Algebra and dynamics of ultrafilters

Professor Yuliya Zelenyuk will present her inaugural lecture on the above topic.

The operation of a discrete semigroup S extends to the Stone-Cech compactification beta S of S so that the left translations by elements of S and all right translations are continuous. The points of beta S are taken to be the ultrafilters on S, the principal ultrafilters being identified with the points of S. The semigroup beta S is interesting both for its own sake and for its applications to Ramsey theory and to topological dynamics. The first example of such application was the proof of Hindman's Theorem. It says that whenever the set N of natural numbers is finitely colored, there is an infinite subset A of N such that the set FS(A) of all finite sums of distinct elements of A is monochrome. He will give a brief introduction to beta S and present some new results.

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