Logic Seminar
Christian Rosendal
UIC
A new proof of Gowers' block Ramsey Theorem
Abstract: I will present the main ideas of a new proof of the fundamental block
Ramsey theorem of Gowers that has had spectacular applications in Banach
space theory. Gowers' original proof cleverly combined Ramsey theory and
game theory to compensate for the fact that a true Ramsey theoretical
statement fails to hold in general, but at the same time involved
approximation arguments compensating for a lack of compactness. This made
the proof somewhat complicated and the ensuing notion of weakly Ramsey
sets involved quantifications over approximations hard to induct over and
extend beyond analytic sets. Our new proof involves a new game, the
infinite asymptotic game, and a new notion of strategically Ramsey sets
which completely echews approximations and allows us to give a very smooth
proof of Gowers' theorem.
seminar begins with tea.
Tuesday November 4, 2008 at 4:00 PM in SEO 612