Date: Thursday, September 30, 2021
Location: 2866 East Hall (4:00 PM to 5:30 PM)
Title: Parametrizing the Ramsey theory of vector spaces
Abstract: In the late 90's, Gowers proved a Ramseytheoretic dichotomy for subspaces of infinitedimensional Banach spaces. The combinatorial essence of this result was later extracted by Rosendal in the setting of discrete vector spaces. Both dichotomies say, roughly, that given a nice (e.g., Borel) partition of the set of infinite block sequences of vectors, there is an infinitedimensional subspace with a wealth of block sequences entirely contained in, or disjoint from, one piece of the partition. We will describe a new "parametrized" form of Rosendal's dichotomy: Given a nice family of partitions indexed by the reals, say, there is a single subspace which witnesses Rosendal's dichotomy for uncountably many of the partitions, simultaneously. We will also give an application to families of linear transformations.
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Speaker: Iian Smythe
Institution: UM
Event Organizer: Andreas R Blass ablass@umich.edu
