The pentagram map and its analogues act on interesting and complicated spaces. The simplest of them is the classical moduli space M0,n of rational curves of genus 0. These moduli spaces have a rich combinatorial structure related to the notion of "Coxeter frieze pattern" and can be understood as a "cluster manifolds". In this talk, I will explain how to describe the action of the pentagram map (and its analogues) in terms of friezes. The main goal is to understand how this action fits with the cluster algebra structure, and in particular, with the canonical (pre)symplectic form.
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