The structure of 2D semi-simple topological field theories
Givental has proposed a structure formula for the higher-
genus Gromov-Witten invariants of varieties whose quantum
cohomology algebra is (generically) semi-simple. This talk
describes the solution of a related question (which implies
Givental's conjecture), namely, the classification of
all possible "couplings to gravity" of a semi-simple 2D
Topological Field theory (= Frobenius algebras). The
result follows from the Mumford conjecture (proved by
Madsen-Weiss) on the cohomology of the stable mapping
class groups.