Tutorial Track
L. Barto: TBA
J. Bergfalk: TBA
P. Larson: Universally Measurable Sets
A subset of a topological space is said to be universally measurable if it is measured by the completion of each countably additive $\sigma$-finite Borel measure on the space. We will survey what is known about universally measurable subsets of Polish spaces, including constructions of exotic examples. We will also present some of the many basic open questions about the universally measurable sets, in particular the question of whether it is consistent that all universally measurable sets have the Baire property. Along the way we will discuss the related notions of universally null, universally categorical and universally Baire sets.
P. Szeptycki: Ramsey theoretic notions of convergence and compactness
Interactions between Ramsey Theory, functional analysis, algebra and topology have a long history. These lectures will focus on various Ramsey theoretic notions of convergence that have arisen independently in the literature. For example, Knaust defined a notion of Ramsey convergence in his study of angelic spaces, Hindman et al to answer a purely topological question, and Banakh and others in connection to topological algebra, specifically the existence of idempotents in topological semi-groups. We will focus on our recent work applying these Ramsey-like convergence properties in the formulation of so-called high-dimensional compactness properties. Some applications, open problems and future directions will also be discussed.
Research Track
Scientific committee
Jan Grebík, Masaryk University, and University of California, Los Angeles
Chris Lambie-Hanson, Institute of Mathematics, Czech Academy of Sciences
