MATH 7810: Logic Seminar: Topics in Ramsey Theory (Fall 2011)

Instructor: Justin Moore

The focus of the topic component of this course will be on generalizations and strengthenings of Ramsey's theorem for partitions of the k-element subsets of N^k: Hindman's Theorem, the Hales-Jewett Theorem, the Halpern-Lauchli Theorem. We will also study Todorcevic's abstraction of Ellentuck's theorem concerning the infinite dimensional analog of Ramsey's theorem.

One of the goals will be to discuss the applications of Ramsey theoretic methods in the study of the geometry of infinite dimensional Banach spaces. The main reference will be Todorcevic's recent book An Introduction to Ramsey Spaces. Prerequisites will be kept to a minimum. Those enrolled will be expected to present talks on the topic of the course. In addition to the topic component of this course, there will also be stand-alone talks by students, faculty, and visitors.