A cluster algebra structure on the coordinate ring of the Sato Grassmannian

Sira Gratz (Aarhus University)

Tuesday 9th June 16:00-17:00
Maths 311B

Abstract

Cluster algebras are algebraic objects that can be constructed from a finite dataset and a simple combinatorial rule. We investigate what happens if this dataset becomes infinite. We will see that objects that arise either as colimits, or as limits, of cluster algebras in an appropriate setting are still controlled by a, now possibly infinite, dataset and a combinatorial rule. This yields, for example, a (pro-)cluster algebra structure on the coordinate ring of the Sato Grassmannian, which plays a fundamental role in the study of the KP-hierarchy.

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