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UBC Theses and Dissertations

Kakeya maximal function conjecture for semialgebraic mappings Rai Choudhuri, Mukul


The Kakeya maximal function conjecture is a quantitative, single scale formulation of the Kakeya conjecture. Recently, algebraic methods have been leading to progress in the Kakeya family of problems. In 2018, Katz and Rogers proved a conjecture concerning the number of 𝛿-tubes with 𝛿-separated directions which intersect a semialgebraic set with proportion at least λ. We will discuss the proof of this result which involves real algebraic geometry. We will then use this result to prove the Kakeya maximal function conjecture for the special case when the mappings are semialgebraic.

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