We consider some simplest and most common finite semigroups that arise frequently in many areas of pure and applied mathematics, in particular, cyclic semigroups and bands. We then consider the question which of them have copies in the Stone-Cech compactification of the natural numbers. The latter itself is a compact right topological semigroup with a very complicated structure and important applications to Ramsey theory and to topological dynamics. The first application to Ramsey theory was the proof of Hindman’s theorem (1974): whenever the set of natural numbers is finitely colored, there is an infinite sequence all of whose sums are monochrome. We show that to every finite semigroup in the Stone-Cech compactification there corresponds a Ramsey theoretic result.
DR. YEVHEN ZELENYUK
UNIVERSITY OF THE WITWATERSRAND,
Johannesburg, South Africa
Lecture 1 : Finite semigroups, 11:00 a.m.
Lecture 2 : Applications to Ramsey theory, 12:00 m.
