UC Davis Mathematics

Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

Braiding for Grassmannian cluster algebras

QMAP Seminar

Speaker: Chris Fraser, University of Minnesota
Related Webpage: https://sites.google.com/site/cmfraser37/
Location: 1147 MSB
Start time: Fri, Feb 14 2020, 12:00PM

Cluster algebras were invented with the goal of abstracting multiplicative properties of canonical basis elements in Lie theory. They have since seen wide application in math and physics. The homogeneous coordinate ring of the Grassmannian is a prototypical example of a cluster algebra. We will explain a (pseudo)-action of an extended affine braid group on the Grassmannian via symmetries of its cluster structure. We will discuss ongoing work with Bernhard Keller in which we interpret this action in terms of Seidel-Thomas spherical twist functors on Jensen-King-Su's additive categorification of the Grassmannian cluster structure.