Caltech/UCLA/USC Joint Analysis Seminar
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