Place: Fields Institute (Room 210)

Date: January 22 , 2016 (13:30-15:00)

Speaker: Diana Ojeda

Title: Topological partition relations for countable ordinals

Abstract:

The subject of topological partition relations provides answers to questions

of the following form: Given a topological space X and a subspace Y, is it

possible to reduce any given coloring of the pairs of elements of X to a simpler

coloring, by passing to a subspace homeomorphic to Y?

I will first present a survey of topological partition relations for countable

ordinals with the order topology. In many instances it is useful to represent

countable ordinals using families of finite sets. I will describe how to obtain

such representations; and will present results from a joint project with William

Weiss, where we obtain topological partition relations for ordinals below $\omega^2$ with the order topology.