Hamiltonian geometry of the associativity equations

The talk concerns the associativity equations or the Witten–Dijkgraaf–Verlinde–Verlinde (WDVV) system of equations. The complete classification of the associativity equations in the case of 3 primary fields with respect to the existence of a first-order Dubrovin–Novikov Hamiltonian operator will be present. Also, we consider reductions on the stationary points of integrals for the associativity equations in the cases of 3 and 4 primary fields. This is a joint work with O.I. Mokhov.