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

Author: Frank Neumann
Publisher: Springer Nature
ISBN: 3030517950
Category : Mathematics
Languages : en
Pages : 240

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Book Description
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: Leila Schneps
Publisher: Cambridge University Press
ISBN: 9780521478212
Category : Mathematics
Languages : en
Pages : 384

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on the Dessins and on certain fundamental groups of moduli spaces was initiated by Alexander Grothendieck in his unpublished Esquisse d'un Programme, and developed by many of the mathematicians who have contributed to this volume.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

Author: Régine Douady
Publisher: Springer Nature
ISBN: 3030327965
Category : Mathematics
Languages : en
Pages : 462

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Book Description
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.

Author: Masanori Morishita
Publisher: Springer Nature
ISBN: 9819992559
Category :
Languages : en
Pages : 268

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Book Description

Author: Athanase Papadopoulos
Publisher: European Mathematical Society
ISBN: 9783037190555
Category : Mathematics
Languages : en
Pages : 888

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Book Description
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.

Author: Leila Schneps
Publisher: Cambridge University Press
ISBN: 0521596416
Category : Mathematics
Languages : en
Pages : 363

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Book Description
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.

Author: Leila Schneps
Publisher: Cambridge University Press
ISBN: 9780521808316
Category : Mathematics
Languages : en
Pages : 486

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Book Description
Table of contents

Author: Ari Laptev
Publisher: European Mathematical Society
ISBN: 9783037190098
Category : Mathematics
Languages : en
Pages : 906

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Book Description
The European Congress of Mathematics, held every four years, has established itself as a major international mathematical event. Following those in Paris, 1992, Budapest, 1996, and Barcelona, 2000, the Fourth European Congress of Mathematics took place in Stockholm, Sweden, June 27 to July 2, 2004, with 913 participants from 65 countries. Apart from seven plenary and thirty three invited lectures, there were six Science Lectures covering the most relevant aspects of mathematics in science and technology. Moreover, twelve projects of the EU Research Training Networks in Mathematics and Information Sciences, as well as Programmes from the European Science Foundation in Physical and Engineering Sciences, were presented. Ten EMS Prizes were awarded to young European mathematicians who have made a particular contribution to the progress of mathematics. Five of the prizewinners were independently chosen by the 4ECM Scientific Committee as plenary or invited speakers. The other five prizewinners gave their lectures in parallel sessions. Most of these contributions are now collected in this volume, providing a permanent record of so much that is best in mathematics today.

Author: Gareth A. Jones
Publisher: Springer
ISBN: 3319247115
Category : Mathematics
Languages : en
Pages : 264

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Book Description
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: Nils Tongring
Publisher: World Scientific
ISBN: 9812701397
Category : Mathematics
Languages : en
Pages : 360

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Book Description
The central theme of this volume is the contemporary mathematics of geometry and physics, but the work also discusses the problem of the secondary structure of proteins, and an overview of arc complexes with proposed applications to macromolecular folding is given. OC Woods Hole has played such a vital role in both my mathematical and personal life that it is a great pleasure to see the mathematical tradition of the 1964 meeting resurrected forty years later and, as this volume shows, resurrected with new vigor and hopefully on a regular basis. I therefore consider it a signal honor to have been asked to introduce this volume with a few reminiscences of that meeting forty years ago.OCO Introduction by R Bott (Wolf Prize Winner, 2000)."