Special Cubic Hodge Integrals and the Fractional Volterra Hierarchy.

	We show that the generating function of cubic Hodge integrals satisfying the local Calabi-Yau condition is the tau function of a particular solution of an integrable hierarchy called the fractional Volterra hierarchy. This integrable hierarchy is a certain generalization of the Volterra lattice hierarchy (also called the discrete KdV hierarchy) which is well known in the theory of nonlinear integrable systems. The talk is based on joint work with Si-Qi Liu, Di Yang and Chunhui Zhou.