[Péter Varjú]]<ref>{{MathGenealogy|id=63054}}</ref>
| doctoral_students = [[James Colliander]]<br>[[Péter Varjú]]<ref>{{MathGenealogy|id=63054}}</ref>
|known_for = [[Analytic number theory]]<br>[[Harmonic analysis]]<br>[[Ergodic theory]]<br>[[Banach space]]s<br>[[Partial differential equations]]
| known_for = [[Analytic number theory]]<br>[[Harmonic analysis]]<br>[[Ergodic theory]]<br>[[Banach space]]s<br>[[Partial differential equation]]s
⚫
| field = [[Mathematical analysis]]
|influences = [[Laurent Schwartz]]<br>[[Bernard Maurey]]<br>[[Gilles Pisier]]<br>[[Vitali Milman]]
⚫
| work_institutions = [[Institute for Advanced Study]]<br>[[University of Illinois Urbana-Champaign]]<br>[[University of California, Berkeley]]
|influenced = [[Terence Tao]]
⚫
| 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)
⚫
|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==
==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=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>
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>
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>
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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 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>
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>
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===Articles===
===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|doi-access=free}} (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|doi-access=free|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|doi-access=free|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/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/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/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=10.1007/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|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|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|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}}
* {{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}}
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* {{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|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|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/|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=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}}
* {{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}}


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==External links==
==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}}
*{{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 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 }}

Latest revision as of 10:09, 21 August 2024

Jean Bourgain
Born(1954-02-28)28 February 1954
Ostend, Belgium
Died22 December 2018(2018-12-22) (aged 64)[2]
Bonheiden, Belgium
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
FieldsMathematical analysis
InstitutionsInstitute for Advanced Study
University of Illinois Urbana-Champaign
University of California, Berkeley
Doctoral advisorFreddy Delbaen
Doctoral studentsJames Colliander
Péter Varjú[1]

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

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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 space of dimension with distortion . 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

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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

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Articles

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Books

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References

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  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. 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.
  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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