A Kakeya maximal function in the (first) Heisenberg group

Department's Seminar
9 April 2024
Start time 
3:00 pm
PovoZero - Via Sommarive 14, Povo (Trento)
Physics Seminar Room, ground floor
Target audience: 
University community
UniTrento students
Contact person: 
Andrea Pinamonti
Contact details: 
Università degli Studi Trento 38123 Povo (TN) - Staff Dipartimento di Matematica
+39 04 61/281508-1625-1701-3786-1980
Pietro Wald (University of Warwick)


The Kakeya conjecture is a prominent open problem in analysis, sitting at the intersection of geometric measure theory, harmonic analysis, and PDE.
In this talk, I will introduce the (first) Heisenberg group and a notion of Kakeya set in this setting. I will then discuss the corresponding Kakeya conjecture (first solved by J. Liu) and present a new solution based on a suitable adaptation of the Kakeya maximal function to the Heisenberg group. This is based on joint work with K. Fässler and A. Pinamonti.

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