Senior Honors Thesis Presentation: "Connections between cluster algebras and Grassmannians, a case study."

Abstract: We take a dive into the theory of cluster algebras, certain commutative rings whose generators and relations are recursively defined, by examining one of the more standard examples: the Grassmannian. In particular, we will discuss how to endow the (homogeneous) coordinate ring of the Grassmannian with a cluster structure. Time permitting, we will also briefly discuss the story for Schubert and Positroid varieties, certain subvarieties of the Grassmannian. The focus will be on the combinatorics involved, and although there may be parts requiring a more advanced algebraic background, most of the talk should be accessible to students familiar with matrix algebra and basic combinatorics.

Host: Laura Escobar Vega