Clement Yung, University of Toronto
Weak A2 spaces, the Kastanas game and strategically Ramsey sets
In the past century, the insight behind the original Ramsey's theorem proved to be applicable to a wide range of mathematics, such as number theory, functional analysis and topology. This spurred two particular directions of Ramsey theory: The first one is known as topological Ramsey theory, a general procedure developed by Todorcevic to prove many seemingly unrelated Ramsey's theorem-like results. The second one is the Ramsey theory of Banach spaces, kickstarted by Gowers' shocking application of Ramsey theory to resolve a long-standing open problem in Banach space theory. In this talk, I introduce the theory of weak A2 spaces, which serves as a possible intersection between these two Ramsey theories and discuss how several infinite games that appeared in these Ramsey theories (the Kastanas game, the Gowers game and the asymptotic game) are closely related.
MC 5479