EVENT DETAILS AND ABSTRACT

Title: Double ramification cycles and quantum integrable hierarchies
Speaker: Paolo Rossi
Speaker Info: Institut de Mathématiques de Bourgogne, Dijon
Brief Description:
Special Note:
Abstract:

n a series of joint papers with A. Buryak we defined and studied a family of quantum integrable hierarchies associated to cohomological field theories. The construction makes use of the intersection theory of the double ramification cycle and the Hodge classes in the moduli space of curves. At the classical limit, our hierarchies are conjectured to be Miura-equivalent to the Dubrovin-Zhang hierarchies associated to the same cohomological field theories (we were able to prove the conjecture in a number of special cases), so our approach provides an effective way of quantizing the Dubrovin-Zhang hierarchies. We also proved certain recursion formulas allowing for explicit computation of the quantum integrable system in a number of interesting cases (KdV, Toda, Gelfand-Dickey, ILW, etc.). Even at the classical level this provides a new, arguably more direct, approach to the connection between Gromov-Witten theory and integrable systems. The quantizations were not previously known.