| The classical theory of dessins d’enfants, which are bipartite maps on compact Riemann surfaces, combinatorial objects used to study branched covers between compact Riemann surfaces and the absolute Galois group of the field rational numbers. In this talk, we show how this theory is naturally extended to non-compact orientable surfaces and, in particular, we observe that the Loch Ness monster (the surface of infinite genus with exactly one end) admits infinitely many regular dessins d’enfants. Finally, we study different holomorphic structures on the Loch Ness monster, which come from homological coverings of compact Riemann surfaces, infinite hyperelliptic curves, and infinite superelliptic curves. Join work with Y. Atarihuana, J.C. García, R.A. Hidalgo and C. Ramírez-Maluendas. |
