Paperback
Series: London Mathematical Society Lecture Note Series (No. 383)
ISBN: 9780521149761
2 b/w illus.
Dimensions: 228 x 152 mm
- available from September 2011
The development of Maxim Kontsevich's initial ideas on motivic integration has unexpectedly influenced many other areas of mathematics, ranging from the Langlands program over harmonic analysis, to non-Archimedean analysis, singularity theory and birational geometry. This book assembles the different theories of motivic integration and their applications for the first time, allowing readers to compare different approaches and assess their individual strengths. All of the necessary background is provided to make the book accessible to graduate students and researchers from algebraic geometry, model theory and number theory. Applications in several areas are included so that readers can see motivic integration at work in other domains. In a rapidly-evolving area of research this book will prove invaluable. This first volume contains introductory texts on the model theory of valued fields, different approaches to non-Archimedean geometry, and motivic integration on algebraic varieties and non-Archimedean spaces.
1. Introduction Raf Cluckers, Johannes Nicaise and Julien Sebag
2. Introduction to the model theory of valued fields Zoe Chatzidakis
3. On the definition of rigid analytic spaces Siegfried Bosch
4. Topological rings in rigid geometry Fumiharu Kato
5. The Grothendieck ring of varieties Johannes Nicaise and Julien Sebag
6. A short course on geometric motivic integration Manuel Blickle
7. Motivic invariants of rigid varieties and applications to complex singularities Johannes Nicaise and Julien Sebag
8. Motivic integration in mixed characteristic with bounded ramification: a summary Raf Cluckers and Francois Loeser.
Paperback
Series: London Mathematical Society Lecture Note Series (No. 384)
ISBN: 9781107648814
11 b/w illus.
Dimensions: 228 x 152 mm
- available from September 2011
The development of Maxim Kontsevich's initial ideas on motivic integration has unexpectedly influenced many other areas of mathematics, ranging from the Langlands program over harmonic analysis, to non-Archimedean analysis, singularity theory and birational geometry. This book assembles the different theories of motivic integration and their applications for the first time, allowing readers to compare different approaches and assess their individual strengths. All of the necessary background is provided to make the book accessible to graduate students and researchers from algebraic geometry, model theory and number theory. Applications in several areas are included so that readers can see motivic integration at work in other domains. In a rapidly-evolving area of research this book will prove invaluable. This second volume discusses various applications of non-Archimedean geometry, model theory and motivic integration and the interactions between these domains.
Preface
1. Heights and measures on analytic spaces: a survey of recent results, and some remarks Antoine Chambert-Loir
2. C-minimal structures without density assumption Francoise Delon
3. Trees of definable sets in Zp Immanuel Halupczok
4. Triangulated motives over Noetherian separated schemes Florian Ivorra
5. A survey of algebraic exponential sums and some applications Emmanuel Kowalski
6. A motivic version of p-adic integration Karl Rokaeus
7. Absolute desingularization in characteristic zero Michael Temkin.
552 pages | 1 halftone, 15 line drawings | 6 x 9 | c 2011
ISBN: 9780226237886
Published April 2011
Chicago Lectures in Mathematics
The study of group actions is more than a hundred years old but remains to this day a vibrant and widely studied topic in a variety of mathematic fields. A central development in the last fifty years is the phenomenon of rigidity, whereby one can classify actions of certain groups, such as lattices in semi-simple Lie groups. This provides a way to classify all possible symmetries of important spaces and all spaces admitting given symmetries. Paradigmatic results can be found in the seminal work of George Mostow, Gergory Margulis, and Robert J. Zimmer, among others.
The papers in Geometry, Rigidity, and Group Actions explore the role of group actions and rigidity in several areas of mathematics, including ergodic theory, dynamics, geometry, topology, and the algebraic properties of representation varieties. In some cases, the dynamics of the possible group actions are the principal focus of inquiry. In other cases, the dynamics of group actions are a tool for proving theorems about algebra, geometry, or topology. This volume contains surveys of some of the main directions in the field, as well as research articles on topics of current interest.
232 pages | 24 line drawings | 6 x 9 | c 2011
ISBN: 9780226569512
Published May 2011
Chicago Lectures in Mathematics
In recent years scholars from a variety of branches of mathematics have made several significant developments in the theory of group actions. Groups of Circle Diffeomorphisms systematically explores group actions on the simplest closed manifold, the circle. As the group of circle diffeomorphisms is an important subject in modern mathematics, this book will be of interest to those doing research in group theory, dynamical systems, low dimensional geometry and topology, and foliation theory. The book is mostly self-contained and also includes numerous complementary exercises, making it an excellent textbook for undergraduate and graduate students.
“This is a wonderful book about ‘mildly’ smooth actions of groups on the most important manifolds in mathematics: the circle and the line. Andres Navas draws upon the classical contributions of Poincare, Denjoy, Holder, Plante, Thompson, Sacksteder, and Duminy, as well as the relatively recent achievements of Margulis and Witte Morris, to offer the first book-length exploration of this topic. The analytic techniques, the dynamical point of view, and the algebraic nature of objects considered here produce a blend of beautiful mathematics that will be used by researchers in several areas of science.”?Rostislav Grigorchuk, Texas A&M University, and Etienne Ghys, Ecole Normale Superieure de Lyon
“Groups of Circle Diffeomorphisms provides a great overview of the research on differentiable group actions on the circle. Navas’s book will appeal to those doing research on differential topology, transformation groups, dynamical systems, foliation theory, and representation theory, and will be a solid base for those who want to further attack problems of group actions on higher dimensional manifolds or of geometric group theory.”?Takashi Tsuboi, University of Tokyo
| Hardcover |
* ISBN 978-3-11-025029-9
Series: de Gruyter Studies in Mathematics 9 to be published April 2011
About this Title
From a review of the first edition: "This book is much more than an introduction to the subject of its title. It covers in depth a broad range of topics in the mathematical theory of phase transition in statistical mechanics and as an up to date reference in its chosen topics it is a work of outstanding scholarship. It is in fact one of the author's stated aims that this comprehensive monograph should serve both as an introductory text and as a reference for the expert. In its latter function it informs the reader about the state of the art in several directions. It is introductory in the sense that it does not assume any prior knowledge of statistical mechanics and is accessible to a general readership of mathematicians with a basic knowledge of measure theory and probability. As such it should contribute considerably to the further growth of the already lively interest in statistical mechanics on the part of probabilists and other mathematicians." Fredos Papangelou, Zentralblatt MATH
The second edition has been extended by a new section on large deviations and some comments on the more recent developments in the area.
**********************************************************************