Invited Addresses

We consider frames and Bessel systems generated by iterations of the form {Ag : g ∈ G, 0 ≤ n < L(g)}, where A is a bounded linear operators on a separable complex Hilbert space H and G is a countable set of vectors in H. The system of iterations mentioned above come from the so called dynamical sampling problem. In dynamical sampling, an unknown function f and its future states Af are coarsely sampled at each time level n, 0 ≤ n < L, where A is an evolution operator that drives the system. The goal is to recover f from these space-time samples. The dynamical sampling problem has connections and applications to other areas of mathematics including, Banach algebras, C∗-algebras, spectral theory of normal operators, and frame theory. Nets Katz (Caltech) Scenes from Kakeya sets in R near the Wolff exponent. Abstract (joint work with Josh Zahl): We discuss some vignettes from an attempt to improve Wolff’s lower bound in R. Conditional on a strong result of discretized sum product type, only a few different scenarios need be considered.joint work with Josh Zahl): We discuss some vignettes from an attempt to improve Wolff’s lower bound in R. Conditional on a strong result of discretized sum product type, only a few different scenarios need be considered. Andrei Lerner (Bar-Ilan University) On pointwise estimates involving sparse operators. Abstract: In this talk we survey several recent results establishing a pointwise domination of Calderón-Zygmund operators by sparse operators defined by