This volume marks the twentieth anniversary of the Bialowieza series of meetings on Differential Geometric Methods in Physics; the anniversary meeting was held during July 1-7, 2001. The Bialowieza meetings, held every year during the first week of July, have now grown into an annual pilgrimage for an international group of physicists and mathematicians. The topics discussed at the meetings, while within the broad area of differential geometric methods in physics, have focused around quantization, coherent states, infinite dimensional systems, symplectic geometry, spectral theory and harmonic analysis. The present volume brings together a set of specially invited papers from leading experts in the various fields, who have contributed to these meetings and whose work represents a cross-section of the topics discussed. Consequently, rather than a proceedings volume, this book embodies the spirit of the Bialowieza workshops and reflects their scientific tenor, as a tribute to the completion of two decades of a shared scientific experience.This book will be of interest to researchers and graduate students working in the area of differential geometric methods in physics, as it gives interesting glimpses into the present state of the art from different points of view.

In Europe's last primeval forest, at Poland's easternmost border with Belarus, the deep past of ancient oaks, woodland bison, and thousands of species of insects and fungi collides with authoritarian and communist histories. Foresters, biologists, environmentalists, and locals project the ancient Białowieża Forest as a series of competing icons in struggles over memory, land, and economy, which are also struggles about whether to log or preserve the woodland; whether and how to celebrate the mixed ethnic Polish/Belarusian peasant past; and whether to align this eastern outpost with ultraright Polish political parties, neighboring Belarus, or the European Union. Eunice Blavascunas provides an intimate ethnographic account, gathered in more than 20 years of research, to untangle complex forest conflicts between protection and use. She looks at which pasts are celebrated, which fester, and which are altered in the tumultuous decades following the collapse of communism. Foresters, Borders, and Bark Beetles is a timely and fascinating work of cultural analysis and storytelling that textures its ethnographic reading of people with the agency of the forest itself and its bark beetle outbreaks, which threaten to alter the very composition of the forest in the age of the Anthropocene.

And conclusions of the workshop on the World Heritage Convention held during the IV World Congress on National Parks and Protected Areas, Caracas, Venezuela, February 1992 / Hemanta Mishra and N. Ishwaran -- From strength to strength : World Heritage in its 20th year / Jim Thorsell -- World Heritage at risk / James R. Paine -- The World Heritage Convention and protected landscapes / Michael Beresford and P.H.C. Lucas -- Wood Buffalo World Heritage Site : threats and possible solutions / Kevin McNamee -- Kluane and Wrangell-St Elias national parks : joint management of North America's largest wilderness / Michael Fay -- Charting a course for a greater Yellowstone tomorrow / Dennis Click -- Colombian-Panamanian border national parks in Darién / Dilver Octavio Pintor Peralta -- Public participation in the management of Huascarán World Heritage Site / Miriam Torres Angeles -- Scientific research in Bialowieza World Heritage Site / Czeslaw Okolow -- Buffer zone management in Sinharaja World Heritage Forest / H.M. Bandaratillake -- Environmental impacts of back-country tourism on three sides of Everest / Alton C. Byers and Kamal Banskota -- Sociocultural impacts of mountain tourism on Nepal's Sagarmatha (Everest) World Heritage Site : implications for sustainable tourism / David W. Robinson -- Manas : World Heritage in danger? / Sanjoy Deb Roy -- The effects of war on World Heritage sites and protected areas in Ethiopia / Tadesse Gebre-Michael, Tesfaye Hundessa and Jesse C. Hillman -- The International Foundation of the Banc d'Arguin / Luc Hoffman and Pierre Campredon -- Ngorongoro : striking a balance between conservation and development / Scott L. Perkin and Paul J. Mshanga -- Monitoring the environmental impacts of tourism on the Great Barrier Reef World Heritage Site / Simon Woodley -- Tourism development and Te Wahipounamu / Bruce Watson -- Application of the World Heritage Convention to Antarctica and the islands of the Southern Ocean / Paul Dingwall.

The Białowieża workshops on Geometric Methods in Physics are among the most important meetings in the field. Every year some 80 to 100 participants from both mathematics and physics join to discuss new developments and to interchange ideas. This volume contains contributions by selected speakers at the XXX meeting in 2011 as well as additional review articles and shows that the workshop remains at the cutting edge of ongoing research. The 2011 workshop focussed on the works of the late Felix A. Berezin (1931–1980) on the occasion of his 80th anniversary as well as on Bogdan Mielnik and Stanisław Lech Woronowicz on their 75th and 70th birthday, respectively. The groundbreaking work of Berezin is discussed from today’s perspective by presenting an overview of his ideas and their impact on further developments. He was, among other fields, active in representation theory, general concepts of quantization and coherent states, supersymmetry and supermanifolds. Another focus lies on the accomplishments of Bogdan Mielnik and Stanisław Lech Woronowicz. Mielnik’s geometric approach to the description of quantum mixed states, the method of quantum state manipulation and their important implications for quantum computing and quantum entanglement are discussed as well as the intricacies of the quantum time operator. Woronowicz’ fruitful notion of a compact quantum group and related topics are also addressed.

The book surveys mathematical relations between classical and quantum mechanics, gravity, time and thermodynamics from various points of view and many sources (with appropriate attribution). The emergence theme is developed with an emphasis on the meaning via mathematics. A background theme of Bohemian mechanics and connections to the quantum equivalence principle of Matone et al. is also developed in great detail. Some original work relating the quantum potential and Ricci flow is also included.

This volume contains cutting-edge research from leading experts in ergodic theory, dynamical systems and group actions. A large part of the volume addresses various aspects of ergodic theory of general group actions including local entropy theory, universal minimal spaces, minimal models and rank one transformations. Other papers deal with interval exchange transformations, hyperbolic dynamics, transfer operators, amenable actions and group actions on graphs.

This book provides an introduction to the theory of quantum groups with emphasis on their duality and on the setting of operator algebras. Part I of the text presents the basic theory of Hopf algebras, Van Daele's duality theory of algebraic quantum groups, and Woronowicz's compact quantum groups, staying in a purely algebraic setting. Part II focuses on quantum groups in the setting of operator algebras. Woronowicz's compact quantum groups are treated in the setting of $C^*$-algebras, and the fundamental multiplicative unitaries of Baaj and Skandalis are studied in detail. An outline of Kustermans' and Vaes' comprehensive theory of locally compact quantum groups completes this part. Part III leads to selected topics, such as coactions, Baaj-Skandalis-duality, and approaches to quantum groupoids in the setting of operator algebras. The book is addressed to graduate students and non-experts from other fields. Only basic knowledge of (multi-) linear algebra is required for the first part, while the second and third part assume some familiarity with Hilbert spaces, $C^*$-algebras, and von Neumann algebras.

This is the first monograph devoted to the Sturm oscillatory theory for infinite systems of differential equations and its relations with the spectral theory. It aims to study a theory of self-adjoint problems for such systems, based on an elegant method of binary relations. Another topic investigated in the book is the behavior of discrete eigenvalues which appear in spectral gaps of the Hill operator and almost periodic Schrödinger operators due to local perturbations of the potential (e.g., modeling impurities in crystals).The book is based on results that have not been presented in other monographs. The only prerequisites needed to read it are basics of ordinary differential equations and operator theory. It should be accessible to graduate students, though its main topics are of interest to research mathematicians working in functional analysis, differential equations and mathematical physics, as well as to physicists interested in spectral theory of differential operators.

Noncommutative geometry is a novel approach which is opening up new possibilities for geometry from a mathematical viewpoint. It is also providing new tools for the investigation of quantum space-time in physics. Recent developments in string theory have supported the idea of quantum spaces, and have strongly stimulated the research in this field. This self-contained volume contains survey lectures and research articles which address these issues and related topics. The book is accessible to both researchers and graduate students beginning to study this subject.

The ambition of this volume is twofold: to provide a comprehensive overview of the field and to serve as an indispensable reference work for anyone who wants to work in it. For example, any philosopher who hopes to make a contribution to the topic of the classical-quantum correspondence will have to begin by consulting Klaas Landsman's chapter. The organization of this volume, as well as the choice of topics, is based on the conviction that the important problems in the philosophy of physics arise from studying the foundations of the fundamental theories of physics. It follows that there is no sharp line to be drawn between philosophy of physics and physics itself. Some of the best work in the philosophy of physics is being done by physicists, as witnessed by the fact that several of the contributors to the volume are theoretical physicists: viz., Ellis, Emch, Harvey, Landsman, Rovelli, 't Hooft, the last of whom is a Nobel laureate. Key features - Definitive discussions of the philosophical implications of modern physics - Masterly expositions of the fundamental theories of modern physics - Covers all three main pillars of modern physics: relativity theory, quantum theory, and thermal physics - Covers the new sciences grown from these theories: for example, cosmology from relativity theory; and quantum information and quantum computing, from quantum theory - Contains special Chapters that address crucial topics that arise in several different theories, such as symmetry and determinism - Written by very distinguished theoretical physicists, including a Nobel Laureate, as well as by philosophers - Definitive discussions of the philosophical implications of modern physics - Masterly expositions of the fundamental theories of modern physics - Covers all three main pillars of modern physics: relativity theory, quantum theory, and thermal physics - Covers the new sciences that have grown from these theories: for example, cosmology from relativity theory; and quantum information and quantum computing, from quantum theory - Contains special Chapters that address crucial topics that arise in several different theories, such as symmetry and determinism - Written by very distinguished theoretical physicists, including a Nobel Laureate, as well as by philosophers