Download or read book Arithmetic Groups and Their Generalizations written by Lizhen Ji and published by American Mathematical Soc.. This book was released on 2008 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: In one guise or another, many mathematicians are familiar with certain arithmetic groups, such as $\mathbf{Z}$ or $\textrm{SL}(n, \mathbf{Z})$. Yet, many applications of arithmetic groups and many connections to other subjects within mathematics are less well known. Indeed, arithmetic groups admit many natural and important generalizations. The purpose of this expository book is to explain, through some brief and informal comments and extensive references, what arithmetic groups and their generalizations are, why they are important to study, and how they can be understood and applied to many fields, such as analysis, geometry, topology, number theory, representation theory, and algebraic geometry. It is hoped that such an overview will shed a light on the important role played by arithmetic groups in modern mathematics. Titles in this series are co-published with International Press, Cambridge, MA.Table of Contents: Introduction; General comments on references; Examples of basic arithmetic groups; General arithmetic subgroups and locally symmetric spaces; Discrete subgroups of Lie groups and arithmeticity of lattices in Lie groups; Different completions of $\mathbb{Q}$ and $S$-arithmetic groups over number fields; Global fields and $S$-arithmetic groups over function fields; Finiteness properties of arithmetic and $S$-arithmetic groups; Symmetric spaces, Bruhat-Tits buildings and their arithmetic quotients; Compactifications of locally symmetric spaces; Rigidity of locally symmetric spaces; Automorphic forms and automorphic representations for general arithmetic groups; Cohomology of arithmetic groups; $K$-groups of rings of integers and $K$-groups of group rings; Locally homogeneous manifolds and period domains; Non-cofinite discrete groups, geometrically finite groups; Large scale geometry of discrete groups; Tree lattices; Hyperbolic groups; Mapping class groups and outer automorphism groups of free groups; Outer automorphism group of free groups and the outer spaces; References; Index. Review from Mathematical Reviews: ...the author deserves credit for having done the tremendous job of encompassing every aspect of arithmetic groups visible in today's mathematics in a systematic manner; the book should be an important guide for some time to come.(AMSIP/43.

Download or read book Introduction to Arithmetic Groups written by Armand Borel and published by American Mathematical Soc.. This book was released on 2019-11-07 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fifty years after it made the transition from mimeographed lecture notes to a published book, Armand Borel's Introduction aux groupes arithmétiques continues to be very important for the theory of arithmetic groups. In particular, Chapter III of the book remains the standard reference for fundamental results on reduction theory, which is crucial in the study of discrete subgroups of Lie groups and the corresponding homogeneous spaces. The review of the original French version in Mathematical Reviews observes that “the style is concise and the proofs (in later sections) are often demanding of the reader.” To make the translation more approachable, numerous footnotes provide helpful comments.

Download or read book Algebraic Groups and Their Generalizations written by Brian Parshall and published by . This book was released on 1994 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Handbook of Teichm ller Theory written by Athanase Papadopoulos and published by European Mathematical Society. This book was released on 2007 with total page 876 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this handbook is Teichmuller theory in a wide sense, namely the theory of geometric structures on surfaces and their moduli spaces. This includes the study of vector bundles on these moduli spaces, the study of mapping class groups, the relation with $3$-manifolds, the relation with symmetric spaces and arithmetic groups, the representation theory of fundamental groups, and applications to physics. Thus the handbook is a place where several fields of mathematics interact: Riemann surfaces, hyperbolic geometry, partial differential equations, several complex variables, algebraic geometry, algebraic topology, combinatorial topology, low-dimensional topology, theoretical physics, and others. This confluence of ideas toward a unique subject is a manifestation of the unity and harmony of mathematics. This volume contains surveys on the fundamental theory as well as surveys on applications to and relations with the fields mentioned above. It is written by leading experts in these fields. Some of the surveys contain classical material, while others present the latest developments of the theory as well as open problems. This volume is divided into the following four sections: The metric and the analytic theory The group theory The algebraic topology of mapping class groups and moduli spaces Teichmuller theory and mathematical physics This handbook is addressed to graduate students and researchers in all the fields mentioned.

Download or read book Algebraic Groups and Their Generalizations written by and published by . This book was released on 1994 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Algebraic Groups and Their Generalizations written by William Joseph Haboush and published by . This book was released on 1994 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Finiteness Properties of Arithmetic Groups Acting on Twin Buildings written by Stefan Witzel and published by Springer. This book was released on 2014-07-16 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing an accessible approach to a special case of the Rank Theorem, the present text considers the exact finiteness properties of S-arithmetic subgroups of split reductive groups in positive characteristic when S contains only two places. While the proof of the general Rank Theorem uses an involved reduction theory due to Harder, by imposing the restrictions that the group is split and that S has only two places, one can instead make use of the theory of twin buildings.

Download or read book Arithmetic Groups and Reduction Theory written by Armand Borel and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents papers and lecture notes from four great contributors of the reduction theory: Armond Borel, Roger Godement, Carl Ludwig Siegel and Andre Weil. They reflect their deep knowledge of the subject and their perspectives.

Download or read book Algebraic Groups and Their Generalizations written by William Joseph Haboush and published by . This book was released on 1994 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Algebraic Groups and Their Generalizations Classical methods written by and published by . This book was released on 1994 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Real Numbers Generalizations of the Reals and Theories of Continua written by P. Ehrlich and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their appearance in the late 19th century, the Cantor--Dedekind theory of real numbers and philosophy of the continuum have emerged as pillars of standard mathematical philosophy. On the other hand, this period also witnessed the emergence of a variety of alternative theories of real numbers and corresponding theories of continua, as well as non-Archimedean geometry, non-standard analysis, and a number of important generalizations of the system of real numbers, some of which have been described as arithmetic continua of one type or another. With the exception of E.W. Hobson's essay, which is concerned with the ideas of Cantor and Dedekind and their reception at the turn of the century, the papers in the present collection are either concerned with or are contributions to, the latter groups of studies. All the contributors are outstanding authorities in their respective fields, and the essays, which are directed to historians and philosophers of mathematics as well as to mathematicians who are concerned with the foundations of their subject, are preceded by a lengthy historical introduction.

Download or read book Advances in String Theory written by Eric R. Sharpe and published by American Mathematical Soc.. This book was released on 2008 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Over the past decade string theory has had an increasing impact on many areas of physics: high energy and hadronic physics, gravitation and cosmology, mathematical physics and even condensed matter physics. The impact has been through many major conceptual and methodological developments in quantum field theory in the past fifteen years. In addition, string theory has exerted a dramatic influence on developments in contemporary mathematics, including Gromov-Witten theory, mirror symmetry in complex and symplectic geometry, and important ramifications in enumerative geometry." "This volume is derived from a conference of younger leading practitioners around the common theme: "What is string theory?" The talks covered major current topics, both mathematical and physical, related to string theory. Graduate students and research mathematicians interested in string theory in mathematics and physics will be interested in this workshop."--BOOK JACKET.

Download or read book Extensions of the Stability Theorem of the Minkowski Space in General Relativity written by Lydia Bieri and published by American Mathematical Soc.. This book was released on 2009-06-30 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: A famous result of Christodoulou and Klainerman is the global nonlinear stability of Minkowski spacetime. In this book, Bieri and Zipser provide two extensions to this result. In the first part, Bieri solves the Cauchy problem for the Einstein vacuum equations with more general, asymptotically flat initial data, and describes precisely the asymptotic behavior. In particular, she assumes less decay in the power of $r$ and one less derivative than in the Christodoulou-Klainerman result. She proves that in this case, too, the initial data, being globally close to the trivial data, yields a solution which is a complete spacetime, tending to the Minkowski spacetime at infinity along any geodesic. In contrast to the original situation, certain estimates in this proof are borderline in view of decay, indicating that the conditions in the main theorem on the decay at infinity on the initial data are sharp. In the second part, Zipser proves the existence of smooth, global solutions to the Einstein-Maxwell equations. A nontrivial solution of these equations is a curved spacetime with an electromagnetic field. To prove the existence of solutions to the Einstein-Maxwell equations, Zipser follows the argument and methodology introduced by Christodoulou and Klainerman. To generalize the original results, she needs to contend with the additional curvature terms that arise due to the presence of the electromagnetic field $F$; in her case the Ricci curvature of the spacetime is not identically zero but rather represented by a quadratic in the components of $F$. In particular the Ricci curvature is a constant multiple of the stress-energy tensor for $F$. Furthermore, the traceless part of the Riemann curvature tensor no longer satisfies the homogeneous Bianchi equations but rather inhomogeneous equations including components of the spacetime Ricci curvature. Therefore, the second part of this book focuses primarily on the derivation of estimates for the new terms that arise due to the presence of the electromagnetic field.

Download or read book Heat Kernel and Analysis on Manifolds written by Alexander Grigoryan and published by American Mathematical Soc.. This book was released on 2009 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This volume contains the expanded lecture notes of courses taught at the Emile Borel Centre of the Henri Poincaré Institute (Paris). In the book, leading experts introduce recent research in their fields. The unifying theme is the study of heat kernels in various situations using related geometric and analytic tools. Topics include analysis of complex-coefficient elliptic operators, diffusions on fractals and on infinite-dimensional groups, heat kernel and isoperimetry on Riemannian manifolds, heat kernels and infinite dimensional analysis, diffusions and Sobolev-type spaces on metric spaces, quasi-regular mappings and p -Laplace operators, heat kernel and spherical inversion on SL 2 (C) , random walks and spectral geometry on crystal lattices, isoperimetric and isocapacitary inequalities, and generating function techniques for random walks on graphs."--Publisher's website.

Download or read book Chern Simons Gauge Theory 20 Years After written by Jørgen E. Andersen and published by American Mathematical Soc.. This book was released on 2011 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1989, Edward Witten discovered a deep relationship between quantum field theory and knot theory, and this beautiful discovery created a new field of research called Chern-Simons theory. This field has the remarkable feature of intertwining a large number of diverse branches of research in mathematics and physics, among them low-dimensional topology, differential geometry, quantum algebra, functional and stochastic analysis, quantum gravity, and string theory. The 20-year anniversary of Witten's discovery provided an opportunity to bring together researchers working in Chern-Simons theory for a meeting, and the resulting conference, which took place during the summer of 2009 at the Max Planck Institute for Mathematics in Bonn, included many of the leading experts in the field. This volume documents the activities of the conference and presents several original research articles, including another monumental paper by Witten that is sure to stimulate further activity in this and related fields. This collection will provide an excellent overview of the current research directions and recent progress in Chern-Simons gauge theory.

Download or read book Lagrangian Intersection Floer Theory written by Kenji Fukaya and published by American Mathematical Soc.. This book was released on 2010-06-21 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a two-volume series research monograph on the general Lagrangian Floer theory and on the accompanying homological algebra of filtered $A_\infty$-algebras. This book provides the most important step towards a rigorous foundation of the Fukaya category in general context. In Volume I, general deformation theory of the Floer cohomology is developed in both algebraic and geometric contexts. An essentially self-contained homotopy theory of filtered $A_\infty$ algebras and $A_\infty$ bimodules and applications of their obstruction-deformation theory to the Lagrangian Floer theory are presented. Volume II contains detailed studies of two of the main points of the foundation of the theory: transversality and orientation. The study of transversality is based on the virtual fundamental chain techniques (the theory of Kuranishi structures and their multisections) and chain level intersection theories. A detailed analysis comparing the orientations of the moduli spaces and their fiber products is carried out. A self-contained account of the general theory of Kuranishi structures is also included in the appendix of this volume.

Download or read book Smooth Compactifications of Locally Symmetric Varieties written by Avner Ash and published by Cambridge University Press. This book was released on 2010-01-14 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new edition of this celebrated and long-unavailable book preserves the original book's content and structure and its unrivalled presentation of a universal method for the resolution of a class of singularities in algebraic geometry.