The Monodromy Group
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The Monodromy Group
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Author : Henryk Zoladek
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-08-10
The Monodromy Group written by Henryk Zoladek and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-10 with Mathematics categories.
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.
The Monodromy Group
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Author : Henryk Żołądek
language : en
Publisher: Springer Nature
Release Date : 2025-05-10
The Monodromy Group written by Henryk Żołądek and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-10 with Mathematics categories.
This book presents the monodromy group, underlining the unifying role it plays in a variety of theories and mathematical areas. 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. In the theory of systems of linear differential equations, one has the Riemann-Hilbert problem, the Stokes phenomena and the hypergeometric functions with their multidimensional generalizations. In the theory of homomorphic foliations, there appear the Ecalle-Voronin-Martinet-Ramis moduli. Moreover, there is a deep connection of monodromy theory with Galois theory of differential equations and algebraic functions. The material is addressed to a wide audience, ranging from specialists in the theory of ordinary differential equations to algebraic geometers. Readers will quickly get introduced to modern and vital mathematical theories, such as singularity theory, analytic theory of ordinary differential equations, holomorphic foliations, Galois theory, and parts of algebraic geometry, without searching in vast literature. This second edition has been enlarged by several sections, presenting new results appeared since the first edition.
Divergent Series Summability And Resurgence I
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Author : Claude Mitschi
language : en
Publisher: Springer
Release Date : 2016-08-27
Divergent Series Summability And Resurgence I written by Claude Mitschi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-27 with Mathematics categories.
Providing an elementary introduction to analytic continuation and monodromy, the first part of this volume applies these notions to the local and global study of complex linear differential equations, their formal solutions at singular points, their monodromy and their differential Galois groups. The Riemann-Hilbert problem is discussed from Bolibrukh’s point of view. The second part expounds 1-summability and Ecalle’s theory of resurgence under fairly general conditions. It contains numerous examples and presents an analysis of the singularities in the Borel plane via “alien calculus”, which provides a full description of the Stokes phenomenon for linear or non-linear differential or difference equations. The first of a series of three, entitled Divergent Series, Summability and Resurgence, this volume is aimed at graduate students, mathematicians and theoretical physicists interested in geometric, algebraic or local analytic properties of dynamical systems. It includes useful exercises with solutions. The prerequisites are a working knowledge of elementary complex analysis and differential algebra.
Gauss Sums Kloosterman Sums And Monodromy Groups
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Author : Nicholas M. Katz
language : en
Publisher: Princeton University Press
Release Date : 1988
Gauss Sums Kloosterman Sums And Monodromy Groups written by Nicholas M. Katz and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
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.
Self Similar Groups
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Author : Volodymyr Nekrashevych
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Self Similar Groups written by Volodymyr Nekrashevych and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Self-similar groups (groups generated by automata) initially appeared as examples of groups that are easy to define but have exotic properties like nontrivial torsion, intermediate growth, etc. This book studies the self-similarity phenomenon in group theory and shows its intimate relationship with dynamical systems and more classical self-similar structures, such as fractals, Julia sets, and self-affine tilings. This connection is established through the central topics of the book, which are the notions of the iterated monodromy group and limit space. A wide variety of examples and different applications of self-similar groups to dynamical systems and vice versa are discussed. In particular, it is shown that Julia sets can be reconstructed from the respective iterated monodromy groups and that groups with exotic properties can appear not just as isolated examples, but as naturally defined iterated monodromy groups of rational functions. The book offers important, new mathematics that will open new avenues of research in group theory and dynamical systems. It is intended to be accessible to a wide readership of professional mathematicians.
Galois Theory Of Linear Differential Equations
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Author : Marius van der Put
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-01-21
Galois Theory Of Linear Differential Equations written by Marius van der Put and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-21 with Mathematics categories.
From the reviews: "This is a great book, which will hopefully become a classic in the subject of differential Galois theory. [...] the specialist, as well as the novice, have long been missing an introductory book covering also specific and advanced research topics. This gap is filled by the volume under review, and more than satisfactorily." Mathematical Reviews
Formal Power Series And Algebraic Combinatorics
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Author : Daniel Krob
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Formal Power Series And Algebraic Combinatorics written by Daniel Krob and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
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...
Galois Groups And Fundamental Groups
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Author : Tamás Szamuely
language : en
Publisher: Cambridge University Press
Release Date : 2009-07-16
Galois Groups And Fundamental Groups written by Tamás Szamuely and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-16 with Mathematics categories.
Ever since the concepts of Galois groups in algebra and fundamental groups in topology emerged during the nineteenth century, mathematicians have known of the strong analogies between the two concepts. This book presents the connection starting at an elementary level, showing how the judicious use of algebraic geometry gives access to the powerful interplay between algebra and topology that underpins much modern research in geometry and number theory. Assuming as little technical background as possible, the book starts with basic algebraic and topological concepts, but already presented from the modern viewpoint advocated by Grothendieck. This enables a systematic yet accessible development of the theories of fundamental groups of algebraic curves, fundamental groups of schemes, and Tannakian fundamental groups. The connection between fundamental groups and linear differential equations is also developed at increasing levels of generality. Key applications and recent results, for example on the inverse Galois problem, are given throughout.
Love And Math
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Author : Edward Frenkel
language : en
Publisher: Hachette UK
Release Date : 2013-10-01
Love And Math written by Edward Frenkel and has been published by Hachette UK this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-01 with Mathematics categories.
An awesome, globe-spanning, and New York Times bestselling journey through the beauty and power of mathematics What if you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of van Gogh and Picasso, weren't even told they existed? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry. In Love and Math, renowned mathematician Edward Frenkel reveals a side of math we've never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space. Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man's journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century's leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat's last theorem, that had seemed intractable before. At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.
Lie Groups And Lie Algebras E B Dynkin S Seminar
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Author : Semen Grigorʹevich Gindikin
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
Lie Groups And Lie Algebras E B Dynkin S Seminar written by Semen Grigorʹevich Gindikin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Lie albegras categories.
In celebration of E.B. Dynkin's 70th birthday, this book presents current papers by those who participated in Dynkin's seminar on Lie groups and Lie algebras in the late 1950s and early 1960s. Dynkin had a major influence not only on mathematics, but also on the students who attended his seminar-many of whom are today's leading mathematicians in Russia and in the U.S. Dynkin's contributions to the theory of Lie groups is well known, and the survey paper by Karpelevich, Onishchik, and Vinberg allows readers to gain a deeper understanding of this work. Features several aspects of modern develo.