  We describe genus g>1 potentials of semisimple Frobenius structures. Our
formula can be considered as a definition in the axiomatic context of Frobenius
manifolds. In Gromov-Witten theory, it becomes a conjecture expressing higher
genus GW-invariants in terms of genus 0 GW-invariants of symplectic manifolds
with generically semisimple quantum cup-product. The conjecture is supported by
the corresponding theorem about equivariant GW-invariants of tori actions with
isolated fixed points. The parallel theory of gravitational descendents is also
presented.
