Kakeya maximal estimates via real algebraic geometry
Jonathan Hickman (University of Edinburgh)
Abstract: The Kakeya (maximal) conjecture concerns how collections of long, thin tubes which point in different directions can overlap. Such geometric problems underpin the behaviour of various important oscillatory integral operators and, consequently, understanding the Kakeya conjecture is a vital step towards many central problems in harmonic analysis. In this talk I will discuss work with K. Rogers and R. Zhang which apply tools from the theory of semialgebraic sets to yield new partial results on the Kakeya conjecture. Also, more recent work with J. Zahl has used these methods to improve the range of estimates on the Fourier restriction conjecture.
mathematical physicsanalysis of PDEsclassical analysis and ODEscombinatoricscomplex variablesfunctional analysisinformation theorymetric geometryoptimization and controlprobability
Audience: researchers in the topic
Probability and Analysis Webinar
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Organizers: | Polona Durcik*, Irina Holmes, Paata Ivanisvili*, Tomasz Tkocz, Beatrice-Helen Vritsiou |
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