A taste of Ergodic Ramsey theory

Abstract: Ergodic Ramsey theory is a branch of mathematics that, loosely speaking, applies Ergodic theory (measurable dynamics) to the study of certain number-theoretic problems.

In this talk I will give a quick introduction to both Ramsey theory and Ergodic theory, and how the two relate via the Furstenberg correspondence principle. I will conclude with a brief discussion of Szemeredi's theorem on arithmetic progressions (often considered a highlight of 20:th century mathematics) and Furstenberg's ergodic-theoretic proof of it. I aim to convey how seemingly very abstract mathematical methods from measure theory and functional analysis can be used to prove easily formulated number-theoretic statements.

Mathematics

Audience: general audience

Gothenburg PhD seminar

Series comments: Rooms and times may vary, please check the latest update. In-person only.