Author: Henryk Zoladek Publisher: Springer Science & Business Media ISBN: 3764375361 Category : Mathematics Languages : en Pages : 589
Book Description
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: Volodymyr Nekrashevych Publisher: American Mathematical Soc. ISBN: 0821838318 Category : Mathematics Languages : en Pages : 248
Book Description
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.
Author: Nicholas M. Katz Publisher: Princeton University Press ISBN: 9780691084336 Category : Mathematics Languages : en Pages : 262
Book Description
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: Finster, Myriam Publisher: KIT Scientific Publishing ISBN: 3731501805 Category : Mathematics Languages : en Pages : 154
Book Description
A translation surface is obtained by taking plane polygons and gluing their edges by translations. We ask which subgroups of the Veech group of a primitive translation surface can be realised via a translation covering. For many primitive surfaces we prove that partition stabilising congruence subgroups are the Veech group of a covering surface. We also address the coverings via their monodromy groups and present examples of cyclic coverings in short orbits, i.e. with large Veech groups.
Author: Emmanuel Breuillard Publisher: Cambridge University Press ISBN: 1107036852 Category : Mathematics Languages : en Pages : 375
Book Description
This collection of survey articles focuses on recent developments at the boundary between geometry, dynamical systems, number theory and combinatorics.
Author: Teresa Crespo Publisher: American Mathematical Soc. ISBN: 082185318X Category : Computers Languages : en Pages : 242
Book Description
Differential Galois theory has seen intense research activity during the last decades in several directions: elaboration of more general theories, computational aspects, model theoretic approaches, applications to classical and quantum mechanics as well as to other mathematical areas such as number theory. This book intends to introduce the reader to this subject by presenting Picard-Vessiot theory, i.e. Galois theory of linear differential equations, in a self-contained way. The needed prerequisites from algebraic geometry and algebraic groups are contained in the first two parts of the book. The third part includes Picard-Vessiot extensions, the fundamental theorem of Picard-Vessiot theory, solvability by quadratures, Fuchsian equations, monodromy group and Kovacic's algorithm. Over one hundred exercises will help to assimilate the concepts and to introduce the reader to some topics beyond the scope of this book. This book is suitable for a graduate course in differential Galois theory. The last chapter contains several suggestions for further reading encouraging the reader to enter more deeply into different topics of differential Galois theory or related fields.
Author: Tamás Szamuely Publisher: Cambridge University Press ISBN: 0521888506 Category : Mathematics Languages : en Pages : 281
Book Description
Assuming little technical background, the author presents the strong analogies between these two concepts starting at an elementary level.
Author: William M. Kantor Publisher: Cambridge University Press ISBN: 052146790X Category : Mathematics Languages : en Pages : 324
Book Description
Silk Hope, NC is a buoyant and moving parable in which two good women find, among the hidden, forgotten virtues of the past, a sustenance to carry them into the future.
Author: Henryk Zoladek
Author: Volodymyr Nekrashevych
Author: Nicholas M. Katz
Author: Finster, Myriam
Author: Emmanuel Breuillard
Author: Robert Curtis
Author: Teresa Crespo
Author: Tamás Szamuely
Author: William M. Kantor
Author: Marvin Tretkoff