Dessins d Enfants on Riemann Surfaces

Author: Gareth A. Jones
Publisher: Springer
ISBN: 3319247115
Format: PDF, Mobi
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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.

Riemann and Klein Surfaces Automorphisms Symmetries and Moduli Spaces

Author: Milagros Izquierdo
Publisher: American Mathematical Soc.
ISBN: 1470410931
Format: PDF
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This volume contains the proceedings of the conference on Riemann and Klein Surfaces, Symmetries and Moduli Spaces, in honor of Emilio Bujalance, held from June 24-28, 2013, at Linköping University. The conference and this volume are devoted to the mathematics that Emilio Bujalance has worked with in the following areas, all with a computational flavor: Riemann and Klein surfaces, automorphisms of real and complex surfaces, group actions on surfaces and topological properties of moduli spaces of complex curves and Abelian varieties.

Symmetries in Graphs Maps and Polytopes

Author: Jozef Širáň
Publisher: Springer
ISBN: 3319304518
Format: PDF, ePub
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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>

Complex Functions

Author: Gareth A. Jones
Publisher: Cambridge University Press
ISBN: 9780521313667
Format: PDF, Mobi
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Elliptic functions and Riemann surfaces played an important role in nineteenth-century mathematics. At the present time there is a great revival of interest in these topics not only for their own sake but also because of their applications to so many areas of mathematical research from group theory and number theory to topology and differential equations. In this book the authors give elementary accounts of many aspects of classical complex function theory including Möbius transformations, elliptic functions, Riemann surfaces, Fuchsian groups and modular functions. A distinctive feature of their presentation is the way in which they have incorporated into the text many interesting topics from other branches of mathematics. This book is based on lectures given to advanced undergraduates and is well-suited as a textbook for a second course in complex function theory. Professionals will also find it valuable as a straightforward introduction to a subject which is finding widespread application throughout mathematics.

Geometry of Riemann Surfaces

Author: Frederick P. Gardiner
Publisher: Cambridge University Press
ISBN: 0521733073
Format: PDF, Kindle
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Riemann surfaces is a thriving area of mathematics with applications to hyperbolic geometry, complex analysis, conformal dynamics, discrete groups, algebraic curves and more. This collection of articles presents original research and expert surveys of important related topics, making the field accessible to research workers, graduate students and teachers.

Riemann Surfaces and Algebraic Curves

Author: Renzo Cavalieri
Publisher: Cambridge University Press
ISBN: 1316798933
Format: PDF, ePub, Mobi
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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.

An Invitation to Algebraic Geometry

Author: Karen E. Smith
Publisher: Springer Science & Business Media
ISBN: 1475744978
Format: PDF, Mobi
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This is a description of the underlying principles of algebraic geometry, some of its important developments in the twentieth century, and some of the problems that occupy its practitioners today. It is intended for the working or the aspiring mathematician who is unfamiliar with algebraic geometry but wishes to gain an appreciation of its foundations and its goals with a minimum of prerequisites. Few algebraic prerequisites are presumed beyond a basic course in linear algebra.

Riemann Surfaces

Author: Simon Donaldson
Publisher: Oxford University Press
ISBN: 0198526393
Format: PDF
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An authoritative but accessible text on one dimensional complex manifolds or Riemann surfaces. Dealing with the main results on Riemann surfaces from a variety of points of view; it pulls together material from global analysis, topology, and algebraic geometry, and covers the essential mathematical methods and tools.

Quantum Triangulations

Author: Mauro Carfora
Publisher: Springer Science & Business Media
ISBN: 3642244394
Format: PDF
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Research on polyhedral manifolds often points to unexpected connections between very distinct aspects of Mathematics and Physics. In particular triangulated manifolds play quite a distinguished role in such settings as Riemann moduli space theory, strings and quantum gravity, topological quantum field theory, condensed matter physics, and critical phenomena. Not only do they provide a natural discrete analogue to the smooth manifolds on which physical theories are typically formulated, but their appearance is rather often a consequence of an underlying structure which naturally calls into play non-trivial aspects of representation theory, of complex analysis and topology in a way which makes manifest the basic geometric structures of the physical interactions involved. Yet, in most of the existing literature, triangulated manifolds are still merely viewed as a convenient discretization of a given physical theory to make it more amenable for numerical treatment. The motivation for these lectures notes is thus to provide an approachable introduction to this topic, emphasizing the conceptual aspects, and probing, through a set of cases studies, the connection between triangulated manifolds and quantum physics to the deepest. This volume addresses applied mathematicians and theoretical physicists working in the field of quantum geometry and its applications.