On the enumeration of surface coverings

We discuss how one can count branched covers of surfaces of prescribed degree and ramification type. Coverings of the sphere with simple ramification and Belyi maps serve us as main examples. We also compare these examples with the problem of counting square-tiled and pillowcase surfaces that is relevant in dynamics.

Attachment	Size
[5]Zograf_2207.pdf [6]	194.63 KB