The Monodromy Group

Author : Henryk Zoladek
Publisher : Springer Science & Business Media
Page : 589 pages
File Size : 42,7 Mb
Release : 2006-08-10
Category : Mathematics
ISBN : 9783764375362

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The Monodromy Group by Henryk Zoladek Pdf

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 : Nicholas M. Katz
Publisher : Princeton University Press
Page : 262 pages
File Size : 42,7 Mb
Release : 1988
Category : Mathematics
ISBN : 0691084335

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Gauss Sums, Kloosterman Sums, and Monodromy Groups by Nicholas M. Katz Pdf

The study of exponential sums over finite fields, begun by Gauss nearly two centuries ago, has been completely transformed in recent years by advances in algebraic geometry, culminating in Deligne's work on the Weil Conjectures. It now appears as a very attractive mixture of algebraic geometry, representation theory, and the sheaf-theoretic incarnations of such standard constructions of classical analysis as convolution and Fourier transform. The book is simultaneously an account of some of these ideas, techniques, and results, and an account of their application to concrete equidistribution questions concerning Kloosterman sums and Gauss sums.

Author : Volodymyr Nekrashevych
Publisher : American Mathematical Society
Page : 248 pages
File Size : 44,5 Mb
Release : 2024-04-05
Category : Mathematics
ISBN : 9781470476915

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Self-Similar Groups by Volodymyr Nekrashevych Pdf

Self-similar groups (groups generated by automata) appeared initially as examples of groups that are easy to define but that enjoy exotic properties like nontrivial torsion, intermediate growth, etc. The book studies the self-similarity phenomenon in group theory and shows its intimate relation with dynamical systems and more classical self-similar structures, such as fractals, Julia sets, and self-affine tilings. The relation is established through the notions of the iterated monodromy group and the limit space, which are the central topics of the book. A wide variety of examples and different applications of self-similar groups to dynamical systems and vice versa are discussed. It is shown in particular how Julia sets can be reconstructed from the respective iterated monodromy groups and that groups with exotic properties appear now not just as isolated examples but as naturally defined iterated monodromy groups of rational functions. The book is intended to be accessible to a wide mathematical readership, including graduate students interested in group theory and dynamical systems.

Author : Finster, Myriam
Publisher : KIT Scientific Publishing
Page : 150 pages
File Size : 48,9 Mb
Release : 2014-09-03
Category : Electronic
ISBN : 9783731501800

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Veech Groups and Translation Coverings by Finster, Myriam Pdf

Author : Chris A.M. Peters,Joseph H. M. Steenbrink
Publisher : Springer Science & Business Media
Page : 470 pages
File Size : 49,8 Mb
Release : 2008-02-27
Category : Mathematics
ISBN : 3540770178

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Mixed Hodge Structures by Chris A.M. Peters,Joseph H. M. Steenbrink Pdf

This is comprehensive basic monograph on mixed Hodge structures. Building up from basic Hodge theory the book explains Delingne's mixed Hodge theory in a detailed fashion. Then both Hain's and Morgan's approaches to mixed Hodge theory related to homotopy theory are sketched. Next comes the relative theory, and then the all encompassing theory of mixed Hodge modules. The book is interlaced with chapters containing applications. Three large appendices complete the book.

Author : Emmanuel Breuillard,Hee Oh
Publisher : Cambridge University Press
Page : 375 pages
File Size : 49,6 Mb
Release : 2014-02-17
Category : Mathematics
ISBN : 9781107036857

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Thin Groups and Superstrong Approximation by Emmanuel Breuillard,Hee Oh Pdf

This collection of survey articles focuses on recent developments at the boundary between geometry, dynamical systems, number theory and combinatorics.

Author : Marvin Tretkoff
Publisher : Unknown
Page : 0 pages
File Size : 42,6 Mb
Release : 1971
Category : Electronic
ISBN : OCLC:1374774383

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Some Applications of the Monodromy Group of a Covering by Marvin Tretkoff Pdf

Author : Nikolai M. Adrianov,Fedor Pakovich,Alexander K. Zvonkin
Publisher : American Mathematical Soc.
Page : 187 pages
File Size : 50,9 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.

Author : Robert M. Guralnick,John Shareshian
Publisher : American Mathematical Soc.
Page : 128 pages
File Size : 48,6 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821839928

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Symmetric and Alternating Groups as Monodromy Groups of Riemann Surfaces I by Robert M. Guralnick,John Shareshian Pdf

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 : Nicholas M. Katz
Publisher : Princeton University Press
Page : 256 pages
File Size : 51,9 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882120

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Gauss Sums, Kloosterman Sums, and Monodromy Groups. (AM-116), Volume 116 by Nicholas M. Katz Pdf

The study of exponential sums over finite fields, begun by Gauss nearly two centuries ago, has been completely transformed in recent years by advances in algebraic geometry, culminating in Deligne's work on the Weil Conjectures. It now appears as a very attractive mixture of algebraic geometry, representation theory, and the sheaf-theoretic incarnations of such standard constructions of classical analysis as convolution and Fourier transform. The book is simultaneously an account of some of these ideas, techniques, and results, and an account of their application to concrete equidistribution questions concerning Kloosterman sums and Gauss sums.

Author : V.I. Arnold,V.V. Goryunov,O.V. Lyashko,V.A. Vasil'ev
Publisher : Springer Science & Business Media
Page : 250 pages
File Size : 46,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642580093

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Singularity Theory I by V.I. Arnold,V.V. Goryunov,O.V. Lyashko,V.A. Vasil'ev Pdf

This is a compact guide to the principles and main applications of Singularity Theory by one of the world’s top research groups. It includes a number of new results as well as a carefully prepared and extensive bibliography that makes it easy to find the necessary details. It’s ideal for any mathematician or physicist interested in modern mathematical analysis.

Author : Leila Schneps,Pierre Lochak
Publisher : Cambridge University Press
Page : 363 pages
File Size : 44,9 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.

Author : Daniel Krob,Alexander A. Mikhalev,Alexander V. Mikhalev
Publisher : Springer Science & Business Media
Page : 815 pages
File Size : 46,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662041666

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Formal Power Series and Algebraic Combinatorics by Daniel Krob,Alexander A. Mikhalev,Alexander V. Mikhalev Pdf

This book contains the extended abstracts presented at the 12th International Conference on Power Series and Algebraic Combinatorics (FPSAC '00) that took place at Moscow State University, June 26-30, 2000. These proceedings cover the most recent trends in algebraic and bijective combinatorics, including classical combinatorics, combinatorial computer algebra, combinatorial identities, combinatorics of classical groups, Lie algebra and quantum groups, enumeration, symmetric functions, young tableaux etc...

Author : M. Kohno
Publisher : Springer Science & Business Media
Page : 539 pages
File Size : 45,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401146050

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Global Analysis in Linear Differential Equations by M. Kohno Pdf

Since the initiative works for global analysis of linear differential equations by G.G. Stokes and B. Riemann in 1857, the Airy function and the Gauss hypergeometric function became the most important and the greatest practical special functions, which have a variety of applications to mathematical science, physics and engineering. The cffcctivity of these functions is essentially due to their "behavior in the large" . For instance, the Airy function plays a basic role in the asymptotic analysis of many functions arising as solutions of differential equations in several problems of applied math ematics. In case of the employment of its behavior, one should always pay attention to the Stokes phenomenon. On the other hand, as is well-known, the Gauss hypergeometric function arises in all fields of mathematics, e.g., in number theory, in the theory of groups and in analysis itself. It is not too much to say that all power series are special or extended cases of the hypergeometric series. For the full use of its properties, one needs connection formulas or contiguous relations.

Author : Benjamin Fine,Anthony M. Gaglione
Publisher : American Mathematical Soc.
Page : 191 pages
File Size : 47,7 Mb
Release : 1990
Category : Mathematics
ISBN : 9780821851166

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Combinatorial Group Theory by Benjamin Fine,Anthony M. Gaglione Pdf

The AMS Special Session on Combinatorial Group Theory--Infinite Groups, held at the University of Maryland in April 1988, was designed to draw together researchers in various areas of infinite group theory, especially combinatorial group theory, to share methods and results. The session reflected the vitality and interests in infinite group theory, with eighteen speakers presenting lectures covering a wide range of group-theoretic topics, from purely logical questions to geometric methods. The heightened interest in classical combinatorial group theory was reflected in the sheer volume of work presented during the session. This book consists of eighteen papers presented during the session. Comprising a mix of pure research and exposition, the papers should be sufficiently understandable to the nonspecialist to convey a sense of the direction of this field. However, the volume will be of special interest to researchers in infinite group theory and combinatorial group theory, as well as to those interested in low-dimensional (especially three-manifold) topology.