The Grothendieck Theory of Dessins D'Enfants

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Publisher : Cambridge University Press
ISBN 13 : 9780521478212
Total Pages : 384 pages
Book Rating : 4.4/5 (782 download)

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Book Synopsis The Grothendieck Theory of Dessins D'Enfants by : Leila Schneps

Download or read book The Grothendieck Theory of Dessins D'Enfants written by Leila Schneps and published by Cambridge University Press. This book was released on 1994-07-28 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dessins d'Enfants are combinatorial objects, namely drawings with vertices and edges on topological surfaces. Their interest lies in their relation with the set of algebraic curves defined over the closure of the rationals, and the corresponding action of the absolute Galois group on them. The study of this group via such realted combinatorial methods as its action on the Dessins and on certain fundamental groups of moduli spaces was initiated by Alexander Grothendieck in his unpublished Esquisse d'un Programme, and developed by many of the mathematicians who have contributed to this volume. The various articles here unite all of the basics of the subject as well as the most recent advances. Researchers in number theory, algebraic geometry or related areas of group theory will find much of interest in this book.

Introduction to Compact Riemann Surfaces and Dessins D'Enfants

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Publisher : Cambridge University Press
ISBN 13 : 0521519632
Total Pages : 311 pages
Book Rating : 4.5/5 (215 download)

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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 and published by Cambridge University Press. This book was released on 2012 with total page 311 pages. 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.

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

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Publisher : Springer
ISBN 13 : 9783030517977
Total Pages : 240 pages
Book Rating : 4.5/5 (179 download)

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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 and published by Springer. This book was released on 2021-09-28 with total page 240 pages. 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.

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

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Publisher : Springer Nature
ISBN 13 : 3030517950
Total Pages : 240 pages
Book Rating : 4.0/5 (35 download)

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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 and published by Springer Nature. This book was released on 2020-09-26 with total page 240 pages. 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.

Dessins d'Enfants on Riemann Surfaces

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Publisher : Springer
ISBN 13 : 3319247115
Total Pages : 259 pages
Book Rating : 4.3/5 (192 download)

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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 and published by Springer. This book was released on 2016-03-23 with total page 259 pages. 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.

Algebra and Galois Theories

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Publisher : Springer Nature
ISBN 13 : 3030327965
Total Pages : 462 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Algebra and Galois Theories by : Régine Douady

Download or read book Algebra and Galois Theories written by Régine Douady and published by Springer Nature. This book was released on 2020-07-13 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: Galois theory has such close analogies with the theory of coverings that algebraists use a geometric language to speak of field extensions, while topologists speak of "Galois coverings". This book endeavors to develop these theories in a parallel way, starting with that of coverings, which better allows the reader to make images. The authors chose a plan that emphasizes this parallelism. The intention is to allow to transfer to the algebraic framework of Galois theory the geometric intuition that one can have in the context of coverings. This book is aimed at graduate students and mathematicians curious about a non-exclusively algebraic view of Galois theory.

Introduction to Compact Riemann Surfaces and Dessins d’Enfants

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Publisher : Cambridge University Press
ISBN 13 : 1139504185
Total Pages : 311 pages
Book Rating : 4.1/5 (395 download)

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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 and published by Cambridge University Press. This book was released on 2011-12-22 with total page 311 pages. 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.

Graphs on Surfaces and Their Applications

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Publisher : Springer Science & Business Media
ISBN 13 : 3540383611
Total Pages : 455 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Graphs on Surfaces and Their Applications by : Sergei K. Lando

Download or read book Graphs on Surfaces and Their Applications written by Sergei K. Lando and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graphs drawn on two-dimensional surfaces have always attracted researchers by their beauty and by the variety of difficult questions to which they give rise. The theory of such embedded graphs, which long seemed rather isolated, has witnessed the appearance of entirely unexpected new applications in recent decades, ranging from Galois theory to quantum gravity models, and has become a kind of a focus of a vast field of research. The book provides an accessible introduction to this new domain, including such topics as coverings of Riemann surfaces, the Galois group action on embedded graphs (Grothendieck's theory of "dessins d'enfants"), the matrix integral method, moduli spaces of curves, the topology of meromorphic functions, and combinatorial aspects of Vassiliev's knot invariants and, in an appendix by Don Zagier, the use of finite group representation theory. The presentation is concrete throughout, with numerous figures, examples (including computer calculations) and exercises, and should appeal to both graduate students and researchers.

Galois Groups and Fundamental Groups

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Publisher : Cambridge University Press
ISBN 13 : 0521888506
Total Pages : 281 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Galois Groups and Fundamental Groups by : Tamás Szamuely

Download or read book Galois Groups and Fundamental Groups written by Tamás Szamuely and published by Cambridge University Press. This book was released on 2009-07-16 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assuming little technical background, the author presents the strong analogies between these two concepts starting at an elementary level.

Davenport–Zannier Polynomials and Dessins d’Enfants

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Publisher : American Mathematical Soc.
ISBN 13 : 1470456346
Total Pages : 187 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Davenport–Zannier Polynomials and Dessins d’Enfants by : Nikolai M. Adrianov

Download or read book Davenport–Zannier Polynomials and Dessins d’Enfants written by Nikolai M. Adrianov and published by American Mathematical Soc.. This book was released on 2020-06-29 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: The French expression “dessins d'enfants” means children's drawings. This term was coined by the great French mathematician Alexandre Grothendieck in order to denominate a method of pictorial representation of some highly interesting classes of polynomials and rational functions. The polynomials studied in this book take their origin in number theory. The authors show how, by drawing simple pictures, one can prove some long-standing conjectures and formulate new ones. The theory presented here touches upon many different fields of mathematics. The major part of the book is quite elementary and is easily accessible to an undergraduate student. The less elementary parts, such as Galois theory or group representations and their characters, would need a more profound knowledge of mathematics. The reader may either take the basic facts of these theories for granted or use our book as a motivation and a first approach to these subjects.

Handbook of Teichmüller Theory

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Publisher : European Mathematical Society
ISBN 13 : 9783037190555
Total Pages : 888 pages
Book Rating : 4.1/5 (95 download)

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Book Synopsis Handbook of Teichmüller Theory by : Athanase Papadopoulos

Download or read book Handbook of Teichmüller Theory written by Athanase Papadopoulos and published by European Mathematical Society. This book was released on 2007 with total page 888 pages. Available in PDF, EPUB and Kindle. Book excerpt: This multi-volume set deals with Teichmuller theory in the broadest sense, namely, as the study of moduli space of geometric structures on surfaces, with methods inspired or adapted from those of classical Teichmuller theory. The aim is to give a complete panorama of this generalized Teichmuller theory and of its applications in various fields of mathematics. The volumes consist of chapters, each of which is dedicated to a specific topic. The volume has 19 chapters and is divided into four parts: The metric and the analytic theory (uniformization, Weil-Petersson geometry, holomorphic families of Riemann surfaces, infinite-dimensional Teichmuller spaces, cohomology of moduli space, and the intersection theory of moduli space). The group theory (quasi-homomorphisms of mapping class groups, measurable rigidity of mapping class groups, applications to Lefschetz fibrations, affine groups of flat surfaces, braid groups, and Artin groups). Representation spaces and geometric structures (trace coordinates, invariant theory, complex projective structures, circle packings, and moduli spaces of Lorentz manifolds homeomorphic to the product of a surface with the real line). The Grothendieck-Teichmuller theory (dessins d'enfants, Grothendieck's reconstruction principle, and the Teichmuller theory of the solenoid). This handbook is an essential reference for graduate students and researchers interested in Teichmuller theory and its ramifications, in particular for mathematicians working in topology, geometry, algebraic geometry, dynamical systems and complex analysis. The authors are leading experts in the field.

Moduli Spaces of Curves, Mapping Class Groups and Field Theory

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Publisher : American Mathematical Soc.
ISBN 13 : 0821831674
Total Pages : 144 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Moduli Spaces of Curves, Mapping Class Groups and Field Theory by : Groupes Modulaires Et Th'orie Des Espaces De Modules Des Courbes

Download or read book Moduli Spaces of Curves, Mapping Class Groups and Field Theory written by Groupes Modulaires Et Th'orie Des Espaces De Modules Des Courbes and published by American Mathematical Soc.. This book was released on 2003 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book grew out of a workshop on the applications of moduli spaces of Riemann surfaces in theoretical physics and number theory and on Grothendieck's dessins d'enfants and their generalizations. Chapter 1 gives an introduction to Teichmuller space that is more concise than the popular textbooks, yet contains full proofs of many useful results which are often difficult to find in the literature. This chapter also contains an introduction to moduli spaces of curves, with a detailed description of the genus zero case, and in particular of the part at infinity. Chapter 2 takes up the subject of the genus zero moduli spaces and gives a complete description of their fundamental groupoids, based at tangential base points neighboring the part at infinity; the description relies on an identification of the structure of these groupoids with that of certain canonical subgroupoids of a free braided tensor category. It concludes with a study of the canonical Galois action on the fundamental groupoids, computed using Grothendick-Teichmuller theory. Finally, Chapter 3 studies strict ribbon categories, which are closely related to braided tensor categories: here they are used to construct invariants of 3-manifolds which in turn give rise to quantum field theories.

Around Grothendieck's Esquisse D'un Programme

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Publisher : Cambridge University Press
ISBN 13 : 9780521596428
Total Pages : 308 pages
Book Rating : 4.5/5 (964 download)

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Book Synopsis Around Grothendieck's Esquisse D'un Programme by : Leila Schneps

Download or read book Around Grothendieck's Esquisse D'un Programme written by Leila Schneps and published by Cambridge University Press. This book was released on 1997-07-10 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first of two companion volumes on anabelian algebraic geometry, this book contains the famous, but hitherto unpublished manuscript 'Esquisse d'un Programme' (Sketch of a Program) by Alexander Grothendieck. This work, written in 1984, fourteen years after his retirement from public life in mathematics, together with the closely connected letter to Gerd Faltings, dating from 1983 and also published for the first time in this volume, describe a powerful program of future mathematics, unifying aspects of geometry and arithmetic via the central point of moduli spaces of curves; it is written in an artistic and informal style. The book also contains several articles on subjects directly related to the ideas explored in the manuscripts; these are surveys of mathematics due to Grothendieck, explanations of points raised in the Esquisse, and surveys on progress in the domains described there.

Uniformizing Dessins and BelyiMaps via Circle Packing

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Publisher : American Mathematical Soc.
ISBN 13 : 0821835238
Total Pages : 118 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Uniformizing Dessins and BelyiMaps via Circle Packing by : Philip L. Bowers

Download or read book Uniformizing Dessins and BelyiMaps via Circle Packing written by Philip L. Bowers and published by American Mathematical Soc.. This book was released on 2004 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction Dessins d'enfants Discrete Dessins via circle packing Uniformizing Dessins A menagerie of Dessins d'enfants Computational issues Additional constructions Non-equilateral triangulations The discrete option Appendix: Implementation Bibliography.

Geometric Galois Actions: Volume 2, The Inverse Galois Problem, Moduli Spaces and Mapping Class Groups

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Publisher : Cambridge University Press
ISBN 13 : 0521596416
Total Pages : 363 pages
Book Rating : 4.5/5 (215 download)

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Book Synopsis Geometric Galois Actions: Volume 2, The Inverse Galois Problem, Moduli Spaces and Mapping Class Groups by : Leila Schneps

Download or read book Geometric Galois Actions: Volume 2, The Inverse Galois Problem, Moduli Spaces and Mapping Class Groups written by Leila Schneps and published by Cambridge University Press. This book was released on 1997-08-07 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys progress in the domains described in the hitherto unpublished manuscript "Esquisse d'un Programme" (Sketch of a Program) by Alexander Grothendieck. It will be of wide interest amongst workers in algebraic geometry, number theory, algebra and topology.

Uniformizing Dessins and Belyi Maps Via Circle Packing

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Publisher :
ISBN 13 : 9781470404062
Total Pages : 97 pages
Book Rating : 4.4/5 (4 download)

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Book Synopsis Uniformizing Dessins and Belyi Maps Via Circle Packing by : Philip L. Bowers

Download or read book Uniformizing Dessins and Belyi Maps Via Circle Packing written by Philip L. Bowers and published by . This book was released on 2014-09-11 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: Grothendieck's theory of Dessins d'Enfants involves combinatorially determined affine, reflective and conformal structures on compact surfaces. This work presents a general method for uniformizing these dessin surfaces and for approximating their associated Belyi meromorphic functions.

A Gentle Course in Local Class Field Theory

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Publisher : Cambridge University Press
ISBN 13 : 1108421776
Total Pages : 309 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis A Gentle Course in Local Class Field Theory by : Pierre Guillot

Download or read book A Gentle Course in Local Class Field Theory written by Pierre Guillot and published by Cambridge University Press. This book was released on 2018-11 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained exposition of local class field theory for students in advanced algebra.