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 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
{\displaystyle l_{p}}
space of dimension
O
(
log
2
(
n
)
)
{\displaystyle O(\log ^{2}(n))}
with distortion
O
(
log
(
n
)
)
{\displaystyle 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
R
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 the
k
{\displaystyle 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 Lp -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.
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