Given infinite cardinals \(\kappa\) and \(\theta\), functions of the form \(c:[\kappa]^2 \rightarrow \theta\) exhibiting certain unboundedness properties provide a strong counterexample to the generalization of Ramsey's theorem to \(\kappa\) and have seen a wide variety of applications. In this talk, we will discuss the existence of such strongly unbounded colorings, focusing in particular on colorings with subadditivity properties. We will then present some applications to general topology. In particular, building on work of Chen-Mertens and Szeptycki, we will prove that the failure of the Singular Cardinals Hypothesis implies the existence of a Fréchet, \(\alpha_1\)-space whose \(G_\delta\)-modification has large tightness. This is joint work with Assaf Rinot.

This talk will be given in mixed mode, in person as well as via Zoom.

If you want to attend in person, please be aware of the fact that you will be required to show proof of your COVID-19 "2.5G" status (vaccinated, recovered, PCR tested) upon entry of the buildings, or during sporadic random checks in the seminar rooms. During the lectures we will also pass around an attendance sheet to facilitate contact tracing. (According to the regulations, this form will be kept for 28 days and destroyed thereafter.)