Introduction To Compact Riemann Surfaces And Dessins Denfants PDF Download
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Author | : Ernesto Girondo |
Publisher | : Cambridge University Press |
Total Pages | : 311 |
Release | : 2012 |
Genre | : Mathematics |
ISBN | : 0521519632 |
Download Introduction to Compact Riemann Surfaces and Dessins D'Enfants Book in PDF, ePub and Kindle
An elementary account of the theory of compact Riemann surfaces and an introduction to the Belyi-Grothendieck theory of dessins d'enfants.
Author | : Gareth A. Jones |
Publisher | : Springer |
Total Pages | : 264 |
Release | : 2016-03-23 |
Genre | : Mathematics |
ISBN | : 3319247115 |
Download Dessins d'Enfants on Riemann Surfaces Book in PDF, ePub and Kindle
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.
Author | : Ernesto Girondo |
Publisher | : Cambridge University Press |
Total Pages | : 311 |
Release | : 2011-12-22 |
Genre | : Mathematics |
ISBN | : 1139504185 |
Download Introduction to Compact Riemann Surfaces and Dessins d’Enfants Book in PDF, ePub and Kindle
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.
Author | : Jürgen Jost |
Publisher | : Springer Science & Business Media |
Total Pages | : 304 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 3662034468 |
Download Compact Riemann Surfaces Book in PDF, ePub and Kindle
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.
Author | : Frank Neumann |
Publisher | : Springer Nature |
Total Pages | : 240 |
Release | : 2020-09-26 |
Genre | : Mathematics |
ISBN | : 3030517950 |
Download Galois Covers, Grothendieck-Teichmüller Theory and Dessins d'Enfants Book in PDF, ePub and Kindle
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.
Author | : Terrence Napier |
Publisher | : Springer Science & Business Media |
Total Pages | : 563 |
Release | : 2011-09-08 |
Genre | : Mathematics |
ISBN | : 0817646930 |
Download An Introduction to Riemann Surfaces Book in PDF, ePub and Kindle
This textbook presents a unified approach to compact and noncompact Riemann surfaces from the point of view of the so-called L2 $\bar{\delta}$-method. This method is a powerful technique from the theory of several complex variables, and provides for a unique approach to the fundamentally different characteristics of compact and noncompact Riemann surfaces. The inclusion of continuing exercises running throughout the book, which lead to generalizations of the main theorems, as well as the exercises included in each chapter make this text ideal for a one- or two-semester graduate course.
Author | : Aaron Wootton |
Publisher | : American Mathematical Society |
Total Pages | : 366 |
Release | : 2022-02-03 |
Genre | : Mathematics |
ISBN | : 1470460254 |
Download Automorphisms of Riemann Surfaces, Subgroups of Mapping Class Groups and Related Topics Book in PDF, ePub and Kindle
Automorphism groups of Riemann surfaces have been widely studied for almost 150 years. This area has persisted in part because it has close ties to many other topics of interest such as number theory, graph theory, mapping class groups, and geometric and computational group theory. In recent years there has been a major revival in this area due in part to great advances in computer algebra systems and progress in finite group theory. This volume provides a concise but thorough introduction for newcomers to the area while at the same time highlighting new developments for established researchers. The volume starts with two expository articles. The first of these articles gives a historical perspective of the field with an emphasis on highly symmetric surfaces, such as Hurwitz surfaces. The second expository article focuses on the future of the field, outlining some of the more popular topics in recent years and providing 78 open research problems across all topics. The remaining articles showcase new developments in the area and have specifically been chosen to cover a variety of topics to illustrate the range of diversity within the field.
Author | : William J. Harvey |
Publisher | : Cambridge University Press |
Total Pages | : 416 |
Release | : 2010-02-11 |
Genre | : Mathematics |
ISBN | : 0521733073 |
Download Geometry of Riemann Surfaces Book in PDF, ePub and Kindle
Original research and expert surveys on Riemann surfaces.
Author | : Renzo Cavalieri |
Publisher | : Cambridge University Press |
Total Pages | : 197 |
Release | : 2016-09-26 |
Genre | : Mathematics |
ISBN | : 1316798933 |
Download Riemann Surfaces and Algebraic Curves Book in PDF, ePub and Kindle
Hurwitz theory, the study of analytic functions among Riemann surfaces, is a classical field and active research area in algebraic geometry. The subject's interplay between algebra, geometry, topology and analysis is a beautiful example of the interconnectedness of mathematics. This book introduces students to this increasingly important field, covering key topics such as manifolds, monodromy representations and the Hurwitz potential. Designed for undergraduate study, this classroom-tested text includes over 100 exercises to provide motivation for the reader. Also included are short essays by guest writers on how they use Hurwitz theory in their work, which ranges from string theory to non-Archimedean geometry. Whether used in a course or as a self-contained reference for graduate students, this book will provide an exciting glimpse at mathematics beyond the standard university classes.
Author | : Jozef Širáň |
Publisher | : Springer |
Total Pages | : 330 |
Release | : 2016-03-26 |
Genre | : Mathematics |
ISBN | : 3319304518 |
Download Symmetries in Graphs, Maps, and Polytopes Book in PDF, ePub and Kindle
This volume contains seventeen of the best papers delivered at the SIGMAP Workshop 2014, representing the most recent advances in the field of symmetries of discrete objects and structures, with a particular emphasis on connections between maps, Riemann surfaces and dessins d’enfant.Providing the global community of researchers in the field with the opportunity to gather, converse and present their newest findings and advances, the Symmetries In Graphs, Maps, and Polytopes Workshop 2014 was the fifth in a series of workshops. The initial workshop, organized by Steve Wilson in Flagstaff, Arizona, in 1998, was followed in 2002 and 2006 by two meetings held in Aveiro, Portugal, organized by Antonio Breda d’Azevedo, and a fourth workshop held in Oaxaca, Mexico, organized by Isabel Hubard in 2010.This book should appeal to both specialists and those seeking a broad overview of what is happening in the area of symmetries of discrete objects and structures.iv>