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Bez Lab
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The lab studies problems at the intersection of Fourier analysis and geometry.
AboutAbout the lab
Around the Fourier restriction conjecture and the Kakeya conjecture
The Bez Lab studies themes related to the Fourier restriction conjecture and the Kakeya conjecture in harmonic analysis and real analysis.
The two conjectures are closely and fruitfully interrelated, and have contributed greatly to recent progress in harmonic analysis and geometric measure theory.
The Brascamp-Lieb inequality is a broad generalization of inequalities such as Hölder's inequality, and it connects to other fields including convex geometry and information theory.
Strichartz estimates, which control the size and decay of solutions to dispersive equations such as the Schrödinger equation, are also one of the lab's research topics.
Key terms
- Kakeya conjecture
- A conjecture asking how small a set can be if it contains a line segment in every direction
- Brascamp-Lieb inequality
- A broad family of inequalities that bound the integral of a product of several functions from above in terms of the size of each function
- Dispersive equations
- Partial differential equations describing waves that spread out as they propagate, such as the Schrödinger equation
ResearchResearch themes
The lab's research fields are harmonic analysis and real analysis, with themes including the Fourier restriction conjecture, the Kakeya conjecture, geometric inequalities, and the theory of partial differential equations. Recently, it has focused in particular on problems related to the Brascamp-Lieb inequality.
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MembersFaculty
- ProfessorNeal BezPublications ↗
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Fourieroperator equation visualization” Glogger / CC BY-SA 3.0 (cropped)
- Fourier Restriction and Kakeya Conjectures and Inequalities: “Perrontree2” 作者不詳 / Public domain (cropped)
- Related lab (Sekiguchi Lab): “HyperProjectionUsingRgl” Hou710 / CC BY-SA 4.0 (cropped)
- Related lab (Shimomura Lab): “Traveling wave” P.wormer / CC BY-SA 3.0 (cropped)
- Related lab (Ishige Lab): “Heat Equation 1D BE Color” Gong Chen, Brandon Cloutier, Ning Li, Benson K. Muite and Paul Rigge with contributions from Sudarshan Balakrishnan, Andre Souza and Jeremy West / CC BY-SA 3.0 (cropped)
- Related lab (Iwaki Lab): “AiryAi Abs Surface” Inductiveload / Public domain (cropped)
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