Double ramification cycles and integrable hierarchies
I will talk about a new construction of a Hamiltonian hierarchy of PDEs associated to a cohomological field theory. The construction is based on the integration over the double ramification cycles and is motivated by Symplectic Field Theory. The hierarchy has a lot of nice properties that follow from the geometry of the double ramification cycles. Conjecturally, in the semisimple case, the new hierarchy is related to the Dubrovin-Zhang hierarchy by a Miura transformation. Finally, I will present a construction of a quantization of our new hierarchy.
My talk is based on our joint work in progress with Paolo Rossi.