On Hamiltonian geometry of the associativity equation


Seminar “Modern Mathematical Physics”

Date and Time: Tuesday, 12 February 2019, at 2:30 PM

Venue: Blokhintsev Hall (4th floor), Bogoliubov Laboratory of Theoretical Physics

Seminar topic: «On Hamiltonian geometry of the associativity equation»

Speaker: N.A. Strizhova (MSU)


The associativity equations or Witten – Dijkgraaf – Verlinde-Verlinde equations appeared during the studies of two dimensional topological field theories and turned to play important role in many problems of mathematics and mathematical physics. O.I. Mokhov has shown that these associativity equations are equivalent to certain integrable non diagonalizable systems of hydrodynamical type. This fact allowed to state the question about hamiltonian geometry of the associativity equations in the form of the systems of hydrodynamical type. Reduction to the set of stationary points of arbitrar evolution flow integral is an important construction given by O.I. Mokhov, which states that this reduction is canonically hamiltonian.
In my talk one presents complete classification of the associativity equations for the case of three primary fields with respect to a given Dubrovin – Novikov hamiltonian structure of the first order, and also one constructs canonical hamiltonian reductions for the associativity equations for the case of three or four primiary fields.
The talk is based on joint papers with O.I. Mokhov.