Analysis and Geometry on Groups


Author: Nicholas T. Varopoulos,L. Saloff-Coste,T. Coulhon
Publisher: Cambridge University Press
ISBN: 9780521088015
Category: Mathematics
Page: 172
View: 6811

Continue Reading →

The geometry and analysis that is discussed in this book extends to classical results for general discrete or Lie groups, and the methods used are analytical, but are not concerned with what is described these days as real analysis. Most of the results described in this book have a dual formulation: they have a "discrete version" related to a finitely generated discrete group and a continuous version related to a Lie group. The authors chose to center this book around Lie groups, but could easily have pushed it in several other directions as it interacts with the theory of second order partial differential operators, and probability theory, as well as with group theory.

Geometric Group Theory


Author: Cornelia Druţu,Michael Kapovich
Publisher: American Mathematical Soc.
ISBN: 1470411040
Category: Geometric group theory
Page: 819
View: 1539

Continue Reading →

The key idea in geometric group theory is to study infinite groups by endowing them with a metric and treating them as geometric spaces. This applies to many groups naturally appearing in topology, geometry, and algebra, such as fundamental groups of manifolds, groups of matrices with integer coefficients, etc. The primary focus of this book is to cover the foundations of geometric group theory, including coarse topology, ultralimits and asymptotic cones, hyperbolic groups, isoperimetric inequalities, growth of groups, amenability, Kazhdan's Property (T) and the Haagerup property, as well as their characterizations in terms of group actions on median spaces and spaces with walls. The book contains proofs of several fundamental results of geometric group theory, such as Gromov's theorem on groups of polynomial growth, Tits's alternative, Stallings's theorem on ends of groups, Dunwoody's accessibility theorem, the Mostow Rigidity Theorem, and quasiisometric rigidity theorems of Tukia and Schwartz. This is the first book in which geometric group theory is presented in a form accessible to advanced graduate students and young research mathematicians. It fills a big gap in the literature and will be used by researchers in geometric group theory and its applications.

Random Walks on Infinite Graphs and Groups


Author: Wolfgang Woess
Publisher: Cambridge University Press
ISBN: 9780521552929
Category: Mathematics
Page: 334
View: 364

Continue Reading →

The main theme of this book is the interplay between random walks and discrete structure theory.

Geometric Group Theory Down Under

Proceedings of a Special Year in Geometric Group Theory, Canberra, Australia, 1996
Author: John Cossey,Charles F. Miller,Walter D. Neumann,Michael Shapiro
Publisher: Walter de Gruyter
ISBN: 311080686X
Category: Mathematics
Page: 344
View: 3852

Continue Reading →

The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

The Large Sieve and its Applications

Arithmetic Geometry, Random Walks and Discrete Groups
Author: E. Kowalski
Publisher: Cambridge University Press
ISBN: 1139472976
Category: Mathematics
Page: N.A
View: 9111

Continue Reading →

Among the modern methods used to study prime numbers, the 'sieve' has been one of the most efficient. Originally conceived by Linnik in 1941, the 'large sieve' has developed extensively since the 1960s, with a recent realisation that the underlying principles were capable of applications going well beyond prime number theory. This book develops a general form of sieve inequality, and describes its varied applications, including the study of families of zeta functions of algebraic curves over finite fields; arithmetic properties of characteristic polynomials of random unimodular matrices; homological properties of random 3-manifolds; and the average number of primes dividing the denominators of rational points on elliptic curves. Also covered in detail are the tools of harmonic analysis used to implement the forms of the large sieve inequality, including the Riemann Hypothesis over finite fields, and Property (T) or Property (tau) for discrete groups.

Graph Directed Markov Systems

Geometry and Dynamics of Limit Sets
Author: R. Daniel Mauldin,Mariusz Urbanski
Publisher: Cambridge University Press
ISBN: 9780521825382
Category: Mathematics
Page: 281
View: 6605

Continue Reading →

Monograph on Graph Directed Markov Systems with backgound and research level material.

Groups, Geometry and Dynamics


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Group theory
Page: N.A
View: 1129

Continue Reading →

Publishes research articles that focus on groups or group actions as well as articles in other areas of mathematics in which groups or group actions are used as a main tool. Covers all topics of modern group theory with preference given to geometric, asymptotic and combinatorial group theory, dynamics of group actions, probabilistic and analytical methods, interaction with ergodic theory and operator algebras, and other related fields.

Automorphic Forms on SL2 (R)


Author: Armand Borel
Publisher: Cambridge University Press
ISBN: 9780521580496
Category: Mathematics
Page: 192
View: 5329

Continue Reading →

An introduction to the analytic theory of automorphic forms in the case of fuchsian groups.

Morse Theoretic Methods in Nonlinear Analysis and in Symplectic Topology


Author: Paul Biran,Octav Cornea,François Lalonde
Publisher: Springer Science & Business Media
ISBN: 1402042663
Category: Mathematics
Page: 462
View: 6525

Continue Reading →

The papers collected in this volume are contributions to the 43rd session of the Seminaire ́ de mathematiques ́ superieures ́ (SMS) on “Morse Theoretic Methods in Nonlinear Analysis and Symplectic Topology.” This session took place at the Universite ́ de Montreal ́ in July 2004 and was a NATO Advanced Study Institute (ASI). The aim of the ASI was to bring together young researchers from various parts of the world and to present to them some of the most signi cant recent advances in these areas. More than 77 mathematicians from 17 countries followed the 12 series of lectures and participated in the lively exchange of ideas. The lectures covered an ample spectrum of subjects which are re ected in the present volume: Morse theory and related techniques in in nite dim- sional spaces, Floer theory and its recent extensions and generalizations, Morse and Floer theory in relation to string topology, generating functions, structure of the group of Hamiltonian di?eomorphisms and related dynamical problems, applications to robotics and many others. We thank all our main speakers for their stimulating lectures and all p- ticipants for creating a friendly atmosphere during the meeting. We also thank Ms. Diane Belanger ́ , our administrative assistant, for her help with the organi- tion and Mr. Andre ́ Montpetit, our technical editor, for his help in the preparation of the volume.

Journal für die reine und angewandte Mathematik


Author: August Leopold Crelle,Carl Wilhelm Borchardt,Leopold Kronecker,Lazarus Fuchs,Kurt Hensel,Helmut Hasse,Friedrich Schottky
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 9318

Continue Reading →

Topics in Geometric Group Theory


Author: Pierre de la Harpe
Publisher: University of Chicago Press
ISBN: 9780226317199
Category: Mathematics
Page: 310
View: 7485

Continue Reading →

In this book, Pierre de la Harpe provides a concise and engaging introduction to geometric group theory, a new method for studying infinite groups via their intrinsic geometry that has played a major role in mathematics over the past two decades. A recognized expert in the field, de la Harpe adopts a hands-on approach, illustrating key concepts with numerous concrete examples. The first five chapters present basic combinatorial and geometric group theory in a unique and refreshing way, with an emphasis on finitely generated versus finitely presented groups. In the final three chapters, de la Harpe discusses new material on the growth of groups, including a detailed treatment of the "Grigorchuk group." Most sections are followed by exercises and a list of problems and complements, enhancing the book's value for students; problems range from slightly more difficult exercises to open research problems in the field. An extensive list of references directs readers to more advanced results as well as connections with other fields.

Solitons

Differential Equations, Symmetries and Infinite Dimensional Algebras
Author: T. Miwa,M. Jimbo,E. Date
Publisher: Cambridge University Press
ISBN: 9780521561617
Category: Mathematics
Page: 108
View: 9741

Continue Reading →

The goal of this book is to investigate the high degree of symmetry that lies hidden in integrable systems.

Reversibility in Dynamics and Group Theory


Author: Anthony G. O'Farrell,Ian Short
Publisher: Cambridge University Press
ISBN: 1107442885
Category: Mathematics
Page: 292
View: 8000

Continue Reading →

An accessible yet systematic account of reversibility that demonstrates its impact throughout many diverse areas of mathematics.

Floer Homology Groups in Yang-Mills Theory


Author: S. K. Donaldson
Publisher: Cambridge University Press
ISBN: 9781139432603
Category: Mathematics
Page: N.A
View: 6341

Continue Reading →

The concept of Floer homology was one of the most striking developments in differential geometry. It yields rigorously defined invariants which can be viewed as homology groups of infinite-dimensional cycles. The ideas led to great advances in the areas of low-dimensional topology and symplectic geometry and are intimately related to developments in Quantum Field Theory. The first half of this book gives a thorough account of Floer's construction in the context of gauge theory over 3 and 4-dimensional manifolds. The second half works out some further technical developments of the theory, and the final chapter outlines some research developments for the future - including a discussion of the appearance of modular forms in the theory. The scope of the material in this book means that it will appeal to graduate students as well as those on the frontiers of the subject.

Large Scale Geometry


Author: Piotr W. Nowak,Guoliang Yu
Publisher: Samfundslitteratur
ISBN: 9783037191125
Category: Mathematics
Page: 189
View: 4015

Continue Reading →

Jordan Structures in Geometry and Analysis


Author: Cho-Ho Chu
Publisher: Cambridge University Press
ISBN: 1139505432
Category: Mathematics
Page: N.A
View: 5270

Continue Reading →

Jordan theory has developed rapidly in the last three decades, but very few books describe its diverse applications. Here, the author discusses some recent advances of Jordan theory in differential geometry, complex and functional analysis, with the aid of numerous examples and concise historical notes. These include: the connection between Jordan and Lie theory via the Tits–Kantor–Koecher construction of Lie algebras; a Jordan algebraic approach to infinite dimensional symmetric manifolds including Riemannian symmetric spaces; the one-to-one correspondence between bounded symmetric domains and JB*-triples; and applications of Jordan methods in complex function theory. The basic structures and some functional analytic properties of JB*-triples are also discussed. The book is a convenient reference for experts in complex geometry or functional analysis, as well as an introduction to these areas for beginning researchers. The recent applications of Jordan theory discussed in the book should also appeal to algebraists.

Discrete and Computational Geometry


Author: Satyan L. Devadoss,Joseph O'Rourke
Publisher: Princeton University Press
ISBN: 9781400838981
Category: Mathematics
Page: 280
View: 4732

Continue Reading →

Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also features numerous exercises and unsolved problems. The essential introduction to discrete and computational geometry Covers traditional topics as well as new and advanced material Features numerous full-color illustrations, exercises, and unsolved problems Suitable for sophomores in mathematics, computer science, engineering, or physics Rigorous but accessible An online solutions manual is available (for teachers only). To obtain access, please e-mail: [email protected]