# The double ramification hierarchy

#### Paolo Rossi, University of Bourgogne, Dijon.

In a series of joint papers with A. Buryak, B. Dubrovin and J. Guéré we investigated Buryak's original construction of the double ramification (DR) hierarchy, a procedure that associates to each cohomological field theory on the moduli space of curves a 1+1 integrable system of PDEs. We uncovered several interesting properties of these integrable systems and extended the construction to include their canonical quantization in a very explicit fashion. Finally we investigated the equivalence of this construction with a quite different one, due to Dubrovin and Zhang and conjectured that, in those case in which the DZ hierarchy is defined, it coincides with the DR hierarchy after a change of coordinates. I will report on this body of work and show some interesting examples.

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