skip to main content

Caltech/UCLA/USC Joint Analysis Seminar

Tuesday, March 1, 2022
2:30pm to 3:30pm
Add to Cal
Online and In-Person Event
A Kaufman-type restricted projection theorem in R^3
Joshua Zahl, Department of Mathematics, University of British Columbia,

In-Person will be held in 310 Linde Hall @ Caltech

In this talk, I will discuss the proof of a conjecture in projection theory posed by Fässler and Orponen. If K is a set in R^3 of Hausdorff dimension at most one and if \gamma is a space curve that obeys a natural non-degeneracy condition, then Fässler and Orponen conjectured that for a typical v \in \gamma, the dimension of the projection K.v must be dim(K). We resolve this conjecture by proving a Kaufman-type bound on the dimension of the set of exceptional projections.

While Fässler and Orponen's conjecture is a question in geometric measure theory, the solution uses ideas from harmonic analysis. In particular, we resolve the conjecture by proving L^p bounds on the Wolff circular maximal function for families of rough curves. This is joint work with Orit Raz, Malabika Pramanik, and Tongou Yang

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].