Cluster algebras, categorification, and some configuration spaces

Abstract: The real part of the configuration space M_{0,n} of n points on a projective line has a connected component which is closely related to the associahedron. As an affine variety, it is defined by explicit equations which are in close connection with exchange relations for cluster variables in type A. This has been generalized to all Dynkin types.

In this talk, we will construct an affine variety associated to any representation-finite finite-dimensional algebra over an algebraically closed field. The equations defining the variety will be obtained from the F-polynomials of indecomposable modules over the algebra. This generalizes previous results, which can be recovered by applying our construction to Jacobian algebras in Dynkin types.

This talk is based on an ongoing project with Nima Arkani-Hamed, Hadleigh Frost, Giulio Salvatori and Hugh Thomas.

K-theory and homologyquantum algebrarings and algebrasrepresentation theory

Audience: researchers in the topic

Paris algebra seminar

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