Place: Fields Institute (Stewart Library)
Date: March 28th, 2016 (13:00-14:00)
Speaker: Iian Smythe
Title: Towards a selective Gowers dichotomy
Abstract: Gowers’ famous dichotomy is an approximate Ramsey theorem for analytic partitions of the space of infinite block sequences in a Banach space, and has been used it to establish important classification results in Banach space theory. In work currently in progress, we attempt to isolate the combinatorial properties of the space of block sequences which enable these constructions, and prove that they can be carried out within “selective” subfamilies. Under large cardinal assumptions, we extend these results to all definable partitions, with the goal of giving “complete combinatorics” for generic ultrafilters of block sequences.