A double ramification (DR) cycle is a cycle in the moduli space of

genus g Riemann surfaces with marked points which is given by genus

g surfaces that are ramified coverings of the Riemann sphere with

prescribed ramification profiles over 0 and infinity. In this

reading seminar, I will review a recent application of the DR cycles

to the construction of (both classical and quantum) integrable

hierarchies associated with any given cohomological field theory,

called the DR hierarchies. It is conjectured by A. Buryak that

for any semisimple cohomological field theory the (classical) DR

hierarchy is Miura equivalent to the Dubrovin-Zhang hierarchy.

Main references:

Buryak - Double ramification cycles and integrable hierarchies, 2014

Buryak and Rossi - Double ramification cycles and quantum integrable systems, 2015