Grassmanian categories of infinite rank
In this talk, I’ll describe our work towards providing an infinite rank version of the Grassmanian cluster categories introduced by Jensen, King and Su. We develop a new combinatorial tool for determining when two k-subsets of the integers are “non-crossing”, or equivalently when two Plücker coordinates of a Grassmanian cluster algebra of infinite rank are “compatible”. We use this tool to show that there is a structure preserving bijection between these Plücker coordinates and the generically free modules of rank 1 in our Grassmanian category of infinite rank, mirroring a result of Jensen, King and Su in the finite case. This is joint work with Man-Wai Cheung, Eleonore Faber, Sira Gratz and Sibylle Schroll.