Tutorial Track
L. Barto: The complexity of constraint problems
I will talk about some results and mathematical techniques that are used to study the computational and descriptive complexity of Constraint Satisfaction Problems (CSPs) and Promise CSPs. The focus will be on concepts and ideas that could potentially be applicable more broadly.
J. Bergfalk: The cohomology of the ordinals
We'll survey cohomological approaches to infinitary combinatorics, and most particularly to that of the ordinals $\omega_n$. The core of this series of talks is ongoing joint work with Chris Lambie-Hanson and Jing Zhang. At the core, in turn, of that work is a stubbornly open question about how far those ordinals' combinatorics are determined by the ZFC axioms alone. We will complain about this question's obstinacy.
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
