I will describe an approach to studying the Kakeya maximal function in high dimensions via the Guth--Katz polynomial partitioning method. Although the approach does not currently produce better bounds than the record set by Katz--Tao, it is rather flexible, provides a lot of interesting structural information and gives rise to some interesting algebraic/geometric problems.
High dimensional Kakeya maximal estimates via polynomial partitioning
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Nom de l'orateur
Jonathan Hickman
Etablissement de l'orateur
University of St Andrews
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