Virasoro constraints for Kontsevich-Hurwitz partition function

Understand

M.Kazarian and S.Lando found a 1-parametric interpolation between Kontsevich and Hurwitz partition functions, which entirely lies within the space of KP tau-functions.

• V.Bouchard and M.Marino suggested that this interpolation satisfies some deformed Virasoro constraints.
• However, they described the constraints in a somewhat sophisticated form of AMM-Eynard equations for the rather involved Lambert spectral curve.
• Here we present the relevant family of Virasoro constraints explicitly.