H-Index & Metrics Top Publications

H-Index & Metrics

Discipline name H-index Citations Publications World Ranking National Ranking
Mathematics H-index 97 Citations 33,267 392 World Ranking 19 National Ranking 13

Research.com Recognitions

Awards & Achievements

2018 - Polish Academy of Science

2018 - Steele Prize for Lifetime Achievement

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.

Overview

What is he best known for?

The fields of study he is best known for:

  • 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.

His most cited work include:

  • 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)

What are the main themes of his work throughout his whole career to date?

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.

He most often published in these fields:

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

What were the highlights of his more recent work (between 2012-2020)?

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

In recent papers he was focusing on the following fields of study:

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.

Between 2012 and 2020, his most popular works were:

  • 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)

In his most recent research, the most cited papers focused on:

  • 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.

Top Publications

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

J. Bourgain.
Geometric and Functional Analysis (1993)

2240 Citations

On lipschitz embedding of finite metric spaces in Hilbert space

J. Bourgain.
Israel Journal of Mathematics (1985)

693 Citations

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

J. Bourgain.
Arkiv för Matematik (1983)

576 Citations

A SUM-PRODUCT ESTIMATE IN FINITE FIELDS, AND APPLICATIONS

Jean Bourgain;Nets Katz;Terence Tao.
Geometric and Functional Analysis (2004)

519 Citations

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

J. Bourgain;V. D. Milman.
Inventiones Mathematicae (1987)

430 Citations

Another look at Sobolev spaces

Jean Bourgain;Haïm Brezis;Petru Mironescu.
(2001)

415 Citations

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

Jean Bourgain.
Annals of Mathematics (1998)

410 Citations

Global Solutions of Nonlinear Schrodinger Equations

Jean Bourgain.
(1999)

391 Citations

Pointwise ergodic theorems for arithmetic sets

Jean Bourgain.
Publications Mathématiques de l'IHÉS (1989)

373 Citations

Besicovitch Type Maximal Operators and Applications to Fourier Analysis.

J. Bourga'in.
Geometric and Functional Analysis (1991)

356 Citations

Profile was last updated on December 6th, 2021.
Research.com Ranking is based on data retrieved from the Microsoft Academic Graph (MAG).
The ranking h-index is inferred from publications deemed to belong to the considered discipline.

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