Thursday, October 26, 2017, from 4 to 5:30pm
East Hall, room 3096
Speaker: David J. Fernández Bretón (University of Michigan)
Title: Higher degree versions of the Central Sets Theorem, II
The Central Sets Theorem is a Ramsey-theoretic result due to Furstenberg, from 1981, and multiple generalizations of it (in a variety of different directions) have been proved afterwards (to the best of my knowledge, the currently most general statement is due to De, Hindman and Strauss in 2008, but there are also many relevant results due to Bergelson). This is the second of a series of two talks, where we will explain how to interpret the Central Sets Theorem as a statement about linear polynomials in a polynomial ring with countably many variables, and prove a couple of natural generalizations involving polynomials of higher degree. The main tool that we use in our proof is the algebra of the Cech–Stone compactification (that is, these are “ultrafilter proofs”).