Recent Developments In The Inverse Galois Problem

Author by : Michael D. Fried
Languange : en
Publisher by : American Mathematical Soc.
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Description : 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.


Geometric Galois Actions Volume 2 The Inverse Galois Problem Moduli Spaces And Mapping Class Groups

Author by : Leila Schneps
Languange : en
Publisher by : Cambridge University Press
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Description : This book surveys progress in the domains described in the hitherto unpublished manuscript "Esquisse d'un Programme" (Sketch of a Program) by Alexander Grothendieck.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.


Arithmetic Fundamental Groups And Noncommutative Algebra

Author by : Karen Redrobe Beckman
Languange : en
Publisher by : American Mathematical Soc.
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Description : The arithmetic and geometry of moduli spaces and their fundamental groups are a very active research area. This book offers a complete overview of developments made over the last decade. The papers in this volume examine the geometry of moduli spaces of curves with a function on them. The main players in Part 1 are the absolute Galois group $G_{\mathbb Q}$ of the algebraic numbers and its close relatives. By analyzing how $G_{\mathbb Q}$ acts on fundamental groups defined by Hurwitz moduli problems, the authors achieve a grand generalization of Serre's program from the 1960s.Papers in Part 2 apply $\theta$-functions and configuration spaces to the study of fundamental groups over positive characteristic fields. In this section, several authors use Grothendieck's famous lifting results to give extensions to wildly ramified covers. Properties of the fundamental groups have brought collaborations between geometers and group theorists. Several Part 3 papers investigate new versions of the genus 0 problem. In particular, this includes results severely limiting possible monodromy groups of sphere covers. Finally, Part 4 papers treat Deligne's theory of Tannakian categories and arithmetic versions of the Kodaira-Spencer map. This volume is geared toward graduate students and research mathematicians interested in arithmetic algebraic geometry.


Inverse Galois Theory

Author by : Gunter Malle
Languange : en
Publisher by : Springer Science & Business Media
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Description : A consistent and near complete survey of the important progress made in the field over the last few years, with the main emphasis on the rigidity method and its applications. Among others, this monograph presents the most successful existence theorems known and construction methods for Galois extensions as well as solutions for embedding problems combined with a collection of the existing Galois realizations.


Encyclopaedia Of Mathematics Supplement Iii

Author by : Michiel Hazewinkel
Languange : en
Publisher by : Springer Science & Business Media
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Description : This is the third supplementary volume to Kluwer's highly acclaimed twelve-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.


Number Theory In Progress

Author by : Kálmán Györy
Languange : en
Publisher by : Walter de Gruyter
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Description : Proceedings of the International Conference on Number Theory organized by the Stefan Banach International Mathematical Center in Honor of the 60th Birthday of Andrzej Schinzel, Zakopane, Poland, June 30-July 9, 1997.


Progress In Galois Theory

Author by : Helmut Voelklein
Languange : en
Publisher by : Springer Science & Business Media
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Description : The theme of this book are the interactions between group theory and algebra/geometry/number theory, showing ubiquity and power of the basic principle of Galois theory. The book presents recent developments in a major line of work about covers of the projective line (and other curves), their fields of definition and parameter spaces, and associated questions about arithmetic fundamental groups. This is intimately tied up with the Inverse Problem of Galois Theory, and uses methods of algebraic geometry, group theory and number theory.


Aspects Of Galois Theory

Author by : Helmut Voelklein
Languange : en
Publisher by : Cambridge University Press
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Description : Collection of articles by leading experts in Galois theory, focusing on the Inverse Galois Problem.


Generic Polynomials

Author by : Christian U. Jensen
Languange : en
Publisher by : Cambridge University Press
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Description : Table of contents


Proceedings Of The International Congress Of Mathematicians

Author by : S.D. Chatterji
Languange : en
Publisher by : Birkhäuser
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Description : Since the first ICM was held in Zürich in 1897, it has become the pinnacle of mathematical gatherings. It aims at giving an overview of the current state of different branches of mathematics and its applications as well as an insight into the treatment of special problems of exceptional importance. The proceedings of the ICMs have provided a rich chronology of mathematical development in all its branches and a unique documentation of contemporary research. They form an indispensable part of every mathematical library. The Proceedings of the International Congress of Mathematicians 1994, held in Zürich from August 3rd to 11th, 1994, are published in two volumes. Volume I contains an account of the organization of the Congress, the list of ordinary members, the reports on the work of the Fields Medalists and the Nevanlinna Prize Winner, the plenary one-hour addresses, and the invited addresses presented at Section Meetings 1 - 6. Volume II contains the invited address for Section Meetings 7 - 19. A complete author index is included in both volumes. '...the content of these impressive two volumes sheds a certain light on the present state of mathematical sciences and anybody doing research in mathematics should look carefully at these Proceedings. For young people beginning research, this is even more important, so these are a must for any serious mathematics library. The graphical presentation is, as always with Birkhäuser, excellent....' (Revue Roumaine de Mathematiques pures et Appliquées)


Abelian Varieties And Number Theory

Author by : Moshe Jarden
Languange : en
Publisher by : American Mathematical Soc.
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Description : This book is a collection of articles on Abelian varieties and number theory dedicated to Gerhard Frey's 75th birthday. It contains original articles by experts in the area of arithmetic and algebraic geometry. The articles cover topics on Abelian varieties and finitely generated Galois groups, ranks of Abelian varieties and Mordell-Lang conjecture, Tate-Shafarevich group and isogeny volcanoes, endomorphisms of superelliptic Jacobians, obstructions to local-global principles over semi-global fields, Drinfeld modular varieties, representations of etale fundamental groups and specialization of algebraic cycles, Deuring's theory of constant reductions, etc. The book will be a valuable resource to graduate students and experts working on Abelian varieties and related areas.


Galois Groups And Fundamental Groups

Author by : Leila Schneps
Languange : en
Publisher by : Cambridge University Press
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Description : Table of contents


Proceedings Of The International Congress Of Mathematicians 2010 Icm 2010 In 4 Volumes Vol I Plenary Lectures And Ceremonies Vols Ii Iv Invited Lectures

Author by : Bhatia Rajendra
Languange : en
Publisher by : World Scientific
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Description : ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.


Women In Numbers Europe

Author by : Marie José Bertin
Languange : en
Publisher by : Springer
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Description : Covering topics in graph theory, L-functions, p-adic geometry, Galois representations, elliptic fibrations, genus 3 curves and bad reduction, harmonic analysis, symplectic groups and mould combinatorics, this volume presents a collection of papers covering a wide swath of number theory emerging from the third iteration of the international Women in Numbers conference, “Women in Numbers - Europe” (WINE), held on October 14–18, 2013 at the CIRM-Luminy mathematical conference center in France. While containing contributions covering a wide range of cutting-edge topics in number theory, the volume emphasizes those concrete approaches that make it possible for graduate students and postdocs to begin work immediately on research problems even in highly complex subjects.


Trends In The Representation Theory Of Finite Dimensional Algebras

Author by : Edward L. Green
Languange : en
Publisher by : American Mathematical Soc.
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Description : This refereed collection of research papers and survey articles reflects the interplay of finite-dimensional algebras with other areas (algebraic geometry, homological algebra, and the theory of quantum groups). Current trends are presented from the discussions at the AMS-IMS-SIAM Joint Summer Research Conference at the University of Washington (Seattle). The volume features several excellent expository articles which will introduce the beginning researcher to cutting-edge topics in representation theory. The book will also provide inspiration to researchers in related areas, as it includes original papers spanning a broad spectrum of representation theory. It's features include: work outlining significant progress on long-standing open problems; survey articles offering both overviews and introductions to various subfields of the topic; and, expositions reflecting the interplay between the representation theory of algebras and other fields.


Advances In Stochastic Inequalities

Author by : Theodore Preston Hill
Languange : en
Publisher by : American Mathematical Soc.
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Description : Contains 15 articles based on invited talks given at an AMS Special Session on 'Stochastic Inequalities and Their Applications' held at Georgia Institute of Technology (Atlanta). This book includes articles that offer a comprehensive picture of this area of mathematical probability and statistics.


Advances In Contemporary Logic And Computer Science

Author by : Walter Alexandre Carnielli
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume presents the proceedings from the Eleventh Brazilian Logic Conference on Mathematical Logic held by the Brazilian Logic Society (co-sponsored by the Centre for Logic, Epistemology and the History of Science, State University of Campinas, Sao Paolo) in Salvador, Bahia, Brazil. The conference and the volume are dedicated to the memory of professor Mario Tourasse Teixeira, an educator and researcher who contributed to the formation of several generations of Brazilian logicians.Contributions were made from leading Brazilian logicians and their Latin-American and European colleagues. All papers were selected by a careful refereeing processs and were revised and updated by their authors for publication in this volume. There are three sections: Advances in Logic, Advances in Theoretical Computer Science, and Advances in Philosophical Logic. Well-known specialists present original research on several aspects of model theory, proof theory, algebraic logic, category theory, connections between logic and computer science, and topics of philosophical logic of current interest. Topics interweave proof-theoretical, semantical, foundational, and philosophical aspects with algorithmic and algebraic views, offering lively high-level research results.


Groups As Galois Groups

Author by : Helmut Volklein
Languange : en
Publisher by : Cambridge University Press
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Description : Develops the mathematical background and recent results on the Inverse Galois Problem.


Computational Algebraic And Analytic Geometry

Author by : Mika Seppälä
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume contains the proceedings of three AMS Special Sessions on Computational Algebraic and Analytic Geometry for Low-Dimensional Varieties held January 8, 2007, in New Orleans, LA; January 6, 2009, in Washington, DC; and January 6, 2011, in New Orleans, LA. Algebraic, analytic, and geometric methods are used to study algebraic curves and Riemann surfaces from a variety of points of view. The object of the study is the same. The methods are different. The fact that a multitude of methods, stemming from very different mathematical cultures, can be used to study the same objects makes this area both fascinating and challenging.


Rigid Analytic Geometry And Its Applications

Author by : Jean Fresnel
Languange : en
Publisher by : Springer Science & Business Media
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Description : Rigid (analytic) spaces were invented to describe degenerations, reductions, and moduli of algebraic curves and abelian varieties. This work, a revised and greatly expanded new English edition of an earlier French text by the same authors, presents important new developments and applications of the theory of rigid analytic spaces to abelian varieties, "points of rigid spaces," étale cohomology, Drinfeld modular curves, and Monsky-Washnitzer cohomology. The exposition is concise, self-contained, rich in examples and exercises, and will serve as an excellent graduate-level text for the classroom or for self-study.


The Rational Function Analogue Of A Question Of Schur And Exceptionality Of Permutation Representations

Author by : Robert M. Guralnick
Languange : en
Publisher by : American Mathematical Soc.
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Description : In 1923 Schur considered the problem of which polynomials $f\in\mathbb{Z}[X]$ induce bijections on the residue fields $\mathbb{Z}/p\mathbb{Z}$ for infinitely many primes $p$. His conjecture, that such polynomials are compositions of linear and Dickson polynomials, was proved by M. Fried in 1970. Here we investigate the analogous question for rational functions, and also we allow the base field to be any number field. As a result, there are many more rational functions for which the analogous property holds. The new infinite series come from rational isogenies or endomorphisms of elliptic curves. Besides them, there are finitely many sporadic examples which do not fit in any of the series we obtain.The Galois theoretic translation, based on Chebotarev's density theorem, leads to a certain property of permutation groups, called exceptionality. One can reduce to primitive exceptional groups. While it is impossible to describe explicitly all primitive exceptional permutation groups, we provide certain reduction results, and obtain a classification in the almost simple case. The fact that these permutation groups arise as monodromy groups of covers of Riemann spheres $f:\mathbb{P}^1\to\mathbb{P}^1$, where $f$ is the rational function we investigate, provides genus $0$ systems.These are generating systems of permutation groups with a certain combinatorial property. This condition, combined with the classification and reduction results of exceptional permutation groups, eventually gives a precise geometric classification of possible candidates of rational functions which satisfy the arithmetic property from above. Up to this point, we make frequent use of the classification of the finite simple groups. Except for finitely many cases, these remaining candidates are connected to isogenies or endomorphisms of elliptic curves. Thus we use results about elliptic curves, modular curves, complex multiplication, and the techniques used in the inverse regular Galois problem to settle these finer arithmetic questions.


Arithmetic And Geometry Around Galois Theory

Author by : Pierre Dèbes
Languange : en
Publisher by : Springer Science & Business Media
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Description : This Lecture Notes volume is the fruit of two research-level summer schools jointly organized by the GTEM node at Lille University and the team of Galatasaray University (Istanbul): "Geometry and Arithmetic of Moduli Spaces of Coverings (2008)" and "Geometry and Arithmetic around Galois Theory (2009)". The volume focuses on geometric methods in Galois theory. The choice of the editors is to provide a complete and comprehensive account of modern points of view on Galois theory and related moduli problems, using stacks, gerbes and groupoids. It contains lecture notes on étale fundamental group and fundamental group scheme, and moduli stacks of curves and covers. Research articles complete the collection.​


Win Women In Numbers

Author by : Alina Carmen Cojocaru
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume is a collection of papers on number theory which evolved out of the workshop WIN - Women in Numbers, held November 2nd-7th, 2008, in Alberta, Canada. The book includes articles showcasing outcomes from collaborative research initiated during the workshop.


Davenport Zannier Polynomials And Dessins D Enfants

Author by : Nikolai M. Adrianov
Languange : en
Publisher by : American Mathematical Soc.
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Description : 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.


Harmonic Functions On Trees And Buildings

Author by : Adam Korányi
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume presents the proceedings of the workshop 'Harmonic Functions on Graphs' held at the Graduate Center of CUNY in the fall of 1995. The main papers present material from four minicourses given by leading experts: D. Cartwright, A. Figa-Talamanca, S. Sawyer and T. Steger. These minicourses are introductions which gradually progress to deeper and less known branches of the subject. One of the topics treated is buildings, which are discrete analogues of symmetric spaces of arbitrary rank; buildings of rank are trees. Harmonic analysis on buildings is a fairly new and important field of research.One of the minicourses discusses buildings from the combinatorial perspective and another examines them from the $p$-adic perspective. The third minicourse deals with the connections of trees with $p$-adic analysis. And the fourth deals with random walks, i.e., with the probabilistic side of harmonic functions on trees. The book also contains the extended abstracts of 19 of the 20 lectures given by the participants on their recent results. These abstracts, well detailed and clearly understandable, give a good cross-section of the present state of research in the field.


Moduli Spaces Of Curves Mapping Class Groups And Field Theory

Author by : Xavier Buff
Languange : en
Publisher by : American Mathematical Soc.
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Description : This book grew out of a workshop on the applications of moduli spaces of Riemann surfaces in theoretical physics and number theory and on Grothendieck's dessins d'enfants and their generalizations. Chapter 1 gives an introduction to Teichmuller space that is more concise than the popular textbooks, yet contains full proofs of many useful results which are often difficult to find in the literature. This chapter also contains an introduction to moduli spaces of curves, with a detailed description of the genus zero case, and in particular of the part at infinity. Chapter 2 takes up the subject of the genus zero moduli spaces and gives a complete description of their fundamental groupoids, based at tangential base points neighboring the part at infinity; the description relies on an identification of the structure of these groupoids with that of certain canonical subgroupoids of a free braided tensor category. It concludes with a study of the canonical Galois action on the fundamental groupoids, computed using Grothendieck-Teichmuller theory. Finally, Chapter 3 studies strict ribbon categories, which are closely related to braided tensor categories: here they are used to construct invariants of 3-manifolds which in turn give rise to quantum field theories.


Lipa S Legacy

Author by : Józef Dodziuk
Languange : en
Publisher by : American Mathematical Soc.
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Description : The mathematical works of Lars Ahlfors and Lipman Bers are fundamental and lasting. They have influenced and altered the development of twentieth century mathematics. The personalities of these two scientists helped create a mathematical family and have had a permanent positive effect on a whole generation of mathematicians. Their mathematical heritage continues to lead succeeding generations. In the fall of 1994, one year after Bers' death, some members of this family decided to inaugurate a series of conferences, The Bers Colloquium, to be held every three years. The theme was to be a topic in the Ahlfors-Bers mathematical tradition, broadly interpreted. Ahlfors died a year after the first colloquium; future colloquia in this series will be called The Ahlfors-Bers Colloquium. The first colloquium was held in October 1995 at the Graduate Center, CUNY in New York. It coincided roughly with the second anniversary of Bers' death. There were six lectures and much informal mathematical discussion. This volume contains papers by the speakers and many of the participants. The broad range of papers indicates how strong and far-reaching Bers' influence has been. The topics represented in the book include Teichmuller theory, Kleinian groups, higher dimensional hyperbolic geometry, geometry of numbers, circle packings, theory of discrete groups, classical complex function theory, one dimensional dynamics, fluid dynamics, quasiconformal mappings in higher dimensions, partial differential equations, and classical algebraic geometry. Features: Twenty-seven very high-level papers on related topics Open problems Expository articles


Operator Theory For Complex And Hypercomplex Analysis

Author by : Enrique Ramírez de Arellano
Languange : en
Publisher by : American Mathematical Soc.
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Description : This book presents a collection of papers on certain aspects of general operator theory related to classes of important operators: singular integral, Toeplitz and Bergman operators, convolution operators on Lie groups, pseudodifferential operators, etc. The study of these operators arises from integral representations for different classes of functions, enriches pure operator theory, and is influential and beneficial for important areas of analysis. Particular attention is paid to the fruitful interplay of recent developments of complex and hypercomplex analysis on one side and to operator theory on the other. The majority of papers illustrate this interplay as well as related applications. The papers represent the proceedings of the conference ``Operator Theory for Complex and Hypercomplex Analysis'', held in December 1994 in Mexico City.


Optimization Methods In Partial Differential Equations

Author by : Steven Cox
Languange : en
Publisher by : American Mathematical Soc.
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Description : The problems considered range from basic theoretical issues in the calculus of variations - such as infinite dimensional Hamilton Jacobi equations, saddle point principles, and issues of unique continuation - to ones focusing on application and computation, where theoretical tools are tuned to more specifically defined problems.