The Grothendieck Theory Of Dessins D Enfants

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The Grothendieck Theory of Dessins D'Enfants

Leila Schneps
The Grothendieck Theory of Dessins D Enfants Book PDF

Author : Leila Schneps
Publisher : Cambridge University Press
Page : 384 pages
File Size : 41,9 Mb
Release : 1994-07-28
Category : Mathematics
ISBN : 0521478219

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The Grothendieck Theory of Dessins D'Enfants by Leila Schneps Pdf

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action on the Dessins and on certain fundamental groups of moduli spaces was initiated by Alexander Grothendieck in his unpublished Esquisse d'un Programme, and developed by many of the mathematicians who have contributed to this volume.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

Ernesto Girondo,Gabino González-Diez
Introduction to Compact Riemann Surfaces and Dessins D Enfants Book PDF

Author : Ernesto Girondo,Gabino González-Diez
Publisher : Cambridge University Press
Page : 311 pages
File Size : 52,5 Mb
Release : 2012
Category : Mathematics
ISBN : 9780521519632

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Introduction to Compact Riemann Surfaces and Dessins D'Enfants by Ernesto Girondo,Gabino González-Diez Pdf

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

Frank Neumann,Sibylle Schroll
Galois Covers Grothendieck Teichm ller Theory and Dessins d Enfants Book PDF

Author : Frank Neumann,Sibylle Schroll
Publisher : Springer Nature
Page : 240 pages
File Size : 52,6 Mb
Release : 2020-09-26
Category : Mathematics
ISBN : 9783030517953

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Galois Covers, Grothendieck-Teichmüller Theory and Dessins d'Enfants by Frank Neumann,Sibylle Schroll Pdf

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

Gareth A. Jones,Jürgen Wolfart
Dessins d Enfants on Riemann Surfaces Book PDF

Author : Gareth A. Jones,Jürgen Wolfart
Publisher : Springer
Page : 259 pages
File Size : 50,9 Mb
Release : 2016-03-23
Category : Mathematics
ISBN : 9783319247113

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Dessins d'Enfants on Riemann Surfaces by Gareth A. Jones,Jürgen Wolfart Pdf

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

Ernesto Girondo,Gabino González-Diez
Introduction to Compact Riemann Surfaces and Dessins d Enfants Book PDF

Author : Ernesto Girondo,Gabino González-Diez
Publisher : Cambridge University Press
Page : 311 pages
File Size : 52,9 Mb
Release : 2011-12-22
Category : Mathematics
ISBN : 9781139504188

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Introduction to Compact Riemann Surfaces and Dessins d’Enfants by Ernesto Girondo,Gabino González-Diez Pdf

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.

Algebra and Galois Theories

Régine Douady,Adrien Douady
Algebra and Galois Theories Book PDF

Author : Régine Douady,Adrien Douady
Publisher : Springer Nature
Page : 462 pages
File Size : 44,7 Mb
Release : 2020-07-13
Category : Mathematics
ISBN : 9783030327965

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Algebra and Galois Theories by Régine Douady,Adrien Douady Pdf

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.

Graphs on Surfaces and Their Applications

Sergei K. Lando,Alexander K. Zvonkin
Graphs on Surfaces and Their Applications Book PDF

Author : Sergei K. Lando,Alexander K. Zvonkin
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 52,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783540383611

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Graphs on Surfaces and Their Applications by Sergei K. Lando,Alexander K. Zvonkin Pdf

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

Tamás Szamuely
Galois Groups and Fundamental Groups Book PDF

Author : Tamás Szamuely
Publisher : Cambridge University Press
Page : 281 pages
File Size : 50,6 Mb
Release : 2009-07-16
Category : Mathematics
ISBN : 9780521888509

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Galois Groups and Fundamental Groups by Tamás Szamuely Pdf

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

Nikolai M. Adrianov,Fedor Pakovich,Alexander K. Zvonkin
Davenport Zannier Polynomials and Dessins d Enfants Book PDF

Author : Nikolai M. Adrianov,Fedor Pakovich,Alexander K. Zvonkin
Publisher : American Mathematical Soc.
Page : 187 pages
File Size : 54,5 Mb
Release : 2020-06-29
Category : Education
ISBN : 9781470456344

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Davenport–Zannier Polynomials and Dessins d’Enfants by Nikolai M. Adrianov,Fedor Pakovich,Alexander K. Zvonkin Pdf

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

Athanase Papadopoulos
Handbook of Teichm ller Theory Book PDF

Author : Athanase Papadopoulos
Publisher : European Mathematical Society
Page : 888 pages
File Size : 43,8 Mb
Release : 2007
Category : Mathematics
ISBN : 3037190558

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Handbook of Teichmüller Theory by Athanase Papadopoulos Pdf

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

Groupes Modulaires Et Th'orie Des Espaces De Modules Des Courbes,Xavier Buff,Jerome Fehrenbach,Pierre Lochak,Pierre Vogel
Moduli Spaces of Curves Mapping Class Groups and Field Theory Book PDF

Author : Groupes Modulaires Et Th'orie Des Espaces De Modules Des Courbes,Xavier Buff,Jerome Fehrenbach,Pierre Lochak,Pierre Vogel
Publisher : American Mathematical Soc.
Page : 144 pages
File Size : 53,9 Mb
Release : 2003
Category : Mathematics
ISBN : 9780821831670

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Moduli Spaces of Curves, Mapping Class Groups and Field Theory by Groupes Modulaires Et Th'orie Des Espaces De Modules Des Courbes,Xavier Buff,Jerome Fehrenbach,Pierre Lochak,Pierre Vogel Pdf

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.

Uniformizing Dessins and Belyi Maps Via Circle Packing

Philip L. Bowers
Uniformizing Dessins and Belyi Maps Via Circle Packing Book PDF

Author : Philip L. Bowers
Publisher : Unknown
Page : 97 pages
File Size : 55,5 Mb
Release : 2014-09-11
Category : Circle packing
ISBN : 1470404060

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Uniformizing Dessins and Belyi Maps Via Circle Packing by Philip L. Bowers Pdf

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.

Around Grothendieck's Esquisse D'un Programme

Leila Schneps,Pierre Lochak
Around Grothendieck s Esquisse D un Programme Book PDF

Author : Leila Schneps,Pierre Lochak
Publisher : Cambridge University Press
Page : 308 pages
File Size : 52,7 Mb
Release : 1997-07-10
Category : Mathematics
ISBN : 0521596424

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Around Grothendieck's Esquisse D'un Programme by Leila Schneps,Pierre Lochak Pdf

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

Philip L. Bowers,Kenneth Stephenson
Uniformizing Dessins and BelyiMaps via Circle Packing Book PDF

Author : Philip L. Bowers,Kenneth Stephenson
Publisher : American Mathematical Soc.
Page : 118 pages
File Size : 48,6 Mb
Release : 2004
Category : Circle packing
ISBN : 9780821835234

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Uniformizing Dessins and BelyiMaps via Circle Packing by Philip L. Bowers,Kenneth Stephenson Pdf

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

Leila Schneps,Pierre Lochak
Geometric Galois Actions Volume 2 The Inverse Galois Problem Moduli Spaces and Mapping Class Groups Book PDF

Author : Leila Schneps,Pierre Lochak
Publisher : Cambridge University Press
Page : 363 pages
File Size : 51,6 Mb
Release : 1997-08-07
Category : Mathematics
ISBN : 9780521596411

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Geometric Galois Actions: Volume 2, The Inverse Galois Problem, Moduli Spaces and Mapping Class Groups by Leila Schneps,Pierre Lochak Pdf

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.