Sagdeev Arsenii

Title: Canonical results in Ramsey theory

Abstract: A typical problem in Ramsey theory is to show that every r-coloring of a sufficiently large 'domain' contains a monochromatic copy of some fixed 'configuration'. In a canonical setting, the number of colors is unbounded, but the goal is to find either a monochromatic, or a rainbow copy. We will discuss classic canonical versions of the Ramsey, Van der Waerden, and Hales–Jewett theorems, as well as our new developments in Euclidean Ramsey theory, and pose several open problems. Joint work with Panna Gehér and Géza Tóth.