On Hamiltonian geometry of the associativity equations
In the case of three primary fields, the associativity equations (the WDVV equations of the two-dimensional topological quantum field theory) can be represented as integrable nondiagonalizable systems of hydrodynamic type (O.I. Mokhov). The Hamiltonian geometry of these systems depends on the metric of the associativity equations: there are examples, which have local homogeneous first-order Hamiltonian structures of the Dubrovin-Novikov type, and examples, which do not have such structures (O.I. Mokhov and E.V. Ferapontov). So there arose the classification problem of the existence of such a Hamiltonian structure for the associativity equations. O.I Mokhov and the author have completely solved this problem. These results will be presented.