This work combines the work of field theorists and general relativists. It features traditional domains of interaction such as perturbation theory, and explores future topics such as measurement theory, string field theory and hidden symmetries for extended objects.

The Relativists and Cosmologists in India organized an international conference in Goa, India, in 1987, known as the International Conference on Gravitation and Cosmology (ICGC-87). Encouraged by the success of this conference it was decided to have such a meeting periodically, once in every four years. Accordingly, ICGC- 91 was held at the Physical Research Laboratory (PRL), Ahmedabad, India. The third International Conference on Gravitation and Cosmology, (ICGC-95) was held at the Inter-University centre for Astronomy and Astrophysics, IUCAA, Pune, India during December 13 - 19, 1995. This series of conferences is co-sponsored by the Indian Association for General Relativity and Gravitation (lAGRG). The Conference had 16 plenary lectures and five workshops altogether. There were three plenary lectures per day and two workshops running parallel each day. We were fortunate in getting plenary speakers who are leading experts in their respective fields drawn from all over the world. The conference was attended by about 105 persons from India and 55 from abroad. We thank all the contributors who have taken time to write up their lectures amidst their busy schedule. We regret we could not get the contributions of a few plenary speakers. We would also like to thank the members of Organizing Committees who have worked hard to make this conference a success.

The International Congress on Mathematical Physics is the flagship conference in this exciting field. Convening every three years, it gives a survey on the progress achieved in all branches of mathematical physics. It also provides a superb platform to discuss challenges and new ideas. The present volume collects material from the XVIth ICMP which was held in Prague, August 2009, and features most of the plenary lectures and invited lectures in topical sessions as well as information on other parts of the congress program. This volume provides a broad coverage of the field of mathematical physics, from dominantly mathematical subjects to particle physics, condensed matter, and application of mathematical physics methods in various areas such as astrophysics and ecology, amongst others.

Low-dimensional statistical models are instrumental in improving our understanding of emerging fields, such as quantum computing and cryptography, complex systems, and quantum fluids. This book of lectures by international leaders in the field sets these issues into a larger and more coherent theoretical perspective than is currently available.

In recent years, it has become increasingly clear that there are important connections relating three concepts -- groupoids, inverse semigroups, and operator algebras. There has been a great deal of progress in this area over the last two decades, and this book gives a careful, up-to-date and reasonably extensive account of the subject matter. After an introductory first chapter, the second chapter presents a self-contained account of inverse semigroups, locally compact and r-discrete groupoids, and Lie groupoids. The section on Lie groupoids in chapter 2 contains a detailed discussion of groupoids particularly important in noncommutative geometry, including the holonomy groupoids of a foliated manifold and the tangent groupoid of a manifold. The representation theories of locally compact and r-discrete groupoids are developed in the third chapter, and it is shown that the C*-algebras of r-discrete groupoids are the covariance C*-algebras for inverse semigroup actions on locally compact Hausdorff spaces. A final chapter associates a universal r-discrete groupoid with any inverse semigroup. Six subsequent appendices treat topics related to those covered in the text. The book should appeal to a wide variety of professional mathematicians and graduate students in fields such as operator algebras, analysis on groupoids, semigroup theory, and noncommutative geometry. It will also be of interest to mathematicians interested in tilings and theoretical physicists whose focus is modeling quasicrystals with tilings. An effort has been made to make the book lucid and 'user friendly"; thus it should be accessible to any reader with a basic background in measure theory and functional analysis.

This volume contains up-to-date accounts of many of the latest developments in gravitation, cosmology and astrophysics, including papers on black hole radiation, empirical tests of gravitational theory, quantum gravity, classical and quantum cosmology, singularities, computational methods, and a number of other topics. The keynote speakers include S Carlip, M Haugan, A Linde, D Page, G Papini, K Schleich, P Szekeres, G Starkman and J York.