Gauss-Manin Connection in Disguise

GMCD aims to unify automorphic forms with topological string partition functions and give a systematic way of studying sub-moduli of moduli spaces using the theory of holomorphic/algebraic foliations. It aims to replace the variation of Hodge structures with certain vector fields whose solutions are a vast generalization of automorphic forms. It aims to return Hodge theory to its origin which is the study of multiple integrals due to Abel, Gauss, Legendre, Poincare', Picard and many others.