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Author : Ernesto Girondo,Gabino González-Diez
Publisher : Cambridge University Press
Page : 311 pages
File Size : 48,8 Mb
Release : 2012
Category : Mathematics
ISBN : 9780521519632
An elementary account of the theory of compact Riemann surfaces and an introduction to the Belyi-Grothendieck theory of dessins d'enfants.
Author : Gareth A. Jones,Jürgen Wolfart
Publisher : Springer
Page : 259 pages
File Size : 55,6 Mb
Release : 2016-03-23
Category : Mathematics
ISBN : 9783319247113
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 : Ernesto Girondo,Gabino González-Diez
Publisher : Cambridge University Press
Page : 311 pages
File Size : 51,8 Mb
Release : 2011-12-22
Category : Mathematics
ISBN : 9781139504188
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.
Author : Leila Schneps
Publisher : Cambridge University Press
Page : 384 pages
File Size : 52,9 Mb
Release : 1994-07-28
Category : Mathematics
ISBN : 0521478219
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 : Frank Neumann,Sibylle Schroll
Publisher : Springer
Page : 240 pages
File Size : 41,8 Mb
Release : 2021-09-28
Category : Mathematics
ISBN : 3030517977
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 : Sergei K. Lando,Alexander K. Zvonkin
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 55,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783540383611
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.
Author : William J. Harvey,Frederick P. Gardiner,Gabino González-Diez,Christos Kourouniotis
Publisher : Cambridge University Press
Page : 416 pages
File Size : 47,6 Mb
Release : 2010-02-11
Category : Mathematics
ISBN : 9780521733076
Original research and expert surveys on Riemann surfaces.
Author : Philip L. Bowers,Kenneth Stephenson
Publisher : American Mathematical Soc.
Page : 118 pages
File Size : 53,8 Mb
Release : 2004
Category : Circle packing
ISBN : 9780821835234
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.
Author : Aaron Wootton,S. Allen Broughton,Jennifer Paulhus
Publisher : American Mathematical Society
Page : 366 pages
File Size : 53,8 Mb
Release : 2022-02-03
Category : Mathematics
ISBN : 9781470460259
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.
Author : Jennifer S. Balakrishnan,Amanda Folsom,Matilde Lalín,Michelle Manes
Publisher : Springer
Page : 195 pages
File Size : 47,7 Mb
Release : 2019-08-01
Category : Mathematics
ISBN : 9783030194789
These proceedings collect several number theory articles, most of which were written in connection to the workshop WIN4: Women in Numbers, held in August 2017, at the Banff International Research Station (BIRS) in Banff, Alberta, Canada. It collects papers disseminating research outcomes from collaborations initiated during the workshop as well as other original research contributions involving participants of the WIN workshops. The workshop and this volume are part of the WIN network, aimed at highlighting the research of women and gender minorities in number theory as well as increasing their participation and boosting their potential collaborations in number theory and related fields.
Author : Frank Neumann,Sibylle Schroll
Publisher : Springer Nature
Page : 240 pages
File Size : 44,8 Mb
Release : 2020-09-26
Category : Mathematics
ISBN : 9783030517953
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 : Renzo Cavalieri,Eric Miles
Publisher : Cambridge University Press
Page : 197 pages
File Size : 41,9 Mb
Release : 2016-09-26
Category : Mathematics
ISBN : 9781107149243
Classroom-tested and featuring over 100 exercises, this text introduces the key algebraic geometry field of Hurwitz theory.
Author : Frances Clare Kirwan
Publisher : Cambridge University Press
Page : 278 pages
File Size : 40,9 Mb
Release : 1992-02-20
Category : Mathematics
ISBN : 0521423538
This development of the theory of complex algebraic curves was one of the peaks of nineteenth century mathematics. They have many fascinating properties and arise in various areas of mathematics, from number theory to theoretical physics, and are the subject of much research. By using only the basic techniques acquired in most undergraduate courses in mathematics, Dr. Kirwan introduces the theory, observes the algebraic and topological properties of complex algebraic curves, and shows how they are related to complex analysis.
Author : Régine Douady,Adrien Douady
Publisher : Springer Nature
Page : 462 pages
File Size : 53,6 Mb
Release : 2020-07-13
Category : Mathematics
ISBN : 9783030327965
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 : Kenneth Stephenson
Publisher : Cambridge University Press
Page : 380 pages
File Size : 45,6 Mb
Release : 2005-04-18
Category : Mathematics
ISBN : 0521823560
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