Title of the course: Ultrafilters and Ramsey Theory
Instructor: Visiting Asst. Prof. Nick Ramsey
Institution: UCLA
Dates: 30 August – 4 Seprember 2021
Prerequisites: None
Level: Graduate, advanced undergraduate
Abstract: A classic theorem of Ramsey states that for any n, there is a k such that a graph of size k must contain either a complete or empty graph of size n. Informally, this suggests that perfect chaos is impossible: inside a graph of sufficiently large size, there must be a large subset which looks very uniform. Later developments in many areas of mathematics–including set theory, additive combinatorics, dynamics, and computer science–offered variations on this theme, producing a body of loosely related results known under the banner `Ramsey Theory.’ In this course, we will introduce ultrafilters and discuss the basics of their applications to combinatorics, with an emphasis on their use in proving Ramsey-theoretic results.
Language: EN