2023 - Research.com Mathematics in United States Leader Award
2018 - Steele Prize for Lifetime Achievement
2018 - Polish Academy of Science
2011 - Member of the National Academy of Sciences
1994 - Fields Medal of International Mathematical Union (IMU) Bourgain's work touches on several central topics of mathematical analysis: the geometry of Banach spaces, convexity in high dimensions, harmonic analysis, ergodic theory, and finally, nonlinear partial differential equations from mathematical physics.
His primary areas of study are Mathematical analysis, Combinatorics, Pure mathematics, Discrete mathematics and Mathematical physics. Sobolev space, Nonlinear Schrödinger equation, Fourier series, Banach space and Initial value problem are among the areas of Mathematical analysis where Jean Bourgain concentrates his study. His Combinatorics study combines topics in areas such as Regular polygon, Algebra over a field and Product.
His work deals with themes such as Almost Mathieu operator and Spectrum, which intersect with Pure mathematics. His Discrete mathematics research is multidisciplinary, relying on both Partial differential equation, Algebra, Property, Upper and lower bounds and Projection. As a part of the same scientific study, Jean Bourgain usually deals with the Mathematical physics, concentrating on Hamiltonian and frequently concerns with Phase space, Dirichlet boundary condition and Linear equation.
Jean Bourgain mostly deals with Combinatorics, Mathematical analysis, Pure mathematics, Discrete mathematics and Mathematical physics. Jean Bourgain has researched Combinatorics in several fields, including Upper and lower bounds and Exponential function. His Upper and lower bounds research incorporates themes from Curvature and Eigenfunction.
The various areas that Jean Bourgain examines in his Mathematical analysis study include Torus and Nonlinear system. Jean Bourgain is involved in the study of Pure mathematics that focuses on Banach space in particular. The concepts of his Discrete mathematics study are interwoven with issues in Algebra over a field and Exponential sum.
Jean Bourgain mainly focuses on Mathematical analysis, Pure mathematics, Combinatorics, Discrete mathematics and Conjecture. He interconnects Decoupling and Torus in the investigation of issues within Mathematical analysis. His work on Affine transformation as part of general Pure mathematics study is frequently connected to Decoupling, therefore bridging the gap between diverse disciplines of science and establishing a new relationship between them.
The Combinatorics study combines topics in areas such as Bounded function and Fourier transform. His work in Discrete mathematics addresses subjects such as Type, which are connected to disciplines such as Congruence relation and Prime. His Conjecture research integrates issues from Curvature and Resolvent.
His primary scientific interests are in Combinatorics, Mathematical analysis, Pure mathematics, Conjecture and Discrete mathematics. As part of the same scientific family, Jean Bourgain usually focuses on Combinatorics, concentrating on Multiplicative function and intersecting with Order, Multiplicative inverse and Multiplicative group. Jean Bourgain regularly ties together related areas like Torus in his Mathematical analysis studies.
His Sobolev space study in the realm of Pure mathematics connects with subjects such as Decoupling and Vinogradov. His study looks at the relationship between Conjecture and topics such as Integer, which overlap with Curvature, Apollonian gasket, Diophantine approximation and Absolute constant. His Discrete mathematics study integrates concerns from other disciplines, such as Action, Monotone polygon, Type, Algebra over a field and Interval.
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Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations
Geometric and Functional Analysis (1993)
On lipschitz embedding of finite metric spaces in Hilbert space
Israel Journal of Mathematics (1985)
Some remarks on Banach spaces in which martingale difference sequences are unconditional
Arkiv för Matematik (1983)
A SUM-PRODUCT ESTIMATE IN FINITE FIELDS, AND APPLICATIONS
Jean Bourgain;Nets Katz;Terence Tao.
Geometric and Functional Analysis (2004)
Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case
Journal of the American Mathematical Society (1999)
Another look at Sobolev spaces
Jean Bourgain;Haïm Brezis;Petru Mironescu.
New volume ratio properties for convex sym-metric bodies in IRn.
J. Bourgain;V. D. Milman.
Inventiones Mathematicae (1987)
QUASI-PERIODIC SOLUTIONS OF HAMILTONIAN PERTURBATIONS OF 2D LINEAR SCHRODINGER EQUATIONS
Annals of Mathematics (1998)
Periodic nonlinear Schrödinger equation and invariant measures
Communications in Mathematical Physics (1994)
Pointwise ergodic theorems for arithmetic sets
Publications Mathématiques de l'IHÉS (1989)
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