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Crossed Products of C*-Algebras, Topological Dynamics, and Classification
This book collects the notes of the lectures given at an Advanced Course on Dynamical Systems at the Centre de Recerca Matemàtica (CRM) in Barcelona. The notes consist of four series of lectures. The first one, given by Andrew Toms, presents the basic properties of the Cuntz semigroup and its role in the classification program of simple, nuclear, separable C*-algebras. The second series of lectures, delivered by N. Christopher Phillips, serves as an introduction to group actions on C*-algebras and their crossed products, with emphasis on the simple case and when the crossed products are classifiable. The third one, given by David Kerr, treats various developments related to measure-theoretic and topological aspects of crossed products, focusing on internal and external approximation concepts, both for groups and C*-algebras. Finally, the last series of lectures, delivered by Thierry Giordano, is devoted to the theory of topological orbit equivalence, with particular attention to the classification of minimal actions by finitely generated abelian groups on the Cantor set.
Operator Algebras and Their Applications II
The study of operator algebras, which grew out of von Neumann's work in the 1920s and the 1930s on modelling quantum mechanics, has in recent years experienced tremendous growth and vitality. This growth has resulted in significant applications in other areas - both within and outside mathematics. The field was a natural candidate for a 1994-1995 program year in Operator Algebras and Applications held at The Fields Institute for Research in the Mathematical Sciences. This volume contains a selection of papers that arose from the seminars and workshops of the program. Topics covered include the classification of amenable C*-algebras, the Baum-Connes conjecture, E[subscript 0] semigroups, subfactors, E-theory, quasicrystals, and the solution to a long-standing problem in operator theory: Can almost commuting self-adjoint matrices be approximated by commuting self-adjoint matrices?
African Economic Outlook 2015 Regional Development and Spatial Inclusion
The African Economic Outlook 2015 analyses Africa’s growing role in the world economy and predicts the continent’s two-year prospects in crucial areas: macroeconomics, financing, trade policies and regional integration, human development, and governance.
Governing Through Goals
A detailed examination of the UN's Sustainable Development Goals and the shift in governance strategy they represent. In September 2015, the United Nations General Assembly adopted the Sustainable Development Goals as part of the 2030 Agenda for Sustainable Development. The Sustainable Development Goals built on and broadened the earlier Millennium Development Goals, but they also signaled a larger shift in governance strategies. The seventeen goals add detailed content to the concept of sustainable development, identify specific targets for each goal, and help frame a broader, more coherent, and transformative 2030 agenda. The Sustainable Development Goals aim to build a universal, integrat...
Mexico and the 2030 Sustainable Development Agenda
This book explores how and why Mexico’s approach to the 2030 Agenda for Sustainable Development and Sustainable Development Goals (SDG) implementation with the López Obrador administration is unsustainable and non-transformative, overshadowed by his vision of Mexico’s “Fourth Transformation”. Approached as a super mantra revolving around “Republican Austerity” and “First, the poor”, it provides original analysis of structural and conjunctural challenges facing Mexico as regards People-, Planet-, and Peace-centered development. The book reveals the promise “First, the poor” is inconsistent with data on Mexico’s poverty reduction (SDG1). Despite record-high spending on s...
Algebraic and Topological Dynamics
This volume contains a collection of articles from the special program on algebraic and topological dynamics and a workshop on dynamical systems held at the Max-Planck Institute (Bonn, Germany). It reflects the extraordinary vitality of dynamical systems in its interaction with a broad range of mathematical subjects. Topics covered in the book include asymptotic geometric analysis, transformation groups, arithmetic dynamics, complex dynamics, symbolic dynamics, statisticalproperties of dynamical systems, and the theory of entropy and chaos. The book is suitable for graduate students and researchers interested in dynamical systems.
Groups and Graphs, Designs and Dynamics
This collection of four short courses looks at group representations, graph spectra, statistical optimality, and symbolic dynamics, highlighting their common roots in linear algebra. It leads students from the very beginnings in linear algebra to high-level applications: representations of finite groups, leading to probability models and harmonic analysis; eigenvalues of growing graphs from quantum probability techniques; statistical optimality of designs from Laplacian eigenvalues of graphs; and symbolic dynamics, applying matrix stability and K-theory. An invaluable resource for researchers and beginning Ph.D. students, this book includes copious exercises, notes, and references.
Cantor Minimal Systems
Within the subject of topological dynamics, there has been considerable recent interest in systems where the underlying topological space is a Cantor set. Such systems have an inherently combinatorial nature, and seminal ideas of Anatoly Vershik allowed for a combinatorial model, called the Bratteli-Vershik model, for such systems with no non-trivial closed invariant subsets. This model led to a construction of an ordered abelian group which is an algebraic invariant of the system providing a complete classification of such systems up to orbit equivalence. The goal of this book is to give a statement of this classification result and to develop ideas and techniques leading to it. Rather than being a comprehensive treatment of the area, this book is aimed at students and researchers trying to learn about some surprising connections between dynamics and algebra. The only background material needed is a basic course in group theory and a basic course in general topology.
