Tao Mai (Baylor University, Texas) : An extension of Hilbert transform to hyperbolic groups
Abstract: The classical Hilbert transform has a natural analogue on the nonabelian free groups by decomposing the free group into disjoint subsets according to the first letter of the reduced words. Mei and Ricard prove that such a transform (decomposition) is unconditional with respect to the noncommutative Lp norm associated with the free group von Neumann algebras for all 1<p<\infty. I plan to talk about a possible extension of the Lp unconditionality of such “transforms” to the general hyperbolic groups.