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 Ramsey-theoretic dichotomy for subspaces of infinite-dimensional 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 infinite-dimensional 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.
Files:
Speaker: Iian Smythe
Institution: UM
Event Organizer: Andreas R Blass ablass@umich.edu
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