Pure Mathematics Colloquium: Arithmetic Ramsey theory

Title: Arithmetic Ramsey theory

Presenter: Joel Moreira (University of Warwick)

Microsoft Teams Meeting 

Summary:

In this talk I will present a survey of arithmetic Ramsey theory. This fascinating subject, which focuses on patterns which arise in arbitrary finite colourings of the natural numbers, combines ideas and tools from diverse areas of mathematics, such as graph theory, Fourier analysis, geometric group theory, and ergodic theory; and has deep connections with number theory and additive combinatorics. The first half of the talk will be dedicated to the history of this subject, and the second to recent progress on a few simple looking but still open problems.