University of Amsterdam.

The so-called moonshine phenomenon relates modular forms and finite group representations. After the celebrated monstrous moonshine, various new examples of moonshine connection have been discovered in recent years. The study of these new moonshine examples has revealed interesting connections to K3 surfaces, arithmetic geometry, and string theory.  In this colloquium I will give an overview of these recent developments. 
 

Abstract: Quantales are ordered algebras which can be thought of as pointfree noncommutative topologies. In recent years, their connections have been studied with fundamental notions in noncommutative geometry such as groupoids and C*-algebras. In particular, the setting of quantales corresponding to étale groupoids has been very well understood: a bijective correspondence has been defined between localic étale groupoids and inverse quantale frames. We present an equivalent but independent way of defining this correspondence for topological étale groupoids and we extend this correspondence to a non-étale setting.