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Intrinsic Approach to Galois Theory of $q$-Difference Equations
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Galois Theories of Linear Difference Equations: An Introduction
This book is a collection of three introductory tutorials coming out of three courses given at the CIMPA Research School “Galois Theory of Difference Equations” in Santa Marta, Columbia, July 23–August 1, 2012. The aim of these tutorials is to introduce the reader to three Galois theories of linear difference equations and their interrelations. Each of the three articles addresses a different galoisian aspect of linear difference equations. The authors motivate and give elementary examples of the basic ideas and techniques, providing the reader with an entry to current research. In addition each article contains an extensive bibliography that includes recent papers; the authors have provided pointers to these articles allowing the interested reader to explore further.
Number Theory
Three major branches of number theory are included in the volume: namely analytic number theory, algebraic number theory, and transcendental number theory. Original research is presented that discusses modern techniques and survey papers from selected academic scholars.
Transcendence in Algebra, Combinatorics, Geometry and Number Theory
This proceedings volume gathers together original articles and survey works that originate from presentations given at the conference Transient Transcendence in Transylvania, held in Brașov, Romania, from May 13th to 17th, 2019. The conference gathered international experts from various fields of mathematics and computer science, with diverse interests and viewpoints on transcendence. The covered topics are related to algebraic and transcendental aspects of special functions and special numbers arising in algebra, combinatorics, geometry and number theory. Besides contributions on key topics from invited speakers, this volume also brings selected papers from attendees.
Summary Catalogue of European Decorative Arts in the J. Paul Getty Museum
J. Paul Getty had a passion for the exquisitely made furniture and decorative objects of eighteenth-century France, which he began collecting in the 1930s. Gillian Wilson, curator of decorative arts since 1971, has broadened and strengthened the collection, adding Boulle furniture, mounted oriental porcelain, tapestries, clocks, ceramics, and more. In the 1980s and 1990s the Museum continued to enlarge its decorative arts holdings, creating a European sculpture department in 1984 and adding glass, maiolica, goldsmiths’ work, pietre dure, and furniture from Italy and Northern Europe. This book is a revised and expanded edition of Decorative Arts: An Illustrated Summary Catalogue of the Collection of the J. Paul Getty Museum (1993). In addition to more than forty recent acquisitions—among these four wall sconces from Versailles that once belonged to Marie Antoinette and an elaborate upholstered bed from the collection of Karl Lagerfeld—it includes the results of years of research. Designed for scholars, students, and devotees of the decorative arts, this volume provides a comprehensive look at the Getty's fine collection.
Planar Algebras in Braided Tensor Categories
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Weak Convergence of Measures
This book provides a thorough exposition of the main concepts and results related to various types of convergence of measures arising in measure theory, probability theory, functional analysis, partial differential equations, mathematical physics, and other theoretical and applied fields. Particular attention is given to weak convergence of measures. The principal material is oriented toward a broad circle of readers dealing with convergence in distribution of random variables and weak convergence of measures. The book contains the necessary background from measure theory and functional analysis. Large complementary sections aimed at researchers present the most important recent achievements. More than 100 exercises (ranging from easy introductory exercises to rather difficult problems for experienced readers) are given with hints, solutions, or references. Historic and bibliographic comments are included. The target readership includes mathematicians and physicists whose research is related to probability theory, mathematical statistics, functional analysis, and mathematical physics.
The Classification of the Finite Simple Groups, Number 8: Part III, Chapters 12–17: The Generic Case, Completed
This book completes a trilogy (Numbers 5, 7, and 8) of the series The Classification of the Finite Simple Groups treating the generic case of the classification of the finite simple groups. In conjunction with Numbers 4 and 6, it allows us to reach a major milestone in our series—the completion of the proof of the following theorem: Theorem O: Let G be a finite simple group of odd type, all of whose proper simple sections are known simple groups. Then either G is an alternating group or G is a finite group of Lie type defined over a field of odd order or G is one of six sporadic simple groups. Put another way, Theorem O asserts that any minimal counterexample to the classification of the finite simple groups must be of even type. The work of Aschbacher and Smith shows that a minimal counterexample is not of quasithin even type, while this volume shows that a minimal counterexample cannot be of generic even type, modulo the treatment of certain intermediate configurations of even type which will be ruled out in the next volume of our series.
Partial Dynamical Systems, Fell Bundles and Applications
Partial dynamical systems, originally developed as a tool to study algebras of operators in Hilbert spaces, has recently become an important branch of algebra. Its most powerful results allow for understanding structural properties of algebras, both in the purely algebraic and in the C*-contexts, in terms of the dynamical properties of certain systems which are often hiding behind algebraic structures. The first indication that the study of an algebra using partial dynamical systems may be helpful is the presence of a grading. While the usual theory of graded algebras often requires gradings to be saturated, the theory of partial dynamical systems is especially well suited to treat nonsatura...
Geometry and Dynamics in Gromov Hyperbolic Metric Spaces
This book presents the foundations of the theory of groups and semigroups acting isometrically on Gromov hyperbolic metric spaces. Particular emphasis is paid to the geometry of their limit sets and on behavior not found in the proper setting. The authors provide a number of examples of groups which exhibit a wide range of phenomena not to be found in the finite-dimensional theory. The book contains both introductory material to help beginners as well as new research results, and closes with a list of attractive unsolved problems.
