Cluster configuration spaces of finite type

Abstract: 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.

mathematical physicscommutative algebraalgebraic geometrycombinatoricsquantum algebrarings and algebrasrepresentation theory

Audience: researchers in the topic

Online Cluster Algebra Seminar (OCAS)