International Laboratory of Cluster Geometry

Name of the project: Cluster algebras and moduli spaces of flat and holomorphic connections

The main objective of this project is the expansion of methods applicable for the computation of the canonical characteristic classes in moduli spaces of complex curves over spaces of flat connections. The modern approach to the computation of integrals of canonical classes is based on topological recursion that allows to recurrently express integrals of characteristic classes. The initial state of the proposed project is the formation of a cluster theory for moduli spaces of curves and the study of their applications in the computation of integrals of canonical classes.