Dana Bartošová - Approximate Ramsey properties for finite-dimensional Banach spaces and simplexes
Channel: Mathematical Logic UFBA
Date: 2015-05-29

Seminar given by Dana Bartošová at the Instituto de Matemática of the Universidade Federal da Bahia - Brazil.
May 27, 2015

Abstract:
We will introduce connections between Ramsey theoretic phenomena and dynamics of topological groups.
In this talk, we will be particularly interested in the group of linear isometries of the universal, approximately homogeneous 
separable Banach space, the Gurarij space, and the group of affine homeomorphisms ofthe universal homogeneous 
compact metrizable simplex, the Poulsen simplex. The major tool is the approximate Ramsey property for the class of 
finite-dimensional Banach spaces and finite-dimensional simplexes, respectively, which we prove by an application of 
the Graham-Rothschild Dual Ramsey theorem. This is a joint work with Jordi Lopez Abad (ICMAT Madrid) and Brice 
Mbombo (USP).