Cluster configuration spaces of finite type

Cluster configuration spaces of finite type

I will talk about a "cluster configuration space" M_D, depending on a finite Dynkin diagram D. The space M_D is an affine algebraic variety that is defined using only the compatibility degree of the corresponding finite-type cluster algebra. In the case that D is of type A, we recover the configuration space M_{0,n} of n (distinct) points in P^1. There are many relations to finite-type cluster theory, but an especially close connection to the finite-type cluster algebra with universal coefficients.

This talk is based on joint works with Nima Arkani-Hamed, Song He, and Hugh Thomas.

Nota: Esta charla es parte del Online Cluster Algebra Seminar organizado por Anna Felikson, Michael Gekhtman, Daniel Labardini-Fragoso, Kyungyong Lee, Pierre-Guy Plamondon, Ralf Schiffler y Khrystyna Serhiyenko.