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- Jean Bourgain

Mathematics

USA

2023

Discipline name
D-index
D-index (Discipline H-index) only includes papers and citation values for an examined
discipline in contrast to General H-index which accounts for publications across all
disciplines.
Citations
Publications
World Ranking
National Ranking

Mathematics
D-index
97
Citations
33,417
477
World Ranking
37
National Ranking
28

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.

- Mathematical analysis
- Quantum mechanics
- Algebra

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.

- Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations (1604 citations)
- On lipschitz embedding of finite metric spaces in Hilbert space (466 citations)
- Some remarks on Banach spaces in which martingale difference sequences are unconditional (394 citations)

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.

- Combinatorics (34.82%)
- Mathematical analysis (29.55%)
- Pure mathematics (23.28%)

- Mathematical analysis (29.55%)
- Pure mathematics (23.28%)
- Combinatorics (34.82%)

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.

- Proof of the main conjecture in Vinogradov’s Mean Value Theorem for degrees higher than three (182 citations)
- The proof of the l 2 Decoupling Conjecture (178 citations)
- Decoupling, exponential sums and the Riemann zeta function (106 citations)

- Mathematical analysis
- Quantum mechanics
- Algebra

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.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations

J. Bourgain.

Geometric and Functional Analysis **(1993)**

2800 Citations

On lipschitz embedding of finite metric spaces in Hilbert space

J. Bourgain.

Israel Journal of Mathematics **(1985)**

742 Citations

Some remarks on Banach spaces in which martingale difference sequences are unconditional

J. Bourgain.

Arkiv för Matematik **(1983)**

615 Citations

A SUM-PRODUCT ESTIMATE IN FINITE FIELDS, AND APPLICATIONS

Jean Bourgain;Nets Katz;Terence Tao.

Geometric and Functional Analysis **(2004)**

564 Citations

Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case

J. Bourgain.

Journal of the American Mathematical Society **(1999)**

513 Citations

Another look at Sobolev spaces

Jean Bourgain;Haïm Brezis;Petru Mironescu.

**(2001)**

494 Citations

New volume ratio properties for convex sym-metric bodies in IRn.

J. Bourgain;V. D. Milman.

Inventiones Mathematicae **(1987)**

494 Citations

QUASI-PERIODIC SOLUTIONS OF HAMILTONIAN PERTURBATIONS OF 2D LINEAR SCHRODINGER EQUATIONS

Jean Bourgain.

Annals of Mathematics **(1998)**

492 Citations

Periodic nonlinear Schrödinger equation and invariant measures

J. Bourgain.

Communications in Mathematical Physics **(1994)**

485 Citations

Pointwise ergodic theorems for arithmetic sets

Jean Bourgain.

Publications Mathématiques de l'IHÉS **(1989)**

470 Citations

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