Geodesic
Covers counting via Feynman calculus
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXI, Tome 403 (2012), pp. 58-80

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Let $G$ be a finite group. In this paper we present a tool for counting the number of principal $G$-bundles over a surface. As an application, we express (nonstandard) generating functions for the double Hurwitz numbers as integrals over commutative Frobenius algebras associated with symmetric groups. 
@article{ZNSL_2012_403_a3,
     author = {M. Karev},
     title = {Covers counting via {Feynman} calculus},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {58--80},
     publisher = {mathdoc},
     volume = {403},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_403_a3/}
}
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M. Karev. Covers counting via Feynman calculus. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXI, Tome 403 (2012), pp. 58-80. http://geodesic.mathdoc.fr/item/ZNSL_2012_403_a3/