Abstract: By "infinite-combinatorial topology" we mean a study of topological objects using tools and ideas from infinitary combinatorics.
We will give an introduction to the part of this field which deals with topological selection principles (i.e., hypotheses concerning the ability to diagonalize sequences of open covers of a given topological space). This is an elegant unified framework introduced by Scheepers to study many classical as well as some new notions in set theoretic topology (e.g.: Menger property, Hurewicz property, Rothberger property C'', Gerlits-Nagy gamma-property, etc. - all definitions will be given in the talk).
Starting from historical motivations and basic definitions, we will survey some results obtained in the last few years. Some of the easier proofs will be sketched, and many fascinating open problems will be introduced.
The talk does not assume prior knowledge.