CRM Fields PIMS Prize Lecture: Prof. Stevo Todorcevic (University of Toronto)

Abstract:

 

 

We give an overview of the most basic Ramsey theoretic principles such as the Hales-Jewett theorem and the Halpern-Läuchli theorem and the corresponding Ramsey space theories that they lead to. The theory has natural counterparts both in the sense of dimensions and cardinalities of the structures. For example, we explain the close relationships between the finite and the infinite-dimensional theory and we also explain the Ramsey theory of finite structures and its close relationship to the Ramsey theory of infinite structures. If time permits we will also explain some of the most recent advances in the density Ramsey theory with a particular emphasis on the new phenomena that show up in the context of infinite structures. We point out some of the successes in applying this theory to, for example, topological dynamics and functional analysis. Professor Todorcevic obtained his Ph.D. in Belgrade and currently holds a Canada Research Chair at the University of Toronto.