Abstract：

The moduli spaces of points on n-spheres carry natural actions of braid groups. For n=0, 1, and 3, we prove that these symmetries extend to actions of mapping class groups of certain positive genus surfaces, through exceptional isomorphisms with certain moduli of local systems. Moreover, the isomorphisms map the Coxeter invariants of points on spheres to the boundary monodromy of the corresponding local systems. We also apply this connection to the study of Stokes matrices and exceptional collections. This talk is based on a prior joint work with Junho Peter Whang.