Geometry and analytic theory of Frobenius manifolds

Abstract

Main mathematical applications of Frobenius manifolds are in the theory of Gromov - Witten invariants, in singularity theory, in differential geometry of the orbit spaces of reflection groups and of their extensions, in the hamiltonian theory of integrable hierarchies. The theory of Frobenius manifolds establishes remarkable relationships between these, sometimes rather distant, mathematical theories.

arXiv comment11 pages, to appear in Proceedings ICM98

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• Helix Structures in Quantum Cohomology of Fano Varieties
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• An update on semisimple quantum cohomology and F-manifolds
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• Global Mirrors and Discrepant Transformations for Toric Deligne-Mumford Stacks
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• Frobenius Manifolds And Virasoro Constraints
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• Moduli, Motives, Mirrors (Plenary talk at the 3rd ECM, Barcelona, July 10-14, 2000)
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