This talk is about a categorification of the coordinate rings of Grassmannians of infinite rank in terms of graded maximal Cohen-Macaulay modules over a hypersurface singularity. This gives an infinite rank analogue of the Grassmannian cluster categories introduced by Jensen, King, and Su. In a special case, when the hypersurface singularity is a curve of countable Cohen-Macaulay type, our category has a combinatorial model by an ``infinity-gon'' and we can determine triangulations of this infinity-gon.

I will first give an introduction to Grassmannian cluster algebras and categories, and then explain our limit constructions. This is joint work with Jenny August, Man-Wai Cheung, Sira Gratz, and Sibylle Schroll.

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Grassmannian Categories Of Infinite Rank And Rings Of Countable Cohen-Macaulay Type