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Click on the cover image above to read some pages of this book! This volume provides an introduction to dessins d'enfants and embeddings of bipartite graphs in compact Riemann surfaces.

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The first part of the book presents basic material, guiding the reader through the current field of research. A key point of the second part is the interplay between the automorphism groups of dessins and their Riemann surfaces, and the action of the absolute Galois group on dessins and their algebraic curves.

It concludes by showing the links between the theory of dessins and other areas of arithmetic and geometry, such as the abc conjecture, complex multiplication and Beauville surfaces. Dessins d'Enfants on Riemann Surfaces will appeal to graduate students and all mathematicians interested in maps, hypermaps, Riemann surfaces, geometric group actions, and arithmetic.

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It is excellently written, and the Chapters are somewhat independent, in the sense that they have their own abstract, keywords and references. Of course, it is worth noting that the authors have contributed themselves to many of the results included in the book, most of which are really recent. The reader interested in diving deeper into any of these aspects will most certainly find this well-written book to be of much help.

The text is also regularly interrupted by formulations of exercises which ask to prove some intermediate result or apply a definition in a particular situation some brief hints are added at the end of the book.

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The book can thus be used as a textbook for a course on this fascinating topic. Help Centre.

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Dessins d'Enfants on Riemann Surfaces

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