Jean Bourgain

Jean Bourgain (2012)

Jean Bourgain (born February 28, 1954 in Ostend ; † December 22, 2018 in Bonheiden ) was a Belgian mathematician .

Life

Bourgain received his doctorate with a research grant (1977 with Freddy Delbaen ) and qualified as a professor (1979) at the Vrije Universiteit Brussel , where he also became professor of mathematics in 1981. From 1985 to 2006 he was Professor at the University of Illinois at Urbana-Champaign and at the same time (from 1985 to 1995) Professor at the Institut des Hautes Études Scientifiques in Bures-sur-Yvette in France. From 1994 he was one of the eight permanent members of the prestigious School of Mathematics at the Institute for Advanced Study at Princeton .

Services

Bourgain has published more than 300 scientific papers on many areas of analysis , the geometry of Banach spaces , harmonic analysis , analytical number theory , combinatorics , ergodic theory, and nonlinear partial differential equations (such as the periodic nonlinear Schrödinger equation). In them he developed a number of new techniques and showed surprising relationships between different areas that shaped the further development of analysis. He proved the uniqueness of the solutions to the initial value problem of the Korteweg-de-Vries equation . In 1986, Bourgain initiated the Ribe program in functional analysis (based on Martin Ribe ) with a thesis on super-reflective spaces.

In 2015, together with Larry Guth and Ciprian Demeter , he proved the main conjecture in Vinogradov's mean theorem .

Honors

Bourgain has received numerous awards for its achievements. In 1983 he received the Salem Prize , in 1985 the Belgian Damry-Deleeuw-Bourlart Prize . In 1990 he was honored by the Académie des Sciences with the Elie Cartan Prize , in 1991 he was awarded the Ostrowski Prize . In 1994 he was finally presented with the Fields Medal as the most important award . In 2010 he received the Shaw Prize for Mathematics and in 2012 the Crafoord Prize . In 2016, Bourgain was awarded the International Antonio Feltrinelli Prize . For 2017 he was awarded the Breakthrough Prize in Mathematics , for 2018 he received the Leroy P. Steele Prize for Lifetime Achievement.

In 1983 he was invited speaker at the International Congress of Mathematicians in Warsaw (New Banach space properties of certain spaces of analytic functions) and in 1986 in Berkeley (Geometry of Banach spaces and harmonic analysis). In 1994 he gave a plenary lecture at the ICM in Zurich: Harmonic analysis and nonlinear partial differential equations, and in 2008 a plenary lecture at the European Congress of Mathematicians in Amsterdam (New Developments in arithmetic combinatorics).

Bourgain was a member of the Royal Flemish Academy of Belgium for Sciences and Arts since 2000, associate member of the French Academy of Sciences and external member of the Polish Academy of Sciences , since 2008 external member of the Academia Europaea and since 2011 of the National Academy of Sciences . He was an honorary doctor of the Hebrew University of Jerusalem , the University of Marne-La-Vallée and the Vrije Universiteit Brussel .

Fonts

Books

• Green's function estimates for lattice Schrödinger operators and applications. Princeton University Press, 2005.
• New classes of spaces. ${\displaystyle L_{p}}$Springer 1981.
• Global solution of nonlinear Schrödinger equations. Springer, 1999.
• Editor with Sergiu Klainerman , Carlos Kenig : Mathematical aspects of nonlinear dispersive equations. Princeton University Press, 2007.

Work (selection)

• New Banach space properties of the disc algebra and . ${\displaystyle H^{\infty }}$Acta Math. 152 (1984), no. 1-2, 1-48.
• The metrical interpretation of superreflexivity in Banach spaces. Israel J. Math. 56 (1986), no. 2, 222230.
• With Vitali Milman : New volume ratio properties for convex symmetric bodies in . ${\displaystyle \mathbb {R} ^{n}}$Invent. Math. 88 (1987) no. 2, 319-340.
• Bounded orthogonal systems and the -set problem. ${\displaystyle \Lambda (p)}$Acta Math. 162 (1989) no. 3-4, 227-245.
• Pointwise ergodic theorems for arithmetic sets. With an appendix by the author, Harry Furstenberg, Yitzhak Katznelson and Donald S. Ornstein. Inst. Hautes Études Sci. Publ. Math. No. 1989, 69: 5-45.
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I. Schrödinger equations. Geom. Funct. Anal. 3 (1993) no. 2, 107-156. II. The KdV equation. Geom. Funct. Anal. 3 (1993) no. 3: 209-262.
• Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations. Ann. of Math. (2) 148 (1998) no. 2, 363-439.
• On the dimension of Kakeya sets and related maximal inequalities. Geom. Funct. Anal. 9 (1999), no. 2, 256-282.
• Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case. J. Amer. Math. Soc. 12 (1999), no. 1, 145-171.
• With Michael Goldstein , Wilhelm Schlag : Anderson localization for Schrödinger operators on with quasi-periodic potential. ${\displaystyle \mathbb {Z} ^{2}}$Acta Math. 188 (2002), no. 1, 41-86.
• With Nets Katz , Terence Tao : A sum-product estimate in finite fields, and applications. Geom. Funct. Anal. 14 (2004), no. 1, 27-57.
• Mit Haïm Brezis : New estimates for elliptic equations and Hodge type systems. J. Eur. Math. Soc. (JEMS) 9 (2007), no. 2, 277-315.
• With Alex Gamburd : Uniform expansion bounds for Cayley graphs of . ${\displaystyle SL_{2}(F_{p})}$Ann. of Math. (2) 167 (2008), no. 2, 625-642.
• With Alex Gamburd, Peter Sarnak : Affine linear sieve, expanders, and sum-product. Invent. Math. 179 (2010), no. 3, 559-644.
• With Alex Kantorovich : On the local-global conjecture for integral Apollonian gaskets. With an appendix by Péter P. Varjú. Invent. Math. 196 (2014), no.3, 589-650.
• With Dong Li : Strong ill-posedness of the incompressible Euler equation in borderline Sobolev spaces. Invent. Math. 201 (2015), no. 1, 97–157.
• With Ciprian Demeter, Larry Guth: Proof of the main conjecture in Vinogradovs mean value theorem for degrees higher than three. Ann. of Math. (2) 184 (2016), no. 2, 633-682.

literature

• Erica Klarreich: Jean Bourgain (1954–2018) . In: Nature . tape 566 , no. 7743 , February 6, 2019, ISSN  0028-0836 , p. 183-183 , doi : 10.1038 / d41586-019-00499-x ( nature.com [accessed February 16, 2019]).

Web links

Commons : Jean Bourgain  - Collection of images, videos and audio files

• Homepage of Jean Bourgain with picture
• List of publications by Jean Bourgain, pdf
• PhD students from Jean Bourgain
• John J. O'Connor, Edmund F. Robertson :  Jean Bourgain. In: MacTutor History of Mathematics archive .
• Author profile in the database zbMATH

proof

1. ^ Décès du mathématicien Jean Bourgain. In: LaLibre.be. Dec. 29, 2018, accessed Dec. 31, 2018.
2. ^ J. Bourgain, C. Demeter, Guth: Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three. Arxiv 2015, appears in Annals of Mathematics.
3. ↑ KVAB class Natuurwetenschappen (Buitenlandse Leden): Page no longer available , search in web archives: kvab.be.