Time allowing, the talk will explore three themes.

1. Structural Ramsey theorems incorporating functions, in addition to relations, into structures. The methods here give a new proof of Pr¨omel’s theorem and yield generalizations of theorems of Neˇsetˇril–R¨odl, Abramson–Harrington, and Pr¨omel.

2. A general, “abstract algebraic” approach to unstructured Ramsey theorems (the classical Ramsey theorem, the Hales–Jewett theorem, and the dual Ramsey theorem of Graham–Rothschild).

3. A self-dual unstructured Ramsey theorem obtained by the methods of 2.