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Introduction to Compact Riemann Surfaces and Dessins D'Enfants

2012 Mathematics
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Release : 2012
Genre : Mathematics
Kind : eBook
Book Rating : 632/5 ( reviews)

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Book Synopsis Introduction to Compact Riemann Surfaces and Dessins D'Enfants by : Ernesto Girondo

Download or read book Introduction to Compact Riemann Surfaces and Dessins D'Enfants written by Ernesto Girondo. This book was released on 2012. Available in PDF, EPUB and Kindle. Book excerpt: An elementary account of the theory of compact Riemann surfaces and an introduction to the Belyi-Grothendieck theory of dessins d'enfants.

Dessins d'Enfants on Riemann Surfaces

2016-03-23 Mathematics
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Release : 2016-03-23
Genre : Mathematics
Kind : eBook
Book Rating : 115/5 ( reviews)

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Book Synopsis Dessins d'Enfants on Riemann Surfaces by : Gareth A. Jones

Download or read book Dessins d'Enfants on Riemann Surfaces written by Gareth A. Jones. This book was released on 2016-03-23. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides an introduction to dessins d'enfants and embeddings of bipartite graphs in compact Riemann surfaces. 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.

Introduction to Compact Riemann Surfaces and Dessins d’Enfants

2011-12-22 Mathematics
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Release : 2011-12-22
Genre : Mathematics
Kind : eBook
Book Rating : 185/5 ( reviews)

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Book Synopsis Introduction to Compact Riemann Surfaces and Dessins d’Enfants by : Ernesto Girondo

Download or read book Introduction to Compact Riemann Surfaces and Dessins d’Enfants written by Ernesto Girondo. This book was released on 2011-12-22. Available in PDF, EPUB and Kindle. Book excerpt: Few books on the subject of Riemann surfaces cover the relatively modern theory of dessins d'enfants (children's drawings), which was launched by Grothendieck in the 1980s and is now an active field of research. In this 2011 book, the authors begin with an elementary account of the theory of compact Riemann surfaces viewed as algebraic curves and as quotients of the hyperbolic plane by the action of Fuchsian groups of finite type. They then use this knowledge to introduce the reader to the theory of dessins d'enfants and its connection with algebraic curves defined over number fields. A large number of worked examples are provided to aid understanding, so no experience beyond the undergraduate level is required. Readers without any previous knowledge of the field of dessins d'enfants are taken rapidly to the forefront of current research.

Compact Riemann Surfaces

2013-04-17 Mathematics
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Release : 2013-04-17
Genre : Mathematics
Kind : eBook
Book Rating : 468/5 ( reviews)

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Book Synopsis Compact Riemann Surfaces by : Jürgen Jost

Download or read book Compact Riemann Surfaces written by Jürgen Jost. This book was released on 2013-04-17. Available in PDF, EPUB and Kindle. Book excerpt: This book is novel in its broad perspective on Riemann surfaces: the text systematically explores the connection with other fields of mathematics. The book can serve as an introduction to contemporary mathematics as a whole, as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. The book is unique among textbooks on Riemann surfaces in its inclusion of an introduction to Teichmüller theory. For this new edition, the author has expanded and rewritten several sections to include additional material and to improve the presentation.

Galois Covers, Grothendieck-Teichmüller Theory and Dessins d'Enfants

2020-09-26 Mathematics
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Release : 2020-09-26
Genre : Mathematics
Kind : eBook
Book Rating : 950/5 ( reviews)

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Book Synopsis Galois Covers, Grothendieck-Teichmüller Theory and Dessins d'Enfants by : Frank Neumann

Download or read book Galois Covers, Grothendieck-Teichmüller Theory and Dessins d'Enfants written by Frank Neumann. This book was released on 2020-09-26. Available in PDF, EPUB and Kindle. Book excerpt: This book presents original peer-reviewed contributions from the London Mathematical Society (LMS) Midlands Regional Meeting and Workshop on 'Galois Covers, Grothendieck-Teichmüller Theory and Dessinsd'Enfants', which took place at the University of Leicester, UK, from 4 to 7 June, 2018. Within the theme of the workshop, the collected articles cover a broad range of topics and explore exciting new links between algebraic geometry, representation theory, group theory, number theory and algebraic topology. The book combines research and overview articles by prominent international researchers and provides a valuable resource for researchers and students alike.

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