Bøger i Progress in Mathematics serien

This self-contained monograph presents a unified exposition of the thermodynamic formalism and some of its main extensions, with emphasis on the relation to dimension theory and multifractal analysis of dynamical systems. In particular, the book considers three different flavors of the thermodynamic formalism, namely nonadditive, subadditive, and almost additive, and provides a detailed discussion of some of the most significant results in the area, some of them quite recent. It also includes a discussion of the most substantial applications of these flavors of the thermodynamic formalism to dimension theory and multifractal analysis of dynamical systems.

Although much of classical ergodic theory is concerned with single transformations and one-parameter flows, the subject inherits from statistical mechanics not only its name, but also an obligation to analyze spatially extended systems with multidimensional symmetry groups. However, the wealth of concrete and natural examples which has contributed so much to the appeal and development of classical dynamics, is noticeably absent in this more general theory. The purpose of this book is to help remedy this scarcity of explicit examples by introducing a class of continuous Zd-actions diverse enough to exhibit many of the new phenomena encountered in the transition from Z to Zd, but which nevertheless lends itself to systematic study: the Zd-actions by automorphisms of compact, abelian groups. One aspect of these actions, not surprising in itself but quite striking in its extent and depth nonetheless, is the connection with commutative algebra and arithmetical algebraic geometry. The algebraic framework resulting from this connection allows the construction of examples with a variety of specified dynamical properties, and by combining algebraic and dynamical tools one obtains a quite detailed understanding of this class of Zd-actions.

Tamari lattices can be realized in terms of polytopes called associahedra, which in fact also appeared first in Tamari's thesis. On the occasion of Dov Tamari's centennial birthday, this book provides an introduction to topical research related to Tamari's work and ideas.

Evolution equations of hyperbolic or more general p-evolution type form an active field of current research. The book gives an overview of a variety of ongoing current research in the field and, therefore, allows researchers as well as students to grasp new aspects and broaden their understanding of the area.

This monograph lays down the foundations of the theory of complex Kleinian groups, a newly born area of mathematics whose origin traces back to the work of Riemann, Poincare, Picard and many others.

Ce travail en deux volumes donne la preuve de la stabilisation de la formule des trace tordue.Stabiliser la formule des traces tordue est la méthode la plus puissante connue actuellement pour comprendre l'action naturelle du groupe des points adéliques d'un groupe réductif, tordue par un automorphisme, sur les formes automorphes de carré intégrable de ce groupe. Cette compréhension se fait en réduisant le problème, suivant les idées de Langlands, à des groupes plus petits munis d'un certain nombre de données auxiliaires; c'est ce que l'on appelle les données endoscopiques. L'analogue non tordu a été résolu par J. Arthur et dans ce livre on suit la stratégie de celui-ci.Publier ce travail sous forme de livre permet de le rendre le plus complet possible. Les auteurs ont repris la théorie de l'endoscopie tordue développée par R. Kottwitz et D. Shelstad et par J.-P. Labesse. Ils donnent tous les arguments des démonstrations même si nombre d'entre eux se trouvent déjà dansles travaux d'Arthur concernant le cas de la formule des traces non tordue.Ce travail permet de rendre inconditionnelle la classification que J. Arthur a donnée des formes automorphes de carré intégrable pour les groupes classiques quasi-déployés, c¿était pour les auteurs une des principales motivations pour l¿écrire.Cette première partie comprend les chapitres préparatoires (I-V).

This monograph focuses on the geometric theory of motivic integration, which takes its values in the Grothendieck ring of varieties. With its extensive discussion of preliminaries and applications, this book is an ideal resource for graduate students of algebraic geometry and researchers of motivic integration.

Brauer had already introduced the defect of a block and opened the way towards a classification by solving all the problems in defects zero and one, and by providing some evidence for the finiteness of the set of blocks with a given defect.

This book is dedicated to study the inverse problem of ordinary differential equations, that is it focuses in finding all ordinary differential equations that satisfy a given set of properties.

This volume contains selected papers authored by speakers and participants of the 2013 Arbeitstagung, held at the Max Planck Institute for Mathematics in Bonn, Germany, from May 22-28.

This lecture notes volume presents significant contributions from the "Algebraic Geometry and Number Theory" Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014. It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology.

This book presents the original proof of Gromov's compactness theorem for pseudo-holomorphic curves in detail. Local properties of pseudo-holomorphic curves are investigated and proved from a geometric viewpoint.

A locally compact group has the Haagerup property, or is a-T-menable in the sense of Gromov, if it admits a proper isometric action on some affine Hilbert space.

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)".

D-modules continues to be an active area of stimulating research in such mathematical areas as algebraic, analysis, differential equations, and representation theory.

Andreas Floer's visions and contributions have significantly influenced the developments of mathematics. This work presents a collection of invited contributions, and survey articles as well as research papers on his fields of interest, bearing testimony of the high esteem and appreciation this brilliant mathematician enjoyed among his colleagues.

Abelian varieties and their moduli are a topic of increasing importance in today`s mathematics, applications ranging from algebraic geometry and number theory to mathematical physics.

Award-winning monograph of the Ferran Sunyer i Balaguer Prize 1997. This book is a self-contained exposition of the spectral theory of Toeplitz operators with piecewise continuous symbols and singular integral operators with piecewise continuous coefficients.

Adams) * Algebraic and geometric aspects of the Knizhnik-Zamolodchikov equations in conformal field theory (P. Bouwknegt) * Application of the representation theory of loop groups to simple models in quantum field theory and to certain integrable systems (A.L. Ruan) * The physics origin of Seiberg-Witten equations in 4-manifold theory (S.

- A nilpotent orbit is an orbit of the adjoint action of G on g which contains the zero element of g in its closure. (For the special linear group 2 G = SL(n,C), whose Lie algebra 9 is all n x n matrices with trace zero, an adjoint orbit consists of all matrices with a given Jordan canonical form;

This book gives an up-to-date account of progress on Pansu's celebrated problem on the sub-Riemannian isoperimetric profile of the Heisenberg group. It develops the methods and tools of sub-Riemannian differential geometry, nonsmooth analysis, and geometric measure theory suitable for attacks on Pansu's problem.

This book examines the range of available tools from analytic number theory that can be applied to study the density of rational points on projective varieties.

Key topics in this volume include: Analytic structures of Quantum Field Theory (QFT), renormalization group methods, gauge QFT, stability properties and extension of the axiomatic framework, QFT on models of curved spacetimes, QFT on noncommutative Minkowski spacetime.

= {~k' k = 0, 1, ... } with transition probability function (t.pJ.) P(x, B), i.e., P(x, B) := Prob (~k+1 E B I ~k = x) for each x E X, B E B, and k = 0,1, .... is said to be stable if there exists a probability measure (p.m.) /.l on B such that (*) VB EB. /.l(B) = Ix /.l(dx) P(x, B) If (*) holds then /.l is called an invariant p.m. for the Me ~.

The Gelfand-Serganova theorem, which allows for the geometric interpretation of matroids as convex polytopes with certain symmetry properties, is presented, and in the final chapter, matroid representations and combinatorial flag varieties are discussed.

The aim of this book is twofold. On the one hand, it gives a quick, self-contained introduction to Poisson geometry and related subjects. Even when it comes to classical results, the book gives new insights. It contains results obtained over the past 10 years which are not available in other books.

This book describes very recent results involving an extensive use of analytical tools in the study of geometrical and topological properties of complete Riemannian manifolds.

Invited articles by top notch expertsFocus is on topics in representation theory of algebraic groups and quantum groupsOf interest to graduate students and researchers in representation theory, group theory, algebraic geometry, quantum theory and math physics

Lie Groups: Structures, Actions, and Representations, In Honor of Joseph A. More precisely, finite groups and classical finite dimensional, as well as infinite-dimensional Lie groups, and algebras play a role.