Chris Lambie-Hanson (Institute of Mathematics, Czech Academy of Sciences) – Set theory, derived functors, and the value of the continuum

The fields of set theory and homological algebra are both centrally concerned with

questions of compactness, regarding the extent to which a structure's global properties are

determined by its local properties. It is thus no surprise that there has been considerable interplay

between these two fields. In this talk we will discuss some recent applications of set-theoretic

techniques to the study of the derived functor of the inverse limit, with further applications to the study

of strong homology and to the developing field of condensed mathematics. We then relate these

applications back to one of the oldest questions in set theory, that of the cardinality of the continuum.

At their core, these applications reduce to simple, purely combinatorial problems that are of interest in

their own right. No prior knowledge of either set theory or homological algebra will be assumed.