Seminar Event Detail


Logic

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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