When a set theorist hears 'combinatorics'

In this talk we will take a tour through some classic and new results in infinite Ramsey theory. Beginning with Ramsey's theorem on colorings of integers, we will see how obtaining larger "homogeneous sets" (i.e., patches of order) within graphs (equivalently, 2-colorings) is sensitive to which infinity you're working with, and even sensitive to the background set theory. We will end by discussing topological colorings (equivalently, in this case, clopen graphs), including a joint result (from a while back) of the speaker with I. Neeman.