Download Full eBooks in PDF
Some Applications Of The Monodromy Group Of A Covering Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Some Applications Of The Monodromy Group Of A Covering book. This book definitely worth reading, it is an incredibly well-written.
Author : Marvin Tretkoff
Publisher : Unknown
Page : 0 pages
File Size : 41,9 Mb
Release : 1971
Category : Electronic
ISBN : OCLC:1374774383
Author : B.A. Dubrovin,A.T. Fomenko,S.P. Novikov
Publisher : Springer Science & Business Media
Page : 452 pages
File Size : 55,9 Mb
Release : 1985-08-05
Category : Mathematics
ISBN : 9780387961620
Up until recently, Riemannian geometry and basic topology were not included, even by departments or faculties of mathematics, as compulsory subjects in a university-level mathematical education. The standard courses in the classical differential geometry of curves and surfaces which were given instead (and still are given in some places) have come gradually to be viewed as anachronisms. However, there has been hitherto no unanimous agreement as to exactly how such courses should be brought up to date, that is to say, which parts of modern geometry should be regarded as absolutely essential to a modern mathematical education, and what might be the appropriate level of abstractness of their exposition. The task of designing a modernized course in geometry was begun in 1971 in the mechanics division of the Faculty of Mechanics and Mathematics of Moscow State University. The subject-matter and level of abstractness of its exposition were dictated by the view that, in addition to the geometry of curves and surfaces, the following topics are certainly useful in the various areas of application of mathematics (especially in elasticity and relativity, to name but two), and are therefore essential: the theory of tensors (including covariant differentiation of them); Riemannian curvature; geodesics and the calculus of variations (including the conservation laws and Hamiltonian formalism); the particular case of skew-symmetric tensors (i. e.
Author : Gary L. Mullen,Peter Jau-Shyong Shiue
Publisher : American Mathematical Soc.
Page : 402 pages
File Size : 53,9 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821851838
Because of their applications in so many diverse areas, finite fields continue to play increasingly important roles in various branches of modern mathematics, including number theory, algebra, and algebraic geometry, as well as in computer science, information theory, statistics, and engineering. Computational and algorithmic aspects of finite field problems also continue to grow in importance. This volume contains the refereed proceedings of a conference entitled Finite Fields: Theory, Applications and Algorithms, held in August 1993 at the University of Nevada at Las Vegas. Among the topics treated are theoretical aspects of finite fields, coding theory, cryptology, combinatorial design theory, and algorithms related to finite fields. Also included is a list of open problems and conjectures. This volume is an excellent reference for applied and research mathematicians as well as specialists and graduate students in information theory, computer science, and electrical engineering.
Author : Henryk Zoladek
Publisher : Springer Science & Business Media
Page : 589 pages
File Size : 41,8 Mb
Release : 2006-08-10
Category : Mathematics
ISBN : 9783764375362
In singularity theory and algebraic geometry, the monodromy group is embodied in the Picard-Lefschetz formula and the Picard-Fuchs equations. It has applications in the weakened 16th Hilbert problem and in mixed Hodge structures. There is a deep connection of monodromy theory with Galois theory of differential equations and algebraic functions. In covering these and other topics, this book underlines the unifying role of the monogropy group.
Author : Lee Paul Neuwirth
Publisher : Princeton University Press
Page : 124 pages
File Size : 44,7 Mb
Release : 1965-03-21
Category : Mathematics
ISBN : 0691079919
The description for this book, Knot Groups. Annals of Mathematics Studies. (AM-56), Volume 56, will be forthcoming.
Author : Lee Paul Neuwirth
Publisher : Princeton University Press
Page : 119 pages
File Size : 47,8 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882038
The description for this book, Knot Groups. Annals of Mathematics Studies. (AM-56), Volume 56, will be forthcoming.
Author : Joint Summ Ams-Ims-Siam,Michael D. Fried,AMS-IMS-SIAM Joint Summer Research Conference on Applications of Curves over Finite Fields,Ams-Ims-Siam Joint Summer Research Conference on Applications of curve
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 42,9 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821809259
This volume presents the results of the AMS-IMS-SIAM Joint Summer Research Conference held at the University of Washington (Seattle). The talks were devoted to various aspects of the theory of algebraic curves over finite fields and its numerous applications. The three basic themes are the following: Curves with many rational points. Several articles describe main approaches to the construction of such curves: the Drinfeld modules and fiber product methods, the moduli space approach, and the constructions using classical curves; Monodromy groups of characteristic $p$ covers. A number of authors presented the results and conjectures related to the study of the monodromy groups of curves over finite fields. In particular, they study the monodromy groups from genus $0$ covers, reductions of covers, and explicit computation of monodromy groups over finite fields; and, Zeta functions and trace formulas.To a large extent, papers devoted to this topic reflect the contributions of Professor Bernard Dwork and his students. This conference was the last attended by Professor Dwork before his death, and several papers inspired by his presence include commentaries about the applications of trace formulas and $L$-function. The volume also contains a detailed introduction paper by Professor Michael Fried, which helps the reader to navigate in the material presented in the book.
Author : Pavel Exner,Jonathan P. Keating,Peter Kuchment,Toshikazu Sunada,Alexander Teplyaev
Publisher : American Mathematical Soc.
Page : 721 pages
File Size : 42,8 Mb
Release : 2008
Category : Combinatorial analysis
ISBN : 9780821844717
This book addresses a new interdisciplinary area emerging on the border between various areas of mathematics, physics, chemistry, nanotechnology, and computer science. The focus here is on problems and techniques related to graphs, quantum graphs, and fractals that parallel those from differential equations, differential geometry, or geometric analysis. Also included are such diverse topics as number theory, geometric group theory, waveguide theory, quantum chaos, quantum wiresystems, carbon nano-structures, metal-insulator transition, computer vision, and communication networks.This volume contains a unique collection of expert reviews on the main directions in analysis on graphs (e.g., on discrete geometric analysis, zeta-functions on graphs, recently emerging connections between the geometric group theory and fractals, quantum graphs, quantum chaos on graphs, modeling waveguide systems and modeling quantum graph systems with waveguides, control theory on graphs), as well as research articles.
Author : Chris Christensen,Ganesh Sundaram,Avinash Sathaye,Chandrajit Bajaj
Publisher : Springer Science & Business Media
Page : 785 pages
File Size : 54,5 Mb
Release : 2011-06-27
Category : Mathematics
ISBN : 9783642184871
Proceedings of the Conference on Algebra and Algebraic Geometry with Applications, July 19 – 26, 2000, at Purdue University to honor Professor Shreeram S. Abhyankar on the occasion of his seventieth birthday. Eighty-five of Professor Abhyankar's students, collaborators, and colleagues were invited participants. Sixty participants presented papers related to Professor Abhyankar's broad areas of mathematical interest. Sessions were held on algebraic geometry, singularities, group theory, Galois theory, combinatorics, Drinfield modules, affine geometry, and the Jacobian problem. This volume offers an outstanding collection of papers by expert authors.
Author : Sergei K. Lando,Alexander K. Zvonkin
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 46,9 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 : Robert M. Guralnick,John Shareshian
Publisher : American Mathematical Soc.
Page : 128 pages
File Size : 46,8 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821839928
The authors consider indecomposable degree $n$ covers of Riemann surfaces with monodromy group an alternating or symmetric group of degree $d$. They show that if the cover has five or more branch points then the genus grows rapidly with $n$ unless either $d = n$ or the curves have genus zero, there are precisely five branch points and $n =d(d-1)/2$. Similarly, if there is a totally ramified point, then without restriction on the number of branch points the genus grows rapidly with $n$ unless either $d=n$ or the curves have genus zero and $n=d(d-1)/2$. One consequence of these results is that if $f:X \rightarrow \mathbb{P 1$ is indecomposable of degree $n$ with $X$ the generic Riemann surface of genus $g \ge 4$, then the monodromy group is $S n$ or $A n$ (and both can occur for $n$ sufficiently large). The authors also show if that if $f(x)$ is an indecomposable rational function of degree $n$ branched at $9$ or more points, then its monodromy group is $A n$ or $S n$.Finally, they answer a question of Elkies by showing that the curve parameterizing extensions of a number field given by an irreducible trinomial with Galois group $H$ has large genus unless $H=A n$ or $S n$ or $n$ is very small.
Author : Stephen D. Smith
Publisher : American Mathematical Soc.
Page : 231 pages
File Size : 52,6 Mb
Release : 2018-04-30
Category : Finite simple groups
ISBN : 9781470442910
Classification of Finite Simple Groups (CFSG) is a major project involving work by hundreds of researchers. The work was largely completed by about 1983, although final publication of the “quasithin” part was delayed until 2004. Since the 1980s, CFSG has had a huge influence on work in finite group theory and in many adjacent fields of mathematics. This book attempts to survey and sample a number of such topics from the very large and increasingly active research area of applications of CFSG. The book is based on the author's lectures at the September 2015 Venice Summer School on Finite Groups. With about 50 exercises from original lectures, it can serve as a second-year graduate course for students who have had first-year graduate algebra. It may be of particular interest to students looking for a dissertation topic around group theory. It can also be useful as an introduction and basic reference; in addition, it indicates fuller citations to the appropriate literature for readers who wish to go on to more detailed sources.
Author : Mahima Ranjan Adhikari
Publisher : Springer
Page : 615 pages
File Size : 41,9 Mb
Release : 2016-09-16
Category : Mathematics
ISBN : 9788132228431
This book provides an accessible introduction to algebraic topology, a field at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book offers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. The book studies a variety of maps, which are continuous functions between spaces. It also reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to engage in further study.
Author : Michael D. Fried,Shreeram Shankar Abhyankar
Publisher : American Mathematical Soc.
Page : 401 pages
File Size : 46,9 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821802991
This book contains the refereed proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Recent Developments in the Inverse Galois Problem, held in July 1993 at the University of Washington, Seattle. A new review of Serre's Topics in Galois Theory serves as a starting point. The book describes the latest research on explicit presentation of the absolute Galois group of the rationals. Containing the first appearance of generalizations of modular curves, the book presents applications that demonstrate the full scope of the Inverse Galois Problem. In particular, the papers collected here show the ubiquity of the applications of the Inverse Galois Problem and its compelling significance. The book will serve as a guide to progress on the Inverse Galois Problem and as an aid in using this work in other areas of mathematics. This includes coding theory and other finite field applications. Group theory and a first course in algebraic curves are sufficient for understanding many papers in the volume. Graduate students will find this an excellent reference to current research, as it contains a list of problems appropriate for thesis material in arithmetic geometry, algebraic number theory, and group theory.
Author : R.W. Carter,J. Saxl
Publisher : Springer Science & Business Media
Page : 388 pages
File Size : 43,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401153089
This volume contains 19 articles written by speakers at the Advanced Study Institute on 'Modular representations and subgroup structure of al gebraic groups and related finite groups' held at the Isaac Newton Institute, Cambridge from 23rd June to 4th July 1997. We acknowledge with gratitude the financial support given by the NATO Science Committee to enable this ASI to take place. Generous financial support was also provided by the European Union. We are also pleased to acknowledge funds given by EPSRC to the Newton Institute which were used to support the meeting. It is a pleasure to thank the Director of the Isaac Newton Institute, Professor Keith Moffatt, and the staff of the Institute for their dedicated work which did so much to further the success of the meeting. The editors wish to thank Dr. Ross Lawther and Dr. Nick Inglis most warmly for their help in the production of this volume. Dr. Lawther in particular made an invaluable contribution in preparing the volume for submission to the publishers. Finally we wish to thank the distinguished speakers at the ASI who agreed to write articles for this volume based on their lectures at the meet ing. We hope that the volume will stimulate further significant advances in the theory of algebraic groups.