There will be a logic seminar next Wednesday, November 2, from 4 to 5:30, in 3096 East Hall.
Peter Krautzberger will speak on “Idempotent Ultrafilters: An Introduction”.
Since the1970s a close relationship has been studied between idempotent ultrafilters and Ramsey-type theorems with an algebraic flavor, most prominently Hindman’s Theorem and the Central Sets Theorem. This connection led to the investigation of the rich algebraic structure that can be found on the ultrafilters on a semigroup.
At next week’s seminar I hope to begin a conversational introduction into the theory behind these results. The initial goal will be to discuss how to extend a semigroup operation to the ultrafilters, Ellis Lemma on the existence of idempotent elements and, if time allows it, the Galvin-Glazer proof of Hindman’s Theorem. I will send out some notes ahead of time so as to facilitate an active discussion of these structures.
This talk will be video recorded. There will also be a Google+ Hangout during the seminar via Peter Krautzberger.