Frobenius manifolds in algebraic geometry and singularity theory

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A Frobenius structure on a complex manifold consists of a multiplication on the tangent bundle and a metric subject to several compatibility conditions. These structures appear in quite different branches of mathematics like singularity theory, algebraic topology or differential geometry. Mirror symmetry, one of the central research areas in mathematics and theoretical physics can be stated as equivalence of Frobenius manifolds. The proposal aims at extending the known classes of equivalent Frobenius structures. In particular, we plan to study semi-simple Frobenius manifolds, the Stokes phenomena and quantum cohomology for orbifolds (manifolds modulo finite group actions). We also seek to understand the meaning of structures known in one type of Frobenius manifolds (like gravitational descendants in Gromov-Witten-theory) on the other side of the mirror picture (e.g. in singularity theory).