Grassmannians are objects of great combinatorial and geometric beauty, which arise in myriad contexts. Their coordinate rings serve as a classic example of cluster algebras, as introduced by Fomin and Zelevinsky at the start of the millennium, and their combinatorics is intimately related to algebraic and geometric concepts such as to representations of algebras and hypersurface singularities. At the core lies the idea of generating an object from a so-called "cluster" via the concept of "mutation".
In this talk, we offer an overview of Grassmannian combinatorics in a cluster theoretic framework, and ultimately take them to the limit to explore the a priori simple question: What happens if we allow infinite clusters? In particular, we introduce the notion of a cluster algebra of infinite rank (based on joint work with Grabowski), and of a Grassmannian category of infinite rank (based on joint work with August, Cheung, Faber and Schroll).
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