Grassmannians, Cluster Algebras and Hypersurface Singularities

Abstract: Grassmannians are objects of great combinatorial and geometric beauty, which arise in myriad contexts. Their coordinate rings serve as a classical example of cluster algebras, and their combinatorics is intimately related to algebraic and geometric concepts such as to representations of algebras and hypersurface singularities.

In this talk, we take these ideas to the limit to explore the a priori simple question: What happens if we allow infinite clusters? In particular, we discuss 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).

mathematical physicscommutative algebraalgebraic geometrycombinatoricsquantum algebrarings and algebrasrepresentation theory

Audience: researchers in the topic

Online Cluster Algebra Seminar (OCAS)