# Quadratic double ramification integrals and the noncommutative KdV hierarchy

@article{Buryak2019QuadraticDR, title={Quadratic double ramification integrals and the noncommutative KdV hierarchy}, author={Alexandr Buryak and Paolo Rossi}, journal={Bulletin of the London Mathematical Society}, year={2019}, volume={53} }

In this paper we compute the intersection number of two double ramification (DR) cycles (with different ramification profiles) and the top Chern class of the Hodge bundle on the moduli space of stable curves of any genus. These quadratic DR integrals are the main ingredients for the computation of the DR hierarchy associated to the infinite‐dimensional partial cohomological field theory given by exp(μ2Θ) , where μ is a parameter and Θ is Hain's theta class, appearing in Hain's formula for the…

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