PIMS-UVic Discrete Math Seminar: Chris Eagle

Structural Ramsey theory generalizes classical Ramsey theory by considering classes of finite sets with additional structure (such as finite groups or finite partial orders) and colourings of their substructures. When the class satisfies an appropriate amalgamation condition it is possible to assemble all of the structures in the class into a countably infinite structure, which is known as the Fraisse limit of the class. The goal of this talk is to describe a deep connection (due to Kechris, Pestov, and Todorcevic) between the structural Ramsey theory of a class of finite structures and the actions of the automorphism group of the class' Fraisse limit. This connection will be illustrated with a Ramsey theorem for finite-dimensional algebras of matrices.