Mathematical Surveys and Monographs, Volume: 145
2008; approx. 566 pp; hardcover
ISBN-10: 0-8218-4305-2
ISBN-13: 978-0-8218-4305-5
Expected publication date is May 2, 2008.
The book gives a detailed presentation of the classification of the simple groups of finite Morley rank which contain a nontrivial unipotent 2-subgroup. They are linear algebraic groups over algebraically closed fields of characteristic 2. Although the story told in the book is inspired by the classification of the finite simple groups, it goes well beyond this source of inspiration. Not only do the techniques adapted from finite group theory cover, in a peculiar way, various portions of the three generations of approaches to finite simple groups but model theoretic methods also play an unexpected role. The book contains a complete account of all this material, part of which has not been published. In addition, almost every general result about groups of finite Morley rank is exposed in detail and the book ends with a chapter where the authors provide a list of open problems in the relevant fields of mathematics. As a result, the book provides food for thought to finite group theorists, model theorists, and algebraic geometers who are interested in group theoretic problems.
Readership
Graduate students and research mathematicians interested in group theory and model theory related to logic.
Table of Contents
Part A. Methods
Tools
K-groups and L-groups
Specialized topics
Generic covering and conjugacy theorems
Part B. Mixed type groups
Mixed type
Part C. Even type groups
Strong embedding and weak embedding
Standard components of type SL_2
The C(G,T) theorem and a plan of attack
Quasithin groups
Conclusion
Bibliography
Index of notation
Index of terminology
Index
Mathematical Surveys and Monographs, Volume: 147
2008; 289 pp; hardcover
ISBN-10: 0-8218-4474-1
ISBN-13: 978-0-8218-4474-8
Expected publication date is March 12, 2008.
For each of the 26 sporadic finite simple groups, the authors construct a 2-completed classifying space using a homotopy decomposition in terms of classifying spaces of suitable 2-local subgroups. This construction leads to an additive decomposition of the mod 2 group cohomology. The authors also summarize the current status of knowledge in the literature about the ring structure of the mod 2 cohomology of sporadic simple groups.
This book begins with a fairly extensive initial exposition, intended for non-experts, of background material on the relevant constructions from algebraic topology, and on local geometries from group theory. The subsequent chapters then use those structures to develop the main results on individual sporadic groups.
Readership
Graduate students and research mathematicians interested in group theory and algebraic topology.
Table of Contents
●Overview of our main results
●Exposition of background material
Review of selected aspects of group cohomology
Simplicial sets and their equivalence with topological spaces
Bousfield-Kan completions and homotopy colimits
Decompositions and ample collections of p-subgroups
2-local geometries for simple groups
●Main results on sporadic groups
Decompositions for the individual sporadic groups
Details of proofs for individual groups
Bibliography
Index
Graduate Studies in Mathematics, Volume: 88
2008; 509 pp; hardcover
ISBN-10: 0-8218-4381-8
ISBN-13: 978-0-8218-4381-9
Expected publication date is April 4, 2008.
/textrm{C}^*-approximation theory has provided the foundation for many
of the most important conceptual breakthroughs and applications of operator
algebras. This book systematically studies (most of) the numerous types
of approximation properties that have been important in recent years: nuclearity,
exactness, quasidiagonality, local reflexivity, and others. Moreover, it
contains user-friendly proofs, insofar as that is possible, of many fundamental
results that were previously quite hard to extract from the literature.
Indeed, perhaps the most important novelty of the first ten chapters is
an earnest attempt to explain some fundamental, but difficult and technical,
results as painlessly as possible. The latter half of the book presents
related topics and applications--written with researchers and advanced,
well-trained students in mind. The authors have tried to meet the needs
both of students wishing to learn the basics of an important area of research
as well as researchers who desire a fairly comprehensive reference for
the theory and applications of textrm{C}^*-approximation theory.
Readership
Graduate students and research mathematicians interested in /textrm{C}^*-algebras
and operator algebras.
Table of Contents
Fundamental facts
Basic theory
Nuclear and exact /textrm{C}^*-algebras: Definitions, basic facts and examples
Tensor products
Constructions
Exact groups and related topics
Amenable traces and Kirchberg's factorization property
Quasidiagonal C*-algebras
AF embeddability
Local reflexivity and other tensor product conditions
Summary and open problems
Special topics
Simple /textrm{C}^*-algebras
Approximation properties for groups
Weak expectation property and local lifting property
Weakly exact von Neumann algebras
Applications
Classification of group von Neumann algebras
Herrero's approximation problem
Counterexamples in textrm{K}-homology and /textrm{K}-theory
Appendices
Ultrafilters and ultraproducts
Operator spaces, completely bounded maps and duality
Lifting theorems
Positive definite functions, cocycles and Schoenberg's Theorem
Groups and graphs
Bimodules over von Neumann algebras
Bibliography
Notation index
Subject index
Graduate Studies in Mathematics, Volume: 89
2008; approx. 196 pp; hardcover
ISBN-10: 0-8218-4467-9
ISBN-13: 978-0-8218-4467-0
Expected publication date is April 11, 2008.
A Course on the Web Graph provides a comprehensive introduction to state-of-the-art research on the applications of graph theory to real-world networks such as the web graph. It is the first mathematically rigorous textbook discussing both models of the web graph and algorithms for searching the web.
After introducing key tools required for the study of web graph mathematics, an overview is given of the most widely studied models for the web graph. A discussion of popular web search algorithms, e.g. PageRank, is followed by additional topics, such as applications of infinite graph theory to the web graph, spectral properties of power law graphs, domination in the web graph, and the spread of viruses in networks.
The book is based on a graduate course taught at the AARMS 2006 Summer School at Dalhousie University. As such it is self-contained and includes over 100 exercises. The reader of the book will gain a working knowledge of current research in graph theory and its modern applications. In addition, the reader will learn first-hand about models of the web, and the mathematics underlying modern search engines.
Readership
Graduate students and research mathematicians interested in graph theory, applied mathematics, probability, and combinatorics.
Table of Contents
●Graphs and probability
●The web graph
●Random graphs
●Models for the web graph
●Searching the web
●The infinite web
●New directions in internet mathematics
●Bibliography
●Index
Contemporary Mathematics, Volume: 452
2008; approx. 193 pp; softcover
ISBN-10: 0-8218-4173-4
ISBN-13: 978-0-8218-4173-0
Expected publication date is April 13, 2008.
The AMS-IMS-SIAM Joint Summer Research Conference "Integer Points in Polyhedra" was held in Snowbird, Utah in June 2006. This proceedings volume contains research and survey articles originating from the conference.
The volume is a cross section of recent advances connected to lattice-point questions. Similar to the talks given at the conference, topics range from commutative algebra to optimization, from discrete geometry to statistics, from mirror symmetry to geometry of numbers. The book is suitable for researchers and graduate students interested in combinatorial aspects of the above fields.
Readership
Graduate students and research mathematicians interested in combinatorics and its applications.
Table of Contents
K. Aardal -- Lattice reformulation of integer programming problems
V. Baldoni, N. Berline, and M. Vergne -- Local Euler-Maclaurin expansion of Barvinok valuations and Ehrhart coefficients of a rational polytope
V. Batyrev and B. Nill -- Combinatorial aspects of mirror symmetry
B. Braun and M. Develin -- Ehrhart polynomial roots and Stanley's non-negativity theorem
J. W. Davis, E. D'Souza, S. Lee, and C. D. Savage -- Enumeration of integer solutions to linear inequalities defined by digraphs
R. Erdahl, A. Ordine, and K. Rybnikov -- Perfect Delaunay polytopes and perfect quadratic functions on lattices
C. Haase and T. B. McAllister -- Quasi-period collapse and GL_n(mathbb{Z})-scissors
congruence in rational polytopes
H. Ohsugi and T. Hibi -- Quadratic Grobner bases arising from combinatorics
K. Karu -- Ehrhart analogue of the h-vector
A. Takemura and R. Yoshida -- Saturation points on faces of a rational polyhedral cone
Z. Xu -- An explicit formulation for two dimensional vector partition functions
M. Beck, B. Nill, B. Reznick, C. Savage, I. Soprunov, and Z. Xu -- Let me tell you my favorite lattice-point problem ...