Abstract: |
The double ramification hierarchies are (classical or quantum, infinite dimensional) integrable systems constructed using the intersection theory of the moduli space of stable marked Riemann surfaces. It was defined by A. Buryak and studied in a number of papers with Dubrovin, Guéré and myself. The entry datum, to which an integrable system is associated, is a Cohomological Field Theory, in the sense of Kontsevich and Manin and the geometry of the double ramification cycle (a compactification of the the locus of curves whose marked points supporting a principal divisor). In this talk I will present the main ideas, examples and applications and I will report on the progress in proving our main conjecture, that the classical DR hierarchy is equivalent (through a change of coordinates) to the Dubrovin-Zhang hierarchy involved in the generalized version of Witten's conjecture. |