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Double ramification cycles and integrable hierarchies

Giulio Ruzza
Monday, June 6, 2016 - 14:00 to 16:00

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

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