Integrability, Quantization and Moduli Spaces of Curves

Abstract

This paper has the purpose of presenting in an organic way a new approach to integrable (1+1)-dimensional field systems and their systematic quantization emerging from intersection theory of the moduli space of stable algebraic curves and, in particular, cohomological field theories, Hodge classes and double ramification cycles. This methods are alternative to the traditional Witten-Kontsevich framework and its generalizations by Dubrovin and Zhang and, among other advantages, have the merit of encompassing quantum integrable systems. Most of this material originates from an ongoing collaboration with A. Buryak, B. Dubrovin and J. Guéré.

References in corpus (3)

• Double ramification cycles on the moduli spaces of curves
• Double ramification cycles and integrable hierarchies
• Gromov-Witten invariants of target curves via Symplectic Field Theory

Cited by in corpus (5)

• DR/DZ equivalence conjecture and tautological relations
• Towards a bihamiltonian structure for the double ramification hierarchy
• Quantum $D_4$ Drinfeld-Sokolov hierarchy and quantum singularity theory
• Moduli spaces of residueless meromorphic differentials and the KP hierarchy
• A generalization of Witten's conjecture for the Pixton class and the noncommutative KdV hierarchy