I gave an hour-long talk to the VUW Discrete Math Seminar on Thursday 17th December 2020, based on this article I wrote.
Abstract: Many key results in infinitary Ramsey theory share the same underlying structure: that of a semigroup split into infinitely many layers. Furthermore, they are often amenable to proof by the same methods. Using nonstandard analysis, we present an abstract framework and general Ramsey theorems for layered semigroups, which include as special cases Gowers’ theorem, Hindman’s theorem, the Graham–Rothschild theorem, and others.