Integrability, Quantization and Moduli Spaces of Curves

Symmetry Integrability and Geometry-Methods and Applications

article

Paolo Rossi¹ 

[1] Université de Bourgogne Franche-Comté

关键词: moduli space of stable curves;    integrable systems;    cohomological field theories;    double ramification cycle;    double ramification hierarchy;   

DOI  :  10.3842/SIGMA.2017.060

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown