Harmonic Analysis
Harmonic analysis studies the Fourier representation of functions and its generalizations, encompassing core topics such as the Fourier transform, restriction theory, oscillatory integrals, and singular integral operators. This field is closely connected to the Kakeya conjecture—there exists a profound duality between the Fourier restriction conjecture and the Kakeya conjecture, with Wolff's wave equation method and Tao's Kakeya estimates serving as representative works bridging the two.
Research Progress
Mark your research stage in this field. Just a rough outline.
领域资源
期刊
- Annals of Mathematics → (Princeton University)
- Journal of the American Mathematical Society (JAMS) → (American Mathematical Society)
学会/组织
- American Mathematical Society (AMS) → (AMS official website)
- International Mathematical Union (IMU) → (IMU official website)
综述/资源库
- arXiv: math.CA Classical Analysis → (arXiv)
- MathSciNet (Mathematical Reviews) → (American Mathematical Society)
Recent Publications
Source:: arXivAuthor A, Author B · 2026-08-15
This paper presents recent developments and open problems in the field, with new results on key conjectures.
Researcher C, Researcher D · 2026-07-22
We introduce a novel approach that unifies several classical results, providing new insights into long-standing questions.
Papers fetched from arXiv API automatically, for reference only. Updated periodically.
全球最好的大学项目
Fudan University
School of Mathematical Sciences — Harmonic Analysis
China · PhD
The School of Mathematical Sciences at Fudan University is one of China's leading institutions in harmonic analysis, encompassing singular integrals, function spaces, and partial differential equations. It provides rigorous analytical training for studying problems related to the Kakeya conjecture.
Massachusetts Institute of Technology
Department of Mathematics — Harmonic Analysis
United States · PhD
The MIT Department of Mathematics has a profound tradition in harmonic analysis, encompassing core areas such as Fourier restriction theory, oscillatory integrals, and Kakeya estimates, making it one of the leading academic centers for research on the Kakeya conjecture.
Princeton University
Department of Mathematics · Harmonic Analysis
United States · PhD
The Department of Mathematics at Princeton University possesses a world-class tradition in harmonic analysis, with the profound influence of the Stein school encompassing restriction theory, singular integrals, the Kakeya problem, and related areas. It is one of the premier academic institutions for research on the Kakeya conjecture.
University of California, Los Angeles
Department of Mathematics, Harmonic Analysis Direction
United States · PhD
The UCLA Department of Mathematics is a world-leading center in harmonic analysis, centered on Terence Tao and encompassing restriction theory, Kakeya estimates, additive combinatorics, and analytic number theory. It is one of the most important academic institutions for research on the Kakeya conjecture.
University of Wisconsin-Madison
Department of Mathematics, Harmonic Analysis Direction
United States · PhD
The Department of Mathematics at the University of Wisconsin-Madison has a deep tradition in harmonic analysis, encompassing singular integrals, function spaces, and partial differential equations. It is a strong academic institution for research on harmonic analysis and problems related to the Kakeya conjecture.
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