On Hamiltonian geometry of the associativity equations and their reductions

The talk concerns with the Hamiltonian geometry of the associativity equations (the Witten–Dijkgraaf–Verlinde–Verlinde system of equations). In this talk, we present a 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. Also, we consider canonical Hamiltonian reductions of the associativity equations in the cases of 3 and 4 primary fields.