Reconstructing Topologies on Monoids.‎‎

Over the past decade, there has been increasing interest in reconstructing compatible topologies on monoids and groups from their algebraic structure. The central theme is the extent to which natural topologies, particularly Polish topologies, are determined by the underlying monoid.

The talk focuses on full transformation monoids and symmetric groups on infinite sets, as well as endomorphism monoids and automorphism groups of key structures and topological spaces. We examine the existence and uniqueness of minimal and maximal Polish topologies, and highlight tools used to identify them, including the Zariski topology, automatic continuity, and variants of property X.