Title: The Semigroup $beta S$
by Dona Strauss (University of Leeds) as part of Topological Groups

Lecture held in Elysium.

Abstract
If $S$ is a discrete semigroup, the semigroup operation on $S$ can be extended to a semigroup operation on its Stone–Čech compactification $beta S$. The properties of the semigroup $beta S$ have been a powerful tool in topological dynamics and combinatorics.

I shall give an introductory description of the semigroup $beta S$, and show how its properties can be used to prove some of the classical theorems of Ramsey Theory.