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# Virasoro constraints for the generationgenerating function of Hurwitz numbers.

Generation

Generating function of the simple Hurwitz numbers is known to be connected with Gromov-Witten potential of the point (Kontsevich $\tau$-function) (see e.g. Ian Goulden, David Jackson and Ravi Vakil). On the other side Virasoro constraints are known to play an imporatant role in the Gromov-Witten theory, in particular for the point.

Is there known the set of Virasoro constraints for the generation generating function of simple (or double) Hurwitz numbers? Any ideas why it should (or should not) exist?

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Generation function of the simple Hurwitz numbers is known to be connected with Gromov-Witten potential of the point (Kontsevich $\tau$-function) (see e.g. Ian Goulden, David Jackson and Ravi Vakil). On the other side Virasoro constraints are known to play an imporatant role in the Gromov-Witten theory, in particular for the point.

Is there known the set of Virasoro constraints for the generation function of simple (or double) Hurwitz numbers? Any ideas why it should (or should not) exist?

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