Geometry and analyti theory of Frobenius manifolds

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. 1991 MS Classification 32G34, 35Q15, 35Q53, 20F55, 53B50 WDVV equations of associativity is the problem of finding of a quasihomogeneous, up to at most quadratic polynomial, function F (t) of the variables t = (t, . . . , t) and of a constant nondegenerate symmetric matrix (