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- W2042818720 abstract "We state and solve a discrete version of the classical Riemann-Hilbert problem. In particular, we associate a Riemann-Hilbert problem to every dessin d'enfants. We show how to compute the solution for a dessin that is a tree. This amounts to finding a Fuchsian differential equation satisfied by the local inverses of a Shabat polynomial. We produce a uni- versal annihilating operator for the inverses of a generic polynomial. We classify those plane trees that have a representation by Mobius transformations and those that have a linear rep- resentation of dimension at most two. This yields an analogue for trees of Schwarz's classical list, that is, a list of those plane trees whose Riemann-Hilbert problem has a hypergeometric solution of order at most two." @default.
- W2042818720 created "2016-06-24" @default.
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- W2042818720 date "2008-08-22" @default.
- W2042818720 modified "2023-09-26" @default.
- W2042818720 title "Dessins d’enfants and differential equations" @default.
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- W2042818720 doi "https://doi.org/10.1090/s1061-0022-08-01033-9" @default.
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