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action on the Dessins and on certain fundamental groups of moduli spaces was initiated by Alexander Grothendieck in his unpublished Esquisse d'un Programme, and developed by many of the mathematicians who have contributed to this volume.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.
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.
Download or read book Galois Covers Grothendieck Teichm ller 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.
Download or read book Galois Covers Grothendieck Teichm ller 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.
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 264 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.
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.
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.
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 463 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.
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.
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.
Download or read book Handbook of Teichm ller 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.
Download or read book Algebraic Geometry and Number Theory written by Hussein Mourtada and published by Birkhäuser. This book was released on 2017-05-07 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This lecture notes volume presents significant contributions from the “Algebraic Geometry and Number Theory” Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014. It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology. Its main aim is to introduce these contemporary research topics to graduate students who plan to specialize in the area of algebraic geometry and/or number theory. All contributions combine main concepts and techniques with motivating examples and illustrative problems for the covered subjects. Naturally, the book will also be of interest to researchers working in algebraic geometry, number theory and related fields.
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.
Download or read book Integrability Quantization and Geometry II Quantum Theories and Algebraic Geometry written by Sergey Novikov and published by American Mathematical Soc.. This book was released on 2021-04-12 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of articles written in memory of Boris Dubrovin (1950–2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions to this collection of papers are split into two parts: “Integrable Systems” and “Quantum Theories and Algebraic Geometry”, reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.
Download or read book Geometry of Riemann Surfaces written by William J. Harvey and published by Cambridge University Press. This book was released on 2010-02-11 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Original research and expert surveys on Riemann surfaces.
Download or read book Automorphisms of Riemann Surfaces Subgroups of Mapping Class Groups and Related Topics written by Aaron Wootton and published by American Mathematical Society. This book was released on 2022-02-03 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Quilts Central Extensions Braid Actions and Finite Groups written by Tim Hsu and published by Springer. This book was released on 2007-05-06 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quilts are 2-complexes used to analyze actions and subgroups of the 3-string braid group and similar groups. This monograph establishes the fundamentals of quilts and discusses connections with central extensions, braid actions, and finite groups. Most results have not previously appeared in a widely available form, and many results appear in print for the first time. This monograph is accessible to graduate students, as a substantial amount of background material is included. The methods and results may be relevant to researchers interested in infinite groups, moonshine, central extensions, triangle groups, dessins d'enfants, and monodromy actions of braid groups.
