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.
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