A Geometric study of hypergeometric functions

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We got the following results concerning hypergeometric functions.0) Studied systems of linear partial differential equations modeled after grassmannians.1) Investigated the Hodge structure of twisted cohomology groups and Got many integral formulae involvinggot twisted Riemann inequalities absolute values in the integrands.2) Got the uniformizing differential equation of the complex hyperbolicstructure on the moduli space of marked cubic surfaces. Proved that it is the restriction of the higher dimensional hypergeometric differential equation onto a d.3) Developed the intersection theory for twisted cycles : got determinantformulae for not necessarily genetic hyperplane arrangements. Got partial results in the case that some quadratic hypersurfaces get into the arrangements.4) Found a hyperlybolic structure on the real locus of the moduli space of marked cubic surfaces. Found that the corresponding group is the hyperbolic Coxeter group ; Constructed automorphic forms by the help of a modular embedding.5) Made a geometric study of the hypergeometric function withFound that the monodromy groups turns out to be scottky imaginary exponents. Groups of genes 2. Constructed a modular ttu with rasp. To the monodromy group.