In broad terms, Ramsey theory can be described as the study of when certain "patterns" must appear in sufficiently large combinatorial structures. Ramsey theory of ordinals and cardinals has been an active 
research area since the introduction of partition calculus by Erdös and Rado in 1950's. These studies were later generalized to topological spaces by Baumgartner.

In recent years, closed and topological partition relations on ordinals has been a focus of research. In this talk, we will first briefly review some results in partition calculus of countable ordinals and their topological counterparts. We will then provide new lower and upper bounds for the closed ordinal Ramsey numbers Rᶜˡ(ω+n,3). This is joint work with Irmak Sağlam.

The talk will be self-contained in the sense that no prior knowledge on Ramsey theory or set theory is necessary.