PUBLICATIONS of the American Mathematical Society up to AMS Individual 20% Member Discount Receive Substantial Discounts on All AMS Published and Co-Published Books!

PUBLICATIONS of the American Mathematical Society up to AMS Individual 20% Member Discount Receive substantial discounts on all AMS published and co-published books!

AMS Textbooks Find the right textbook for your course! The AMS publishes many high-quality books for use in the classroom. To view a comprehensive list of our most widely adopted textbooks, please visit www.ams.org/bookstore/textbooks

To Prospective Contents Authors 3 Featured Selections If you would like to submit a manuscript to the AMS, please visit www.ams.org/authors 13 Algebra and Algebraic Geometry 15 Analysis 16 Applications 16 Differential Equations Applied Mathematics The AMS book publication program on 17 Discrete Mathematics and Combinatorics applied and interdisciplinary mathematics 18 Geometry and Topology strengthens the connections between white --> mathematics and other disciplines, 19 Logic and Foundations highlighting the areas where mathematics 20 Mathematical Physics is most relevant. These publications help mathematicians understand how 21 Number Theory mathematical ideas may benefit other 22 Applied Mathematics sciences, while offering researchers outside of mathematics important tools to advance 24 Memoirs of the AMS their profession. To view all of our applied 25 AMS-Distributed Publications mathematics publications, go to: www.ams.org/bookstore/appliedmath 26 Index 30 Ordering Information

Order Online | www.ams.org/bookstore fe atured Selections Elliptic Partial Differential Equations TEXTBOOK TEXTBOOKS 1 Second Edition FROM THE AMS Q I N G H A N Qing Han, University of Notre Dame, IN, and Fanghua Lin, Courant Institute, New York F A N G H U A L I N

University, NY TEXTBOOK Elliptic Partial This volume is based on PDE courses given by the authors at the Courant Institute and at the Differential Equations University of Notre Dame, Indiana. Presented are basic methods for obtaining various a priori esti- Second Edition mates for second-order equations of elliptic type with particular emphasis on maximal principles, Harnack inequalities, and their applications. The equations considered in the book are linear; however, the presented methods also apply to nonlinear problems. This second edition has been thoroughly revised and in a new chapter the authors discuss several methods for proving the existence of solutions of primarily the Dirichlet problem for various types of elliptic equations.

READERSHIP: Graduate students and research mathematicians interested in elliptic PDEs. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University. Courant Lecture Notes, Volume 1

2011; 147 pp.; softcover; ISBN: 978-0-8218-5313-9; List US$31; AMS members US$24.80; Order code: CLN/1.R

Table of Contents Contents Preface ix Chapter 1. Harmonic Functions Chapter 2. Maximum Principles Chapter 3. Weak Solutions: Part I Chapter 4. Weak Solutions, Part II Chapter 5. Viscosity Solutions Chapter 6. Existence of Solutions Bibliography

Elliptic Partial Differential Equations by Qing Han and FangHua Lin is one of the best textbooks I know. It is the perfect introduction to PDE. In 150 pages or so it covers an amazing amount of wonderful and extraordinary useful material. I have used it as a textbook at both graduate and undergraduate levels which is possible since it only requires very little background material yet it covers an enormous amount of material. In my opinion it is a must read for all interested in analysis and geometry, and for all of my own PhD students it is indeed just that. I cannot say enough good things about it—it is a wonderful book. [ —Tobias Colding ]

Order Online | www.ams.org/bookstore Featured Selections FeatureD Selections

TEXTBOOK A Basic Course in Partial Differential Equations TEXTBOOKS FROM THE AMS A Basic Course in Qing Han, University of Notre Dame, IN Partial Differential Equations Among the many introductory texts on partial differential equations, this treatment departs from TEXTBOOK others in its awareness of the more advanced subjects in the background. In both explaining how to solve linear PDEs and teaching readers how to think about general equations, this text carries Qing Han relevance for students who will not pursue the subject further as well as for those who will go on to more advanced courses on PDEs. Based on one-semester courses taught by the author at the University of Notre Dame, the text Graduate Studies in Mathematics features the main extra ingredient of estimates for solutions of PDEs, primarily the “a priori” esti- Volume 120 mates. These estimates are crucial tools for proving the existence and uniqueness of solutions to American Mathematical Society PDEs, especially significant for nonlinear equations. Another important emphasis of this book involves its focus on simple models of PDEs, with detailed study of these equations. Chapters are devoted to the Laplace equation, the heat equation and the wave equation, and several methods are used for the study of each, exploring their advantages and disadvantages. This text is designed specifically for use by first-year graduate students in mathematics, but also can be used by students in applied mathematics, physics or engineering. In deriving explicit expressions of solutions and a priori estimates, the book serves as both a concise overview and an ideal introduction to further study. READERSHIP: Advanced undergraduate and graduate students interested in PDEs. Graduate Studies in Mathematics, Volume 120

2011; 293 pp.; hardcover; ISBN: 978-0-8218-5255-2; List US$63; AMS members US$50.40; Order code: GSM/120

TEXTBOOK A Course in Minimal Surfaces TEXTBOOKS FROM THE AMS Tobias Holck Colding, Massachusetts Institute of Technology, Cambridge, MA, and A Course in William P. Minicozzi II, Johns Hopkins University, Baltimore, MD Minimal Surfaces

TEXTBOOK Minimal surfaces date back to Euler and Lagrange, and many of the techniques developed have been critical to the study of geometry and partial differential equations. This book offers a thor- Tobias Holck Colding William P. Minicozzi II ough introduction to classical results and modern techniques in minimal surfaces, while also offering significant coverage of current research topics. The authors, recipients of the Oswald Veblen Prize in 2010 for their work on minimal surfaces, Graduate Studies in Mathematics open with the basic properties of minimal surfaces, including the monotonicity formula for area Volume 121 and the Bernstein theorem. Chapters 2 and 3 address generalizations of the Bernstein theorem and American Mathematical Society a proof of a generalization. The authors proceed with a solution to the classical Plateau problem for maps from surfaces, and later discuss the theory of minimal surfaces in three-manifolds. Among the various ways of approaching the subject of minimal surfaces, these experts have chosen to focus on aspects of the theory related to partial differential equations. The book also includes applications of minimal surfaces to fields such as low dimensional topology, general relativity and materials science. Only a basic knowledge of differential geometry and some familiarity with partial differential equations are required of readers. The book includes many illustrations and exercises, and is ideal for an advanced undergraduate or second-year graduate course. READERSHIP: Graduate students and research mathematicians interested in the theory of minimal surfaces. Graduate Studies in Mathematics, Volume 121

2011; 313 pp.; hardcover; ISBN: 978-0-8218-5323-8; List US$63; AMS members US$50.40; Order code: GSM/121

Order by Phone | 1-401-455-4000 or 1-800-321-4267 Featured Selections FeatureD Selections

Algebraic Groups and Differential Galois Theory TEXTBOOK TEXTBOOKS Teresa Crespo, Universitat de Barcelona, Spain, and Zbigniew Hajto, Jagiellonian Algebraic GroupsFROM THE AMS University, Kraków, Poland and Differential Galois Theory Differential Galois theory has been the subject of major research activity in recent years, covering TEXTBOOK

areas ranging from elaboration of more general theories to applications to classical and quantum Teresa Crespo mechanics. This book introduces the topic through a self-contained presentation of Picard-Vessiot Zbigniew Hajto theory, or Galois theory of linear differential equations.

The first two parts of the book, on algebraic geometry and algebraic groups, include all questions Graduate Studies in Mathematics

necessary to develop differential Galois theory. Chapter 5 addresses the Picard-Vessiot extension, Volume 122 speaking of this as a field in order to keep the analogy with the splitting field in the polynomial Galois theory. The last chapter presents classical notions such as the monodromy group, Fuchsian American Mathematical Society equations and hypergeometric equations. Each chapter ends with exercise statements that involve direct application of the theory as well as working out some topics beyond it. The clarity of exposition and the completeness of proofs enhance the appeal of the text. The book’s inclusion of the results of algebraic geometry and algebraic groups necessary to develop Galois theory in its whole makes the material accessible to graduate students with a knowledge of commutative algebra and complex analysis at an undergraduate level. The book can form the basis for a graduate course of one or two semesters. READERSHIP: Graduate students and research mathematicians interested in algebraic methods in differential equations, differential Galois theory, and dynamical systems. Graduate Studies in Mathematics, Volume 122

2011; 225 pp.; hardcover; ISBN: 978-0-8218-5318-4; List US$53; AMS members US$42.40; Order code: GSM/122

Lectures on Linear Partial Differential Equations TEXTBOOK TEXTBOOKS Gregory Eskin, University of California, Los Angeles, CA Lectures onFR OMLinear THE AMS Partial Differential Departing from lengthier texts on the subject of linear partial differential equations, Gregory Eskin Equations offers a reader-friendly introduction to the modern theory of the subject. The author’s clear, acces- TEXTBOOK

sible approach to the material makes this book ideal for a first graduate course in linear partial Gregory Eskin differential equations. Based on the author’s lectures on partial differential equations for courses taught at UCLA, the book opens with the elementary theory of distributions and Fourier transforms of the distribu- Graduate Studies in Mathematics

tions, with applications to partial differential equations with constant coefficients. The author Volume 123 proceeds into other important topics such as the Cauchy problem for parabolic and hyperbolic equations, boundary value problems for elliptic equations, heat trace asymptotics, and scattering American Mathematical Society theory. More advanced topics include the global theory of Fourier integral operators and the oblique derivative problem. About 10 to 15 exercises at the end of each chapter range from relatively simple study aids to difficult problems covering topics not included in the book. Eskin sets out to present complete proofs in an accessible and self-contained form. His emphasis on clarity makes this text a shorter and more accessible presentation than comparable books on the subject. READERSHIP: Graduate students and research mathematicians interested in partial differential equations. Graduate Studies in Mathematics, Volume 123

2011; approximately 411 pp.; hardcover; ISBN: 978-0-8218-5284-2; List US$74; AMS members US$59.20; Order code: GSM/123

Order Online | www.ams.org/bookstore GSM

124

Featured FeatureD Selections Selections TEXTBOOK Toric Varieties TEXTBOOKS FROM THE AMS David A. Cox, Amherst College, MA, John B. Little, College of the Holy Cross, Worcester, Toric Varieties MA, and Henry K. Schenck, University of Illinois at Urbana-Champaign, IL

TEXTBOOK Toric varieties form a beautiful and accessible part of modern algebraic geometry. This book covers David A. Cox the standard topics inToric toric geometry; a novel feature Varieties is that each of the first nine chapters contains John B. Little an introductory section on the necessary background material in algebraic geometry. Other Henry K. Schenck topics covered include quotient constructions, vanishing theorems, equivariant cohomology, GIT Toric Cox, Varieties Little, Schenck and quotients, the secondary fan, and the minimal model program for toric varieties. The subject lends

Graduate Studies in Mathematics itself to rich examples reflected in the 134 illustrations included in the text. The book also explores Toric varieties form a Volume 124 connections with commutative algebra and polyhedral geometry, treating both polytopes and their beautiful and accessible American Mathematical Society unbounded cousins, polyhedra. There are appendices on the history of toric varieties and the part of modern algebraic computational tools available to investigate nontrivial examples in toric geometry. geometry. This book Readers of this book should be familiar with the material covered in basic graduate courses in covers the standard algebra and topology, and to a somewhat lesser degree, complex analysis. In addition, the authors topics in toric geom- assume that the reader has had some previous experience with algebraic geometry at an advanced etry; a novel feature is undergraduate level. The book will be a useful reference for graduate students and researchers who that each of the ﬁ rst are interested in algebraic geometry, polyhedral geometry, and toric varieties. Graduate students and research mathematicians interested in algebraic geometry, nine chapters contains Amherst Affairs. CourtesyCollege of of Public READERSHIP: David A. Cox an introductory section on the necessary background material in algebraic geom- polyhedral geometry, and toric varieties. etry. Other topics covered include quotient constructions, vanishing theorems, Graduate Studies Johnin Mathematics, B. Volume Little 124 equivariant cohomology, GIT quotients, the secondary fan, and the minimal model 2011; approximately 858 pp.; hardcover; ISBN: 978-0-8218-4819-7; List US$95; AMS members US$76; Order code: program for toric varieties. The subject lends itself to rich examples reﬂ ected in GSM/124 the 134 illustrations included in the text. The book also explores connections Henry K. Schenck with commutative algebra and polyhedral geometry, treating both polytopes and their unbounded cousins, polyhedra. There are appendices on the history of toric varieties and the computational tools available to investigate nontrivial examples in toric geometry. This masterfully written book will become a standard text on toric Readers of this book should be familiar with the material covered in basic grad- varieties, serving both students and researchers. The book's leisurely pace and uate courses in algebra and topology, and to a somewhat lesser degree, complex wealth of background material makes it perfect for graduate courses on toric analysis. In addition, the authors assume that the reader has had some previous varieties or for self-study. Researchers will discover gems throughout the book experience with algebraic geometry at an advanced undergraduate level. The book and will find it to be a valuable resource. will be a useful reference for graduate students and researchers who are interested -- Sheldon Katz in algebraic geometry, polyhedral geometry, and toric varieties.

[ Graduate Studies Table of Contents ] in Mathematics

Basic theory of toric varieties Topics in toric geometry For additional information Volume 124 * Affine toric varieties * Toric surfaces and updates on this book, visit * Projective toric varieties * Toric resolutions and toric singularities www.ams.org/bookpages/gsm-124 * Normal toric varieties * The topology of toric varieties * Divisors on toric varieties * Toric Hirzebruch-Riemann-Roch GSM/124 AMS on the Web * Homogeneous coordinates on toric varieties * Toric GIT and the secondary fan www.ams.orgwww.ams.org AMS * Line bundles on toric varietiesAmerican Mathematical* Geometry of the secondary Society fan * Projective toric morphisms * The history of toric varieties * The canonical divisor of a toric variety * Computational methods * Sheaf cohomology of toric varieties * Spectral sequences * Bibliography 6 * Index

Order by Phone | 1-401-455-4000 or 1-800-321-4267

3-color cover PMS 632 (light blue), PMS 302(blue), 123 (yellow) 872 pages • backspace 2 1/2 inch • 7 x 10 inches Featured Selections FeatureD Selections

Understanding Numbers in Elementary School Mathematics TEXTBOOK TEXTBOOKS Hung-Hsi Wu, University of California, Berkeley, CA FROM THE AMS

This is a textbook for pre-service elementary school teachers and for current teachers who are

taking professional development courses. By emphasizing the precision of mathematics, the expo- TEXTBOOK sition achieves a logical and coherent account of school mathematics at the appropriate level for the readership. Wu provides a comprehensive treatment of all the standard topics about numbers in the school mathematics curriculum: whole numbers, fractions, and rational numbers. Assuming no previous knowledge of mathematics, the presentation develops the basic facts about numbers from the beginning and thoroughly covers the subject matter for grades K through 7. Every single assertion is established in the context of elementary school mathematics in a manner that is completely consistent with the basic requirements of mathematics. While it is a textbook for pre-service elementary teachers, it is also a reference book that school teachers can refer to for explanations of well-known but hitherto unexplained facts. For example, the sometimes-puzzling concepts of percent, ratio, and rate are each given a treatment that is down to earth and devoid of mysticism. The fact that a negative times a negative is a positive is explained in a leisurely and comprehensible fashion. READERSHIP: Pre-service elementary school teachers and current teachers interested in a logical and coherent account of school mathematics. 2011; approximately 552 pp.; hardcover; ISBN: 978-0-8218-5260-6; List US$79; AMS members US$63.20; Order code: MBK/79

Geometry TEXTBOOK TEXTBOOKS A Guide for Teachers FROM THE AMS

Judith D Sally, Northwestern University, Evanston, IL, and Paul J Sally, Jr, University of Chicago, IL TEXTBOOK

This geometry book is written foremost for future and current middle school teachers, but is also designed for elementary and high school teachers. The book consists of ten seminars covering in a rigorous way the fundamental topics in school geometry, including all of the significant topics in high school geometry. The seminars are crafted to clarify and enhance understanding of the subject. Concepts in plane and solid geometry are carefully explained, and activities that teachers can use in their classrooms are emphasized. The book draws on the pictorial nature of geometry since that is what attracts students at every level to the subject. The book should give teachers a firm foundation on which to base their instruction in the elementary and middle grades. In addition, it should help teachers give their students a solid basis for the geometry that they will study ] in high school. The book is also intended to be a source for problems in geometry for enrichment programs such as Math Circles and Young Scholars. READERSHIP: Undergraduate students interested in secondary education, particularly the teaching of geometry, and current middle school teachers teaching geometry. Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI). MSRI Mathematical Circles Library, Volume 3

2011; approximately 205 pp.; softcover; ISBN: 978-0-8218-5362-7; List US$39; AMS members US$31.20; Order code: MCL/3

Order Online | www.ams.org/bookstore Featured Selections FeatureD Selections

TEXTBOOK Elliptic Curves, Modular Forms, and Their L-functions TEXTBOOKS FROM THE AMS Álvaro Lozano-Robledo, University of Connecticut, Storrs, CT

Many of the simply stated problems in number theory can be obscured amid the depth of the TEXTBOOK theory developed to understand them. In this book, Álvaro Lozano-Robledo introduces these problems in a manner that highlights their connections while keeping the number theory at the forefront of the discussion. The book focuses on three types of mathematical objects that appear so distinct but have surprising connections: elliptic curves, modular forms and L-functions. An important theme in this regard is an explanation of the statement of the modularity theorem, previously known as the Taniyama-Shimura-Weil conjecture. To emphasize the theorem’s importance, Lozano-Robledo discusses one of its most renowned consequences: Fermat’s last theorem. Rather than emphasizing hard proofs, the book concentrates on motivating the definitions, explaining the statements of the theorems, making connections, and offering numerous examples. Five appendices offer concise introductions to topics that will be new to many students. The author’s direct, relaxed writing style makes this book accessible to advanced undergraduates and graduate students. This big-picture view of a fast-growing theory is designed to motivate students to explore these mathematical objects in their full detail. READERSHIP: Undergraduate and graduate students interested in number theory and L-functions. Student Mathematical Library, Volume 58

2011; 195 pp.; softcover; ISBN: 978-0-8218-5242-2; List US$37; AMS members US$29.60; Order code: STML/58

TEXTBOOK Introduction to Representation Theory TEXTBOOKS FROM THE AMS Pavel Etingof, Massachusetts Institute of Technology, Cambridge, MA, Oleg Golberg, Sebastian Hensel, Universität Bonn, Germany, Tiankai Liu, Massachusetts Institute of Technology, Cambridge, MA, Alex Schwendner, Two Sigma Investments, New York, NY, TEXTBOOK Dmitry Vaintrob, Harvard University, Cambridge, MA, and Elena Yudovina, University of Cambridge, United Kingdom

with historical interludes by Slava Gerovitch, Massachusetts Institute of Technology, Cambridge, MA

Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a “holistic” introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra. READERSHIP: Undergraduate and graduate students interested in algebra and representation theory. Student Mathematical Library, Volume 59

2011; approximately 232 pp.; softcover; ISBN: 978-0-8218-5351-1; List US$42; AMS members US$33.60; Order code: STML/59

Order by Phone | 1-401-455-4000 or 1-800-321-4267

Rich Schwartz Featured Selections FeatureD Selections

Mostly Surfaces TEXTBOOK TEXTBOOKS Richard Evan Schwartz, Brown University, Providence, RI FROM THE AMS

This book presents a number of topics related to surfaces, such as Euclidean, spherical and hyper-

bolic geometry, the fundamental group, universal covering surfaces, Riemannian manifolds, the TEXTBOOK Gauss-Bonnet Theorem, and the Riemann mapping theorem. The main idea is to get to some interesting mathematics without too much formality. The book also includes some material only tangentially related to surfaces, such as the Cauchy Rigidity Theorem, the Dehn Dissection Theorem, and the Banach–Tarski Theorem. The goal of the book is to present a tapestry of ideas from various areas of mathematics in a clear and rigorous yet informal and friendly way. Prerequisites include undergraduate courses in real analysis and in linear algebra, and some knowledge of complex analysis. READERSHIP: Undergraduate students interested in geometry and topology of surfaces. Student Mathematical Library, Volume 60

2011; approximately 312 pp.; softcover; ISBN: 978-0-8218-5368-9; List US$47; AMS members US$37.60; Order code: STML/60

Table of Contents

* Book overview * Definition of a surface * The gluing construction * The fundamental group * Examples of fundamental groups * Covering spaces and the deck group * Existence of universal covers * Euclidean geometry * Spherical geometry * Hyperbolic geometry * Riemann metrics on surfaces * Hyperbolic surfaces * A primer on complex analysis * Disk and plane rigidity * The Schwarz-Christoffel transformation * Riemann surfaces and uniformization * Flat cone surfaces * Translation surfaces and the Veech group * Continued fractions * Teichmüller space and moduli space * Topology of Teichmüller space * The Banach Tarski theorem * Dehn's dissection theorem * The Cauchy rigidity theorem * Bibliography * Index

Order Online | www.ams.org/bookstore

Rich Schwartz Featured Selections FeatureD Selections

Mathematical Surveys and Monographs Renormalization and Effective Field Theory Volume 170

Renormalization Kevin Costello, Northwestern University, Evanston, IL and Effective Field Theory Quantum field theory has had a significant effect on geometry and other branches of mathematics, but the difficulties inherent in renormalization have made the theory largely inaccessible to mathematicians. This book provides complete mathematical foundations for the theory of perturbative Kevin Costello quantum field theory, making it possible for graduate students with knowledge of basic functional analysis and homological algebra to understand the theory. The author, who has earned a high reputation for his work on renormalization, has based this book on Wilson’s ideas of low-energy effective field theory and on the Batalin-Vilkovisky formalism. American Mathematical Society He presents, for example, a cohomological proof of perturbative renormalizability of Yang-Mills theory. The author’s insightful use of the renormalization group and effective field theory to analyze perturbative renormalization is seen as a catalyst for a wider use of these topics. This could lead to an eventual nonperturbative understanding. This book exposes mathematicians to a fascinating subject invented by physicists, while at the same time explaining to physicists how a master mathematician should proceed in order to grasp the subject. The author effectively tells a mathematical tale while incorporating modern physical understanding. READERSHIP: Graduate students and research mathematicians interested in quantum field theory and mathematical physics. Mathematical Surveys and Monographs, Volume 170

2011; 251 pp.; hardcover; ISBN: 978-0-8218-5288-0; List US$84; AMS members US$67.20; Order code: SURV/170

Mathematical Surveys and Monographs Eigenvalue Distribution of Large Random Matrices Volume 171 Eigenvalue Distribution of Leonid Pastur and Mariya Shcherbina, Ukrainian National Academy of Sciences, Large Random Kharkov, Ukraine Matrices The growing field of random matrix theory has a variety of techniques and results and a wide Leonid Pastur range of applications in mathematics and related disciplines. This book offers a detailed introduc- Mariya Shcherbina tion to the subject, presenting basic facts with its look at classical ensembles and outlining recent advances with its examination of invariant ensembles and ensembles with independent entries. The book treats three main themes: the properties of nonrandom limiting Normalized Counting Measure of eigenvalues, the fluctuation laws of linear eigenvalue statistics, and the local regimes. American Mathematical Society The book proceeds from classical ensembles to the invariant ensembles of hermitian and real symmetric matrices to ensembles with independent and weakly dependent entries. The text includes many of the authors’ results on main aspects of the theory, allowing for a personal perspective on the subject. The authors use a unified approach essentially based on the Stieltjes transform and orthogonal polynomials. Random matrix theory, in its synthesis of ideas from spectral theory, probability theory, and mathematical and theoretical physics, employs concepts that unify branches of mathematics that have not been closely related in the past. This book offers a self-contained presentation that will appeal to a number of graduate students and researchers, working in areas from analysis to combinatorics to mathematical physics. READERSHIP: Graduate students and research mathematicians interested in random matrix theory and its applications. Mathematical Surveys and Monographs, Volume 171

2011; approximately 634 pp.; hardcover; ISBN: 978-0-8218-5285-9; List US$105; AMS members US$84; Order code: SURV/171

Order by Phone | 1-401-455-4000 or 1-800-321-4267 Featured Selections FeatureD Selections

Mathematical Surveys and Geometric Approximation Algorithms Monographs Volume 173

Sariel Har-Peled, University of Illinois at Urbana-Champaign, IL Geometric Approximation Exact algorithms for dealing with geometric objects are complicated, hard to implement in prac- Algorithms tice, and slow. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms tend to be simple, fast, and more robust than their exact counterparts. Sariel Har-Peled This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are also surveyed. Other topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings. The topics covered are relatively independent and are supplemented by exercises. American Mathematical Society Close to 200 color figures are included in the text to illustrate proofs and ideas. READERSHIP: Graduate students and research mathematicians interested in the theory and practice of computational geometry. SURV Mathematical Surveys and Monographs, Volume 173

2011; approximately 358 pp.; hardcover; ISBN: 978-0-8218-4911-8; List US$98; AMS members US$78.40; Order code: SURV/173 ULECT GSM

Measure and Integration TEXTBOOK TEXTBOOKS Sterling K. Berberian FROM THE AMS

While many experts have explored the subject of measure theory, Sterling Berberian in this text Measure and has selected topics in a fashion that makes this book a classic for first- and second-year graduate IntegraTEXTBOOKtion students learning the theory of measure and integration. The text is self-contained and the material is presented in a highly flexible manner, with the author casting the Monotone Convergence Sterling K. Berberian Theorem in the leading role throughout. Part I of the book, comprising the first seven chapters, addresses measure and integration over an

abstract measure space. Topics include measures and outer measures, measurable functions, inte- AMS CHELSEA PUBLISHING grable functions, convergence theorems for sequences of integrable functions, Fubini’s theorem on American Mathematical Society • Providence, Rhode Island iterated integration, and the Radon-Nikodym theorem. Part II begins with the general theory being specialized to the context of locally compact spaces in Chapter 8. In Chapter 9 the general theory is applied to the study of invariant integration over locally compact groups, culminating in the construction of the group algebra of a locally compact group. Part I is designed to be easily accessible to the first-year graduate student who has taken an introductory course in the theory of sets. The more advanced material inclining toward functional analysis in Part II is designed for advanced graduate study. Berberian has arranged the topics to make this text a solid introduction to measure and integration. READERSHIP: Graduate students interested in teaching and learning the theory of measure and integration. AMS Chelsea Publishing, Volume 241

312 pp.; hardcover; ISBN: 978-0-8218-5328-3; List US$51; AMS members US$45.90; Order code: CHEL/241.H

Order Online | www.ams.org/bookstore Featured Selections

Sturm-Liouville Operators and Applications Sturm-Liouville Revised Edition Operators and Applications Vladimir A. Marchenko, Verkin Institute for Low Temperature Physics and Engineering, Revised Edition Kharkov, Ukraine Vladimir A. Marchenko The spectral theory of Sturm-Liouville operators is a classical domain of analysis, comprising a wide variety of problems. Besides the basic results on the structure of the spectrum and the

AMS CHELSEA PUBLISHING eigenfunction expansion of regular and singular Sturm-Liouville problems, it is in this domain American Mathematical Society • Providence, Rhode Island that one-dimensional quantum scattering theory, inverse spectral problems, and the surprising connections of the theory with nonlinear evolution equations first become related. The main goal of this book is to show what can be achieved with the aid of transformation operators in spectral theory as well as in their applications. The main methods and results in this area (many of which SURV are credited to the author) are for the first time examined from a unified point of view. The direct and inverse problems of spectral analysis and the inverse scattering problem are solved with the help of the transformation operators in both self-adjoint and nonself-adjoint cases. The asymptotic formulae for spectral functions, trace formulae, and the exact relation (in both directions) between the smoothness of potential and the asymptotics of eigenvalues (or the lengths of ULECT gaps in the spectrum) are obtained. Also, the applications of transformation operators and their GSMgeneralizations to soliton theory (i.e., solving nonlinear equations of Korteweg-de Vries type) are considered. The new Chapter 5 is devoted to the stability of the inverse problem solutions. The estimation of the accuracy with which the potential of the Sturm-Liouville operator can be restored from the scattering data or the spectral function, if they are only known on a finite interval of a spectral parameter (i.e., on a finite interval of energy), is obtained. READERSHIP: Graduate students and research mathematicians interested in operator theory. AMS Chelsea Publishing, Volume 373

2011; 393 pp.; hardcover; ISBN: 978-0-8218-5316-0; List US$61; AMS members US$54.90; Order code: CHEL/373.H

BioMath in the Schools

Margaret B. Cozzens and Fred S. Roberts, Rutgers University, Piscataway, NJ, Editors

Even though contemporary biology and mathematics are inextricably linked, high school biology and mathematics courses have traditionally been taught in isolation. But this is beginning to change. This volume presents papers related to the integration of biology and mathematics in high school classes. The first part of the book provides the rationale for integrating mathematics and biology in high school courses as well as opportunities for doing so. The second part explores the development and integration of curricular materials and includes responses from teachers. Papers in the third part of the book explore the interconnections between biology and mathematics in light of new technologies in biology. The last paper in the book discusses what works and what doesn’t and presents positive responses from students to the integration of mathematics and biology in their classes. READERSHIP: High school teachers, education specialists, graduate students, and research mathematicians interested in mathematics and biology education. Co-published with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1–7 were co-published with the Association for Computer Machinery (ACM). DIMACS: Series in Discrete Mathematics and Theoretical Computer Science, Volume 76

2011; 245 pp.; hardcover; ISBN: 978-0-8218-4295-9; List US$52; AMS members US$41.60; Order code: DIMACS/76

Order by Phone | 1-401-455-4000 or 1-800-321-4267 NEW TITLESAnalysis by Subject Area Algebra and Algebraic Geometry A. Vargas, who greatly contributed to the development CONTEMPORARY Groups, Algebras and Applications of Lie theory in Córdoba. MATHEMATICS 5 3 7 César Polcino Milies, University of São Paulo, The papers give a broad overview of these subjects and also of the recent developments of the authors’ Brazil, Editor Groups, Algebras research. and Applications This book contains the proceedings of the XVIII Latin READERSHIP: Graduate students and research math- César Polcino Milies American Algebra Colloquium, held from August 3–8, Editor ematicians interested in Lie theory and its applications. 2009, in São Paulo, Brazil. Contemporary Mathematics, Volume 544 It includes research articles as well as up-to-date 2011; 159 pp.; softcover; ISBN: 978-0-8218-5259-0; List surveys covering several directions of current research American Mathematical Society US$59; AMS members US$47.20; Order code: CONM/544 in algebra.

Mathematical Surveys and READERSHIP: Graduate students and research math- Monographs Volume 174 ematicians interested in group theory, associative and Hereditary Noetherian Prime Rings Hereditary non-associative algebras, and coding theory. Noetherian Contemporary Mathematics, Volume 537 and Idealizers Prime Rings and Idealizers 2011; 324 pp.; softcover; ISBN: 978-0-8218-5239-2; List Lawrence S. Levy, University of Wisconsin, US$105; AMS members US$84; Order code: CONM/537 Madison, WI, and J. Chris Robson, University of Leeds, United Kingdom Lawrence S. Levy J. Chris Robson Harmonic Analysis on Reductive, The direct sum behaviour of its projective modules is a fundamental property of any ring. Hereditary American Mathematical Society p-adic Groups Noetherian prime rings are perhaps the only noncommutative Noetherian rings for which this direct sum Robert S. Doran, Texas Christian University, Ft. behaviour (for both finitely and infinitely generated Worth, TX, Paul J. Sally, Jr., University of Chicago, projective modules) is well-understood, yet highly IL, and , Texas Christian University, Loren Spice nontrivial. Ft. Worth, TX, Editors This book surveys material previously available only This volume contains the proceedings of the in the research literature. It provides a re-worked and AMS Special Session on Harmonic Analysis and simplified account, with improved clarity, fresh insights Representations of Reductive, p-adic Groups, which and many original results about finite length modules, was held on January 16, 2010, in San Francisco, injective modules and projective modules. It culmi- California. nates in the authors’ surprisingly complete structure The papers in this volume present both expository and theorem for projective modules which involves two research articles on these and related topics, presenting independent additive invariants: genus and Steinitz a broad picture of the current state of the art in p-adic class. Several applications demonstrate its utility. harmonic analysis. The concepts are liberally illustrated The theory, extending the well-known module theory with examples, usually appropriate for an upper-level of commutative Dedekind domains and of hereditary graduate student in representation theory or number orders, develops via a detailed study of simple modules. theory. The concrete case of the two-by-two special This relies upon the substantial account of idealizer linear group is a constant touchstone. subrings which forms the first part of the book and READERSHIP: Graduate students and research math- provides a useful general construction tool for inter- ematicians interested in representations of p-adic esting examples. groups. The book assumes some knowledge of noncommuta- Contemporary Mathematics, Volume 543 tive Noetherian rings, including Goldie’s theorem. 2011; 277 pp.; softcover; ISBN: 978-0-8218-4985-9; List Beyond that, it is largely self-contained, thanks to the US$99; AMS members US$79.20; Order code: CONM/543 appendix which provides succinct accounts of Artinian serial rings and, for arbitrary rings, results about lifting direct sum decompositions from finite length images of New Developments in Lie Theory projective modules. The appendix also describes some and Its Applications open problems. The history of the topics is surveyed at appropriate Carina Boyallian, Esther Galina, and Linda Saal, points. Universidad Nacional de Córdoba, Argentina, READERSHIP: Graduate students and research Editors mathematicians interested in algebra, in particular, This volume contains the proceedings of the Seventh noncommutative rings. Workshop in Lie Theory and Its Applications, which Mathematical Surveys and Monographs, Volume 174 was held November 27–December 1, 2009 at the 2011; 228 pp.; hardcover; ISBN: 978-0-8218-5350-4; List Universidad Nacional de Córdoba, in Córdoba, US$84; AMS members US$67.20; Order code: SURV/174 Argentina. The workshop was preceded by a special event, “Encuentro de teoria de Lie”, held November 23–26, 2009, in honor of the sixtieth birthday of Jorge 13

Order Online | www.ams.org/bookstore Algebra and Algebraic Geometry Analysis

Mathematical Surveys and Monographs Volume 172 The Classification of Finite Simple Eisenstein Series and Automorphic The Classification of Finite Simple Groups -Functions Groups L Groups of Characteristic 2 Type Groups of Characteristic 2 Type Freydoon Shahidi, Purdue University, West Michael Aschbacher Lafayette, IN Richard Lyons Michael Aschbacher, California Institute of Stephen D. Smith Colloquium Publications, Volume 58 Ronald Solomon Technology, Pasadena, CA, Richard Lyons, Rutgers 2010; 210 pp.; hardcover; ISBN: 978-0-8218-4989-7; List University, Piscataway, NJ, Stephen D. Smith, US$55; AMS members US$44; Order code: COLL/58 University of Illinois at Chicago, IL, and Ronald American Mathematical Society Solomon, The Ohio State University, Columbus, OH Algebra: Chapter 0 The book provides an outline and modern overview of Paolo Aluffi, Florida State University, Tallahassee, the classification of the finite simple groups. It primarily FL covers the “even case”, where the main groups arising Graduate Studies in Mathematics, Volume 104 are Lie-type (matrix) groups over a field of characteristic 2009; 713 pp.; hardcover; ISBN: 978-0-8218-4781-7; List 2. The book thus completes a project begun by Daniel US$89; AMS members US$71.20; Order code: GSM/104 Gorenstein’s 1983 book, which outlined the classification of groups of “noncharacteristic 2 type”. However, this book provides much more. Chapter 0 Galois Theory for Beginners is a modern overview of the logical structure of the entire classification. Chapter 1 is a concise but complete A Historical Perspective outline of the “odd case” with updated references, while Jörg Bewersdorff Chapter 2 sets the stage for the remainder of the book with a similar outline of the “even case”. The remaining Translated by David Kramer six chapters describe in detail the fundamental results Student Mathematical Library, Volume 35 whose union completes the proof of the classifica- 2006; 180 pp.; softcover; ISBN: 978-0-8218-3817-4; List tion theorem. Several important subsidiary results are US$35; AMS members US$28; Order code: STML/35 also discussed. In addition, there is a comprehensive listing of the large number of papers referenced from the literature. Appendices provide a brief but valuable Random Matrix Theory: Invariant modern introduction to many key ideas and techniques of the proof. Some improved arguments are developed, Ensembles and Universality along with indications of new approaches to the entire Percy Deift, Courant Institute of Mathematical classification—such as the second and third generation Sciences, New York University, NY, and Dimitri projects—although there is no attempt to cover them Gioev, University of Rochester, NY, and Wilshire comprehensively. Associates Inc., Santa Monica, CA The work should appeal to a broad range of mathemati- Titles in this series are co-published with the Courant cians—from those who just want an overview of the Institute of Mathematical Sciences at New York main ideas of the classification, to those who want a University. reader’s guide to help navigate some of the major papers, Courant Lecture Notes, Volume 18 and to those who may wish to improve the existing 2009; 217 pp.; softcover; ISBN: 978-0-8218-4737-4; List proofs. US$33; AMS members US$26.40; Order code: CLN/18 READERSHIP: Graduate students and research mathematicians interested in classification of finite simple groups. An Introduction to the History of Mathematical Surveys and Monographs, Volume 172 Algebra 2011; 347 pp.; hardcover; ISBN: 978-0-8218-5336-8; List US$94; AMS members US$75.20; Order code: SURV/172 Solving Equations from Mesopotamian Times to the Renaissance Also available in this subject Jacques Sesiano, Swiss Federal Institute of Technology, Lausanne, Switzerland Algebra Translated by Anna Pierrehumbert Mathematical World, Volume 27 Mark R. Sepanski, Baylor University, Waco, TX 2009; 174 pp.; softcover; ISBN: 978-0-8218-4473-1; List US$35; AMS members US$28; Order code: MAWRLD/27 Pure and Applied Undergraduate Texts, Volume 11 2010; 256 pp.; hardcover; ISBN: 978-0-8218-5294-1; List US$62; AMS members US$49.60; Order code: AMSTEXT/11

Order by Phone | 1-401-455-4000 or 1-800-321-4267 Algebra and Algebraic Geometry Analysis

CONTEMPORARY Spectral Theory and Geometric MATHEMATICS Analysis Analysis 5 3 4 Aspects of Aspects of Operator Algebras and Maxim Braverman, Northeastern University, Operator Algebras Boston, MA, Leonid Friedlander, University of and Applications Applications Pere Ara Arizona, Tucson, AZ, Thomas Kappeler, University Fernando Lledó Francesc Perera Pere Ara, Universitat Autònoma de Barcelona, of Zürich, Switzerland, Peter Kuchment, Texas Editors Spain, Fernando Lledó, University Carlos III de A&M University, College Station, TX, and Peter Madrid, Spain, and Francesc Perera, Universitat Topalov and Jonathan Weitsman, Northeastern American Mathematical Society Autònoma de Barcelona, Spain, Editors University, Boston, MA, Editors

This volume contains survey papers on the theory This volume contains the proceedings of the confer- CONTEMPORARY of operator algebras based on lectures given ence on Spectral Theory and Geometric Analysis, held MATHEMATICS at the “Lluís Santaló” Summer School of the Real at Northeastern University, Boston, MA, from July 5 3 5 Sociedad Matemática Española, held in July 2008 at 29–August 2, 2009, which honored Mikhail Shubin on Spectral Theory and the Universidad Internacional Menéndez Pelayo, in his 65th birthday. Geometric Analysis Maxim Braverman Santander (Spain). Leonid Friedlander The papers in this volume cover important topics in Thomas Kappeler Peter Kuchment Topics in this volume cover current fundamental aspects spectral theory and geometric analysis such as resolu- Peter Topalov Jonathan Weitsman of the theory of operator algebras, which have important tions of smooth group actions, spectral asymptotics, Editors applications such as: solutions of the Ginzburg–Landau equation, scattering • K-Theory, the Cuntz semigroup, and Classification theory, Riemann surfaces of infinite genus, tropical American Mathematical Society for C∗-algebras mathematics and geometric methods in the analysis of flows in porous media, and artificial black holes. • Modular Theory for von Neumann algebras and applications to Quantum Field Theory READERSHIP: Graduate students and research mathematicians interested in spectral theory and geometry • Amenability, Hyperbolic Groups, and Operator analysis. Algebras. Contemporary Mathematics, Volume 535 The theory of operator algebras, introduced in the thir- 2011; 213 pp.; softcover; ISBN: 978-0-8218-4948-4; List ties by J. von Neumann and F. J. Murray, was developed US$79; AMS members US$63.20; Order code: CONM/535 in close relationship with fundamental aspects of functional analysis, ergodic theory, harmonic analysis, and quantum physics. More recently, this field has shown many other fruitful interrelations with several areas of Concentration, Functional mathematics and mathematical physics. Inequalities and Isoperimetry READERSHIP: Graduate students and research math- Christian Houdré, Georgia Institute of Technology, C∗ ematicians interested in operator algebras, -algebras, Atlanta, GA, Michel Ledoux, Université Paul K and -theory. Sabatier, Toulouse, France, Emanuel Milman, Contemporary Mathematics, Volume 534 Technion-Israel Institute of Technology, Haifa, Israel, 2011; 168 pp.; softcover; ISBN: 978-0-8218-4905-7; List and Mario Milman, Florida Atlantic University, US$69; AMS members US$55.20; Order code: CONM/534 Boca Raton, FL, Editors The volume contains the proceedings of the international workshop on Concentration, Functional Inequalities and Isoperimetry, held at Florida Atlantic University in Boca Raton, Florida, from October 29– November 1, 2009. The interactions between concentration, isoperimetry and functional inequalities have led to many significant advances in functional analysis and probability theory. Important progress has also taken place in combinatorics, geometry, harmonic analysis and mathematical physics, to name but a few fields, with recent new applications in random matrices and information theory. READERSHIP: Graduate students and research mathematicians interested in the interplay between analysis, probability, and geometry. Contemporary Mathematics, Volume 545 2011; 211 pp.; softcover; ISBN: 978-0-8218-4971-2; List US$79; AMS members US$63.20; Order code: CONM/545

Order Online | www.ams.org/bookstore AnalysisApplications ~ Differential Equations

CONTEMPORARY MATHEMATICS Dynamical Numbers: Interplay 5 3 6 Applications between Dynamical Systems and Cross Disciplinary Number Theory Advances in QuantumSUR V Cross Disciplinary Advances in Computing Quantum Computing Sergiy Kolyada, National Academy of Science of Kazem Mahdavi Deborah Koslover Ukraine, Kiev, Ukraine, Yuri Manin, Max Planck Leonard L. Brown III ULECT , , and Editors Kazem MahdaviGSM Deborah Koslover Leonard Institute for Mathematics, Bonn, Germany, Martin , University of Texas at Tyler, TX, L. Brown III Möller, Goethe-Universität, Frankfurt, Frankfurt Editors American Mathematical Society am Main, Germany, Pieter Moree, Max Planck This volume contains a collection of papers, written Institute for Mathematics, Bonn, Germany, and CONTEMPORARY by physicists, computer scientists, and mathemati- Thomas Ward, University of East Anglia, Norwich, MATHEMATICS cians, from the Conference on Representation Theory, United Kingdom, Editors 5 4 0 Quantum Field Theory, Category Theory, and Quantum This volume contains papers from the special program Nonlinear Elliptic Partial Information Theory, which was held at the University of Differential Equations and international conference on Dynamical Numbers Texas at Tyler from October 1–4, 2009. Denis Bonheure Mabel Cuesta which were held at the Max-Planck Institute in Bonn, Enrique J. Lami Dozo Quantum computing is a field at the interface of the Peter Takáˇc Germany in 2009. Jean Van Schaftingen Michel Willem physical sciences, computer sciences and mathematics. Editors These papers reflect the extraordinary range and depth As such, advances in one field are often overlooked of the interactions between ergodic theory and dynam- by practitioners in other fields. This volume brings ical systems and number theory. Topics covered in the American Mathematical Society together articles from each of these areas to make book include stationary measures, systems of enumer- students, researchers and others interested in quantum ation, geometrical methods, spectral methods, and computation aware of the most current advances. It is algebraic dynamical systems. hoped that this work will stimulate future advances in the field. READERSHIP: Graduate students and research mathematicians interested in ergodic theory, dynamical READERSHIP: Graduate students and research math- systems, and number theory. ematicians interested in quantum computing. Contemporary Mathematics, Volume 532 Contemporary Mathematics, Volume 536 2010; 242 pp.; softcover; ISBN: 978-0-8218-4958-3; List 2011; 152 pp.; softcover; ISBN: 978-0-8218-4975-0; List US$79; AMS members US$63.20; Order code: CONM/532 US$59; AMS members US$47.20; Order code: CONM/536

Differential Equations Nonlinear Elliptic Partial Differential Equations Symmetry for Elliptic PDEs Denis Bonheure, Université Libre de Bruxelles, Alberto Farina, Université de Picardie Jules Verne, Belgium, Mabel Cuesta, Université du Littoral, Amiens, France, and Enrico Valdinoci, Università Calais, France, Enrique J. Lami Dozo, Université Di Roma Tor Vergata, Rome, Italy, Editors Libre de Bruxelles, Belgium, Peter Takácˇ, Universität Rostock, Germany, and Jean Van This volume contains contributions from the INdAM Schaftingen and Michel Willem, Université School on Symmetry for Elliptic PDEs, which was held Catholique de Louvain, Louvain-la-Neuve, Belgium, May 25–29, 2009, in Rome, Italy. The school marked Editors “30 years after a conjecture of De Giorgi, and related problems” and provided an opportunity for experts to This volume contains papers on semi-linear and quasi- discuss the state of the art and open questions on the linear elliptic equations from the workshop on Nonlinear subject. Elliptic Partial Differential Equations, in honor of Jean- Motivated by the classical rigidity properties of the Pierre Gossez’s 65th birthday, held September 2–4, 2009 minimal surfaces, De Giorgi proposed the study of the at the Université Libre de Bruxelles, Belgium. one-dimensional symmetry of the monotone solutions The workshop reflected Gossez’s contributions of a semilinear, elliptic partial differential equation. in nonlinear elliptic PDEs and provided an opening Impressive advances have recently been made in this to new directions in this very active research area. field, though many problems still remain open. Several Presentations covered recent progress in Gossez’s generalizations to more complicated operators have favorite topics, namely various problems related to the attracted the attention of pure and applied mathemati- p-Laplacian operator, the antimaximum principle, the cians, both for their important theoretical problems Fucˇík Spectrum, and other related subjects. This volume and for their relation, among others, with the gradient will be of principle interest to researchers in nonlinear theory of phase transitions and the dynamical systems. analysis, especially in partial differential equations of elliptic type. READERSHIP: Graduate students and research mathematicians interested in elliptic PDEs. READERSHIP: Graduate students and research math- Contemporary Mathematics, Volume 528 ematicians interested in nonlinear partial differential 2010; 137 pp.; softcover; ISBN: 978-0-8218-4804-3; List equations. US$59; AMS members US$47.20; Order code: CONM/528 Contemporary Mathematics, Volume 540 2011; 259 pp.; softcover; ISBN: 978-0-8218-4907-1; List US$89; AMS members US$71.20; Order code: CONM/540 16

Order by Phone | 1-401-455-4000 or 1-800-321-4267 AnalysisApplications ~ Differential Equations Discrete Mathematics and Combinatorics

Combinatorial Problems and CONTEMPORARY MATHEMATICS Discrete Mathematics and Exercises 5 3 1 Combinatorics Combinatorics Second Edition and Graphs Richard A. Brualdi László Lovász, Eötvös Loránd University, Budapest, Samad Hedayat Combinatorics and Graphs Hadi Kharaghani Gholamreza B. Khosrovshahi Hungary Shahriar Shahriari Richard A. Brualdi, University of Wisconsin, Editors AMS Chelsea Publishing, Volume 361 Madison, WI, Samad Hedayat, University of Illinois 1979; 639 pp.; hardcover; ISBN: 978-0-8218-4262-1; List at Chicago, IL, Hadi Kharaghani, University US$69; AMS members US$62.10; Order code: CHEL/361.H American Mathematical Society of Lethbridge, AB, Canada, Gholamreza B. Khosrovshahi, IPM, Tehran, Iran, and Shahriar Shahriari, Pomona College, Claremont, CA, Editors A Discrete Transition to Advanced This volume contains a collection of papers presented Mathematics at the international conference IPM 20—Combinatorics 2009, which was held at the Institute for Research in Bettina Richmond and Thomas Richmond, Fundamental Sciences in Tehran, Iran, May 15–21, Western Kentucky University, Bowling Green, KY 2009. Pure and Applied Undergraduate Texts, Volume 3 2004; 424 pp.; hardcover; ISBN: 978-0-8218-4789-3; List The conference celebrated IPM’s 20th anniversary US$72; AMS members US$57.60; Order code: AMSTEXT/3 and was dedicated to Reza Khosrovshahi, one of the founders of IPM and the director of its School of Mathematics from 1996 to 2007, on the occasion of his 70th birthday. Spectral Graph Theory The conference attracted an international group of Fan R. K. Chung, University of Pennsylvania, distinguished researchers from many different parts of Philadelphia, PA combinatorics and graph theory, including permuta- CBMS Regional Conference Series in Mathematics, tions, designs, graph minors, graph coloring, graph Number 92 eigenvalues, distance regular graphs and association 1997; 212 pp.; softcover; ISBN: 978-0-8218-0315-8; List schemes, hypergraphs, and arrangements. US$30; AMS members US$24; All Individuals US$24; Order code: CBMS/92 READERSHIP: Graduate students interested in combinatorics. Contemporary Mathematics, Volume 531 Inevitable Randomness in Discrete 2010; 264 pp.; softcover; ISBN: 978-0-8218-4865-4; List US$89; AMS members US$71.20; Order code: CONM/531 Mathematics József Beck, Rutgers, The State University of New Also available in this subject Jersey, Piscataway, NJ University Lecture Series, Volume 49 2009; 250 pp.; softcover; ISBN: 978-0-8218-4756-5; List The Erdo ˝ s Distance Problem US$59; AMS members US$47.20; Order code: ULECT/49 Julia Garibaldi, Alex Iosevich, University of Rochester, NY, and Steven Senger, University of A Course in Convexity Missouri-Columbia, MO , University of Michigan, Ann Student Mathematical Library, Volume 56 Alexander Barvinok 2011; 150 pp.; softcover; ISBN: 978-0-8218-5281-1; List Arbor, MI US$29; AMS members US$23.20; Order code: STML/56 Graduate Studies in Mathematics, Volume 54 2002; 366 pp.; hardcover; ISBN: 978-0-8218-2968-4; List US$65; AMS members US$52; Order code: GSM/54 Thirty-three Miniatures Mathematical and Algorithmic Applications of Linear Algebra Jirˇí Matousˇek, Charles University, Prague, Czech Republic Student Mathematical Library, Volume 53 2010; 182 pp.; softcover; ISBN: 978-0-8218-4977-4; List US$36; AMS members US$28.80; Order code: STML/53

Order Online | www.ams.org/bookstore Geometry and Topology

The volume contains four parts corresponding to the Geometry and Topology four main focal points of the conference: algebraic geometry and fundamental groups, braids and knots, Grassmannians, Moduli Spaces and hyperplane arrangements, and singularities. Together, Vector Bundles the papers provide an overview of the current status of a broad range of topological questions in Algebraic David A. Ellwood, Clay Mathematics Institute, Geometry. Cambridge, MA, and Emma Previato, Boston READERSHIP: Graduate students and research University, MA, Editors mathematicians interested in algebraic geometry and fundamental groups, braids and knots, hyperplane This collection of cutting-edge articles on vector arrangements, and singularity theory. ONTEMPORARY bundles and related topics originated from a CMI C Contemporary Mathematics, Volume 538 MATHEMATICS workshop, held in October 2006, that brought together 5 3 8 a community indebted to the pioneering work of P. E. 2011; 467 pp.; softcover; ISBN: 978-0-8218-4890-6; List Newstead, visiting the United States for the first time US$135; AMS members US$108; Order code: CONM/538 Topology of Algebraic Varieties since the 1960s. Moduli spaces of vector bundles were and Singularities then in their infancy, but are now, as demonstrated by

José Ignacio Cogolludo-Agustín Eriko Hironaka this volume, a powerful tool in symplectic geometry, Interactions Between Hyperbolic Editors number theory, mathematical physics, and algebraic Geometry, Quantum Topology and geometry. In fact, the impetus for this volume was to Number Theory American Mathematical Society offer a sample of the vital convergence of techniques and fundamental progress, taking place in moduli spaces at Abhijit Champanerkar, College of Staten Island, the outset of the twenty-first century. CUNY, Staten Island, NY, Oliver Dasbach, This volume contains contributions by J. E. Andersen Louisiana State University, Baton Rouge, LA, and N. L. Gammelgaard (Hitchin’s projectively flat Efstratia Kalfagianni, Michigan State University, connection and Toeplitz operators), M. Aprodu and East Lansing, MI, Ilya Kofman, College of Staten G. Farkas (moduli spaces), D. Arcara and A. Bertram Island, CUNY, Staten Island, NY, Walter Neumann, (stability in higher dimension), L. Jeffrey (intersection Barnard College, Columbia University, New York, cohomology), J. Kamnitzer (Langlands program), M. NY, and Neal Stoltzfus, Louisiana State University, Lieblich (arithmetic aspects), P. E. Newstead (coherent Baton Rouge, LA, Editors systems), G. Pareschi and M. Popa (linear series on Abelian varieties), and M. Teixidor i Bigas (bundles over This book is based on a 10-day workshop given by reducible curves). leading experts in hyperbolic geometry, quantum These articles do require a working knowledge of topology and number theory, in June 2009 at Columbia algebraic geometry, symplectic geometry and func- University. Each speaker gave a minicourse consisting tional analysis, but should appeal to practitioners in a of three or four lectures aimed at graduate students diversity of fields. No specialization should be neces- and recent PhDs. The proceedings of this enormously sary to appreciate the contributions, or possibly to be successful workshop can serve as an introduction to stimulated to work in the various directions opened this active research area in a way that is expository and by these path-blazing ideas; to mention a few, the broadly accessible to graduate students. Langlands program, stability criteria for vector bundles Although many ideas overlap, the twelve expository/ over surfaces and threefolds, linear series over abelian research papers in this volume can be grouped into four varieties and Brauer groups in relation to arithmetic rough categories: properties of moduli spaces. (1) different approaches to the Volume Conjecture, and READERSHIP: Graduate students and research relations between the main quantum and geometric mathematics interested in algebraic, symplectic, and invariants; differential geometry. (2) the geometry associated to triangulations of hyper- Titles in this series are co-published with the Clay bolic 3-manifolds; Mathematics Institute (Cambridge, MA). (3) arithmetic invariants of hyperbolic 3-manifolds; Clay Mathematics Proceedings, Volume 14 (4) quantum invariants associated to knots and hyper- 2011; 180 pp.; softcover; ISBN: 978-0-8218-5205-7; List US$55; AMS members US$44; Order code: CMIP/14 bolic 3-manifolds. The workshop, the conference that followed, and these proceedings continue a long tradition in quantum and Topology of Algebraic Varieties and geometric topology of bringing together ideas from diverse areas of mathematics and physics, and highlights Singularities the importance of collaborative research in tackling big José Ignacio Cogolludo-Agustín, Universidad problems that require expertise in disparate disciplines. de Zaragoza, Spain, and Eriko Hironaka, Florida READERSHIP: Graduate students and research math- State University, Tallahassee, FL, Editors ematicians interested in hyperbolic geometry, quantum topology and number theory. This volume contains invited expository and research Contemporary Mathematics, Volume 541 papers from the conference Topology of Algebraic Varieties, in honor of Anatoly Libgober’s 60th birthday, 2011; 257 pp.; softcover; ISBN: 978-0-8218-4960-6; List US$89; AMS members US$71.20; Order code: CONM/541 held June 22–26, 2009, in Jaca, Spain. 18

Order by Phone | 1-401-455-4000 or 1-800-321-4267 Geometry and Topology ~ Logic and Foundations

Harmonic Maps and Differential CONTEMPORARY MATHEMATICS Geometry Logic and Foundations 5 4 2 Harmonic Maps E. Loubeau, Université de Bretagne, Brest, France, Ultrafilters across Mathematics and Differential and S. Montaldo, University of Cagliari, Italy, Vitaly Bergelson, Ohio State University, Columbus, Geometry Editors E. Loubeau S. Montaldo OH, Andreas Blass, University of Michigan, Ann Editors This volume contains the proceedings of a conference Arbor, MI, Mauro Di Nasso, Università di Pisa, held in Cagliari, Italy, from September 7–10, 2009, to Italy, and Renling Jin, College of Charleston, SC, celebrate John C. Wood’s 60th birthday. Editors American Mathematical Society These papers reflect the many facets of the theory of This volume originated from the International Congress harmonic maps and its links and connections with other “ULTRAMATH: Applications of Ultrafilters and CONTEMPORARY topics in Differential and Riemannian Geometry. Two MATHEMATICS Ultraproducts in Mathematics”, which was held in Pisa, 5 3 3 long reports, one on constant mean curvature surfaces Italy, from June 1–7, 2008. by F. Pedit and the other on the construction of harmonic Set Theory and maps by J. C. Wood, open the proceedings. These are The volume aims to present the state-of-the-art of appli- Its Applications cations in the whole spectrum of mathematics which are L. Babinkostova followed by a mix of surveys on Prof. Wood’s area of A. E. Caicedo grounded on the use of ultrafilters and ultraproducts. It S. Geschke expertise: Lagrangian surfaces, biharmonic maps, locally M. Scheepers conformally Kähler manifolds and the DDVV conjec- contains two general surveys on ultrafilters in set theory Editors ture, as well as several research papers on harmonic and on the ultraproduct construction. maps. Other research papers in the volume are devoted The papers are intended to be accessible and interesting American Mathematical Society to Willmore surfaces, Goldstein-Pedrich flows, contact for mathematicians who are not experts on ultrafilters pairs, prescribed Ricci curvature, conformal fibrations, and ultraproducts. Greater prominence has been given the Fadeev-Hopf model, the Compact Support Principle to results that can be formulated and presented in non- and the curvature of surfaces. special terms and be, in principle, understandable by READERSHIP: Graduate students and research math- any mathematician, and to those results that connect ematicians interested in differential geometry and different areas of mathematics, revealing new facets of harmonic maps. known important topics. Contemporary Mathematics, Volume 542 READERSHIP: Graduate students and research math- 2011; 284 pp.; softcover; ISBN: 978-0-8218-4987-3; List ematicians interested in the theory of ultrafilters and US$99; AMS members US$79.20; Order code: CONM/542 ultraproducts.. Contemporary Mathematics, Volume 530 2010; 200 pp.; softcover; ISBN: 978-0-8218-4833-3; List Also available in this subject US$69; AMS members US$55.20; Order code: CONM/530

Poncelet’s Theorem Set Theory and Its Applications Leopold Flatto L. Babinkostova and A. E. Caicedo, Boise State 2009; 240 pp.; hardcover; ISBN: 978-0-8218-4375-8; List University, ID, S. Geschke, University of Bonn, US$49; AMS members US$39.20; Order code: MBK/56 Germany, and M. Scheepers, Boise State University, ID, Editors Seifert Fiberings This book consists of several survey and research papers covering a wide range of topics in active areas of set Kyung Bai Lee, University of Oklahoma, Norman, theory and set theoretic topology. Some of the articles OK, and Frank Raymond, University of Michigan, present, for the first time in print, knowledge that has Ann Arbor, MI been around for several years and known intimately to Mathematical Surveys and Monographs, Volume 166 only a few experts. The surveys bring the reader up to 2010; 396 pp.; hardcover; ISBN: 978-0-8218-5231-6; List date on the latest information in several areas that have US$99; AMS members US$79.20; Order code: SURV/166 been surveyed a decade or more ago. Topics covered in the volume include combinatorial and descriptive set theory, determinacy, iterated forcing, Ramsey theory, Differential Topology selection principles, set-theoretic topology, and universality, among others. Graduate students and researchers , Massachusetts Institute of Victor Guillemin in logic, especially set theory, descriptive set theory, and Technology, Cambridge, MA, and Alan Pollack set-theoretic topology, will find this book to be a very AMS Chelsea Publishing, Volume 370 valuable reference. 2010; 222 pp.; hardcover; ISBN: 978-0-8218-5193-7; List US$40; AMS members US$36; Order code: CHEL/370.H READERSHIP: Graduate students and research mathematicians interested in set theory and its modern applications. Contemporary Mathematics, Volume 533 2011; 307 pp.; softcover; ISBN: 978-0-8218-4812-8; List US$105; AMS members US$84; Order code: CONM/533

Order Online | www.ams.org/bookstore Mathematical Physics

CONTEMPORARY MATHEMATICS Combinatorics and Physics 5 2 7 Mathematical Physics Kurusch Ebrahimi-Fard, Universidad de Zaragoza, Mirror Symmetry Mirror Symmetry and Tropical Spain, Matilde Marcolli, California Institute of and Tropical Geometry Technology, Pasadena, CA, and Walter D. van Ricardo Castaño-Bernard Geometry , Radboud University Nijmegen, The Yan Soibelman Suijlekom Ilia Zharkov Editors Ricardo Castaño-Bernard, Yan Soibelman, and Netherlands, Editors Ilia Zharkov, Kansas State University, Manhattan, This book is based on the mini-workshop KS, Editors American Mathematical Society Renormalization, held in December 2006, and the This volume contains contributions from the conference Combinatorics and Physics, held in March NSF-CBMS Conference on Tropical Geometry and 2007. Both meetings took place at the Max-Planck- CONTEMPORARY Institut für Mathematik in Bonn, Germany. MATHEMATICS Mirror Symmetry, which was held from December 5 3 9 13–17, 2008 at Kansas State University in Manhattan, Research papers in the volume provide an overview Combinatorics Kansas. of applications of combinatorics to various problems, and Physics It gives an excellent picture of numerous connections such as applications to Hopf algebras, techniques to of mirror symmetry with other areas of mathematics renormalization problems in quantum field theory, as Kurusch Ebrahimi-Fard Matilde Marcolli well as combinatorial problems appearing in the context Walter D. van Suijlekom (especially with algebraic and symplectic geometry) as Editors well as with other areas of mathematical physics. The of the numerical integration of dynamical systems, in techniques and methods used by the authors of the noncommutative geometry and in quantum gravity. American Mathematical Society volume are at the frontier of this very active area of In addition, it contains several introductory notes on research. renormalization Hopf algebras, Wilsonian renormaliza- READERSHIP: Graduate students and research math- tion and motives. ematicians interested in mirror symmetry. READERSHIP: Graduate students and research math- Contemporary Mathematics, Volume 527 ematicians interested in applications of combinatorics 2010; 168 pp.; softcover; ISBN: 978-0-8218-4884-5; List to physics. US$69; AMS members US$55.20; Order code: CONM/527 Contemporary Mathematics, Volume 539 2011; 465 pp.; softcover; ISBN: 978-0-8218-5329-0; List US$130; AMS members US$104; Order code: CONM/539 Entropy and the Quantum Robert Sims, University of Arizona, Tucson, AZ, Also available in this subject and Daniel Ueltschi, University of Warwick, Coventry, United Kingdom, Editors Lectures on Quantum Mechanics for These lecture notes provide a pedagogical introduction to quantum mechanics and to some of the mathematics Mathematics Students that has been motivated by this field. They are a product L. D. Faddeev, Steklov Mathematical Institute, of the school “Entropy and the Quantum”, which took St. Petersburg, Russia, and O. A. Yakubovskiı˘, St. place in Tucson, Arizona, in 2009. They have been Petersburg University, Russia written primarily for young mathematicians, but they will also prove useful to more experienced analysts with an appendix by Leon Takhtajan and mathematical physicists. In the first contribution, Student Mathematical Library, Volume 47 William Faris introduces the mathematics of quantum 2009; 234 pp.; softcover; ISBN: 978-0-8218-4699-5; List mechanics. Robert Seiringer and Eric Carlen review US$39; AMS members US$31.20; Order code: STML/47 certain recent developments in stability of matter and analytic inequalities, respectively. Bruno Nachtergaele and Robert Sims review locality results for quantum Quantum Mechanics for systems, and Christopher King deals with additivity conjectures and quantum information theory. The final Mathematicians article, by Christian Hainzl, describes applications of Leon A. Takhtajan, Stony Brook University, NY analysis to the Shandrasekhar limit of stellar masses. Graduate Studies in Mathematics, Volume 95 READERSHIP: Graduate students and research 2008; 387 pp.; hardcover; ISBN: 978-0-8218-4630-8; List mathematicians interested in mathematical aspects of US$69; AMS members US$55.20; Order code: GSM/95 quantum physics. Contemporary Mathematics, Volume 529 2010; 202 pp.; softcover; ISBN: 978-0-8218-5247-7; List Quantum Field Theory US$69; AMS members US$55.20; Order code: CONM/529 A Tourist Guide for Mathematicians Gerald B. Folland, University of Washington, Seattle, WA Mathematical Surveys and Monographs, Volume 149 2008; 325 pp.; hardcover; ISBN: 978-0-8218-4705-3; List US$89; AMS members US$71.20; Order code: SURV/149

Order by Phone | 1-401-455-4000 or 1-800-321-4267 Number Theory

Number Theory WIN—Women in Numbers Research Directions in Number Theory On Certain L-Functions Alina-Carmen Cojocaru, University of Illinois at James Arthur, University of Toronto, ON, Chicago, IL, and Institute of Mathematics “Simion Canada, James W. Cogdell, Ohio State University, Stoilow” of the Romanian Academy, Bucharest, Columbus, OH, Steve Gelbart, Weizmann Institute Romania, Kristin Lauter, Microsoft Research, of Science, Rehovot, Israel, David Goldberg, Redmond, WA, Rachel Pries, Colorado State Purdue University, West Lafayette, IN, Dinakar University, Fort Collins, CO, and Renate Scheidler, Ramakrishnan, California Institute of Technology, University of Calgary, AB, Canada, Editors Pasadena, CA, and Jiu-Kang Yu, Purdue University, This volume is a collection of papers on number theory FIELDS INSTITUTE West Lafayette, IN, Editors which evolved out of the workshop WIN—Women COMMUNICATIONS

In Numbers, held November 2–7, 2008, at the Banff HE IELDS NSTITUTE FOR ESEARCH IN ATHEMATICAL CIENCES This volume constitutes the proceedings of a confer- T F I R M S International Research Station (BIRS) in Banff, Alberta, ence, “On Certain L-functions”, held July 23–27, 2007 WIN—Women in Numbers Canada. It includes articles showcasing outcomes from Research Directions at Purdue University, West Lafayette, Indiana. The in Number Theory collaborative research initiated during the workshop conference was organized in honor of the 60th birthday Alina-Carmen Cojocaru Kristin Lauter as well as survey papers aimed at introducing graduate Rachel Pries of Freydoon Shahidi, widely recognized as having Renate Scheidler made groundbreaking contributions to the Langlands students and recent PhDs to important research topics Editors in number theory. American Mathematical Society program. The Fields Institute for Research in Mathematical Sciences The articles in this volume represent a snapshot of the The contributions in this volume span a wide range state of the field from several viewpoints. Contributions of topics in arithmetic geometry and algebraic, algo- illuminate various areas of the study of geometric, rithmic, and analytic number theory. Clusters of papers analytic, and number theoretic aspects of automorphic center around the four topics of moduli spaces and forms and their L-functions, and both local and global Shimura curves, curves and Jacobians over finite fields, theory are addressed. Galois covers of function fields in positive characteristic, and zeta functions of graphs, with a fifth group Topics discussed in the articles include Langlands of three individual articles on modular forms, Iwasawa functoriality, the Rankin–Selberg method, the theory, and Galois representations, respectively. Langlands–Shahidi method, motivic Galois groups, Shimura varieties, orbital integrals, representations of The workshop and this volume are part of a broader p-adic groups, Plancherel formula and its conse- WIN initiative, whose goals are to highlight and increase quences, the Gross–Prasad conjecture, and more. The the research activities of women in number theory and volume also includes an expository article on Shahidi’s to train female graduate students in number theory and contributions to the field, which serves as an introduc- related fields. tion to the subject. READERSHIP: Graduate students and research math- Experts will find this book a useful reference, and begin- ematicians interested in number theory. ning researchers will be able to use it to survey major Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, results in the Langlands program. Ontario, Canada). READERSHIP: Graduate students and research math- Fields Institute Communications, Volume 60 ematicians interested in analytic number theory and 2011; 288 pp.; hardcover; ISBN: 978-0-8218-5226-2; List automorphic forms. US$107; AMS members US$85.60; Order code: FIC/60 Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA). Clay Mathematics Proceedings, Volume 13 Also available in this subject 2011; 647 pp.; softcover; ISBN: 978-0-8218-5204-0; List US$129; AMS members US$103.20; Order code: CMIP/13 The Ultimate Challenge The 3x 1 Problem + Jeffrey C. Lagarias, University of Michigan, Ann Arbor, MI, Editor 2010; 344 pp.; hardcover; ISBN: 978-0-8218-4940- 8; List US$59; AMS members US$47.20; Order code: MBK/78

Order Online | www.ams.org/bookstore MEMOIRS Applied Mathematicsof the AMS

Applied mathematics was once only associated with the natural sciences and engineering, yet over the last 50 years it has blossomed to include many fascinating subjects outside the physical sciences. Such areas include game theory, biomathematics and mathematical economy demonstrating mathematics' presence throughout everyday human activity. The AMS book publication program on applied and interdisciplinary mathematics strengthens the connections between mathematics and other disciplines, highlighting the areas where mathematics is most relevant. These publications help mathematicians understand how mathematical ideas may benefit other sciences, while offering researchers outside of mathematics important tools to advance their profession.

Algebra and Algebraic Training Manual on Transport Differential Equations and Fluids Geometry John C. Neu, University of A Geometric Approach to Free Algebraic Geometric Codes: California, Berkeley, CA Boundary Problems Graduate Studies in Mathematics, Basic Notions Volume 109 Luis Caffarelli, University of Texas, Austin, TX, and Sandro Salsa, Michael Tsfasman, Serge Vlaˇdut¸, 2010; 265 pp.; hardcover; ISBN: 978-0- 8218-4083-2; List US$59; AMS members Politecnico di Milano, Italy and Dmitry Nogin US$47.20; Order code: GSM/109 Graduate Studies in Mathematics, Mathematical Surveys and Volume 68 Monographs, Volume 139 2005; 270 pp.; hardcover; ISBN: 978-0- 2007; 338 pp.; hardcover; ISBN: 978-0- 8218-3784-9; List US$51; AMS members 8218-4306-2; List US$89; AMS members Computational Complexity US$40.80; Order code: GSM/68 US$71.20; Order code: SURV/139 Theory Steven Rudich, Carnegie Mellon Analysis University, Pittsburgh, PA, and Avi Optimal Control of Partial Wigderson, Institute for Advanced Differential Equations Study, Princeton, NJ, Editors Topics in Optimal Theory, Methods and Applications Transportation Titles in this series are co-published with the Institute for Advanced Study/Park Fredi Tröltzsch, Technische City Mathematics Institute. Cédric Villani, École Normale Universität Berlin, Germany IAS/Park City Mathematics Series, Supérieure de Lyon, France Volume 10 Translated by Jürgen Sprekels Graduate Studies in Mathematics, 2004; 389 pp.; hardcover; ISBN: 978-0- Graduate Studies in Mathematics, Volume 58 8218-2872-4; List US$72; AMS members Volume 112 2003; 370 pp.; hardcover; ISBN: 978-0- US$57.60; Order code: PCMS/10 2010; 399 pp.; hardcover; ISBN: 978-0- 8218-3312-4; List US$62; AMS members 8218-4904-0; List US$69; AMS members US$49.60; Order code: GSM/58 US$55.20; Order code: GSM/112 Cryptography: An Introduction Applications V. V. Yaschenko, Moscow Center for Differential Equations, Continuous Mathematics Education, Mechanics, and Computation Introduction to the Russia, Editor Mathematics of Finance Student Mathematical Library, Volume Richard S. Palais, University of 18 California, Irvine, CA, and Robert R. J. Williams, University of 2002; 229 pp.; softcover; ISBN: 978-0- A. Palais, University of Utah, Salt California, San Diego, La Jolla, CA 8218-2986-8; List US$43; AMS members Lake City, UT US$34.40; Order code: STML/18 Graduate Studies in Mathematics, Student Mathematical Library, Volume Volume 72 51 2006; 150 pp.; hardcover; ISBN: 978-0- 2009; 313 pp.; softcover; ISBN: 978-0- 8218-3903-4; List US$39; AMS members Geometric Approximation 8218-2138-1; List US$51; AMS members US$31.20; Order code: GSM/72 Algorithms US$40.80; Order code: STML/51 Sariel Har-Peled, University of Illinois at Urbana-Champaign, IL Mathematical Surveys and Monographs, Volume 173 2011; 362 pp.; hardcover; ISBN: 978-0- 8218-4911-8; List US$98; AMS members US$78.40; Order code: SURV/173 22 22 Order by Phone | 1-401-455-4000 or 1-800-321-4267 Applied Mathematics Applied Mathematics

Discrete Mathematics Computational Topology Probability and and Combinatorics An Introduction Statistics

Herbert Edelsbrunner, Duke www.ams.org/bookstore/appliedmath Stable Marriage and University, Durham, NC, and Lectures on the Its Relation to Other Geomagic, Research Triangle Mathematics of Finance Combinatorial Problems Park, NC, and John L. Harer, Duke University, Durham, NC Ioannis Karatzas, Columbia An Introduction to the University, New York, NY Mathematical Analysis of 2010; 241 pp.; hardcover; ISBN: 978- Titles in this series are co-published Algorithms 0-8218-4925-5; List US$59; AMS with the Centre de Recherches members US$47.20; Order code: Mathématiques. Donald E. Knuth, Stanford MBK/69 CRM Monograph Series, Volume 8 University, CA 1997; 148 pp.; softcover; ISBN: 978-0-8218-0909-9; List US$45; Titles in this series are co-published AMS members US$36; Order code: with the Centre de Recherches Mathematical Physics Mathématiques. CRMM/8.S CRM Proceedings & Lecture Quantum Mechanics for Notes, Volume 10 Mathematicians 1997; 74 pp.; softcover; ISBN: 978- Lectures on Monte Carlo 0-8218-0603-6; List US$22; AMS Leon A. Takhtajan, Stony Brook Methods members US$17.60; Order code: University, NY CRMP/10 Neal Madras, York University, Graduate Studies in Mathematics, Toronto, ON, Canada Volume 95 2008; 387 pp.; hardcover; ISBN: 978- Titles in this series are co-published General Interest 0-8218-4630-8; List US$69; AMS with The Fields Institute for members US$55.20; Order code: Research in Mathematical Sciences GSM/95 (Toronto, Ontario, Canada). A Gentle Introduction to Fields Institute Monographs, Game Theory Volume 16 Mathematical Methods in 2002; 103 pp.; hardcover; ISBN: 978- Saul Stahl, University of Kansas, 0-8218-2978-3; List US$34; AMS Lawrence, KS Quantum Mechanics members US$27.20; Order code: Mathematical World, Volume 13 FIM/16 1999; 176 pp.; softcover; ISBN: 978- With Applications to 0-8218-1339-3; List US$28; AMS Schrödinger Operators members US$22.40; Order code: Mathematical Statistics MAWRLD/13 Gerald Teschl, University of Vienna, Austria Asymptotic Minimax Theory Graduate Studies in Mathematics, Modelling in Healthcare Volume 99 Alexander Korostelev, Wayne 2009; 305 pp.; hardcover; ISBN: 978- State University, Detroit, MI, and The Complex Systems Modelling 0-8218-4660-5; List US$59; AMS Olga Korosteleva, California Group (CSMG), The IRMACS members US$47.20; Order code: State University, Long Beach, CA GSM/99 Center, Simon Fraser University, Graduate Studies in Mathematics, Burnaby, BC, Canada Volume 119 2010; 218 pp.; hardcover; ISBN: 978- 2011; 246 pp.; hardcover; ISBN: 978- 0-8218-4969-9; List US$69; AMS Lectures on Quantum 0-8218-5283-5; List US$63; AMS members US$55.20; Order code: Mechanics for Mathematics members US$50.40; Order code: MBK/74 Students GSM/119 L. D. Faddeev, Steklov Geometry and Mathematical Institute, St. Filtering and Prediction: A Topology Petersburg, Russia, and O. A. Primer Yakubovskiı˘, St. Petersburg University, Russia B. Fristedt, N. Jain, and N. Portraits of the Earth Krylov, University of Minnesota, with an appendix by Leon Minneapolis, MN A Mathematician Looks at Takhtajan Student Mathematical Library, Maps Student Mathematical Library, Volume 38 Volume 47 2007; 252 pp.; softcover; ISBN: 978- Timothy G. Feeman, Villanova 2009; 234 pp.; softcover; ISBN: 978- 0-8218-4333-8; List US$39; AMS University, PA 0-8218-4699-5; List US$39; AMS members US$31.20; Order code: Mathematical World, Volume 18 members US$31.20; Order code: STML/38 2002; 123 pp.; softcover; ISBN: 978- STML/47 0-8218-3255-4; List US$28; AMS members US$22.40; Order code: MAWRLD/18

23 Order Online | www.ams.org/bookstore MEMOIRS of the AMS

EMOIRS Two Kinds of Derived Positive Definiteness of M of the American Mathematical Society Algebra and Algebraic Categories, Koszul Functions with Applications Volume 211 Number 992 Geometry Iwasawa Theory, Duality, and Comodule- to Operator Norm Projective Modules, Contramodule Inequalities and Modular Centres of Centralizers Representations of Unipotent Elements in Correspondence Hideki Kosaki, Kyushu Ralph Greenberg Simple Algebraic Groups Leonid Positselski, Institute University, Fukuoka, Japan for Information Transmission Volume 212, Number 997 R. Lawther, Girton College, Problems, Moscow, Russia 2011; 80 pp.; softcover; ISBN: 978-0- American Mathematical Society 8218-5307-8; List US$66; Individual University of Cambridge, Volume 212, Number 996 member US$39.60; Order code: England, and D. M. Testerman, 2011; 133 pp.; softcover; ISBN: 978- MEMO/212/997 EMOIRS École Polytechnique Federale de 0-8218-5296-5; List US$71; Individual M of the American Mathematical Society Lausanne, Switzerland member US$42.60; Order code:

Volume 210 Number 987 Volume 210, Number 988 MEMO/212/996 188 pp.; softcover; ISBN: 978-0-8218- Geometry and Definable Additive 4769-5; List US$83; Individual member Categories: Purity and Topology Model Theory US$49.80; Order code: MEMO/210/988 On Systems of Equations over Free Partially Mike Prest Q-Valued Functions Towards Non-Abelian p Commutative Groups Revisited -adic Hodge Theory in the Montserrat Casals-Ruiz and Ilya Camillo De Lellis, University American Mathematical Society Good Reduction Case Kazachkov, McGill University, of Zurich, Switzerland, and Montreal, QC, Canada Emanuele Nunzio Spadaro, Martin C. Olsson, University of To view more books Volume 212, Number 999 University of Bonn, Germany California, Berkeley, CA 2011; 153 pp.; softcover; ISBN: 978- in this series, go to Volume 211, Number 991 Volume 210, Number 990 0-8218-5258-3; List US$77; Individual 2011; 79 pp.; softcover; ISBN: 978-0- www.ams.org/memo 2011; 157 pp.; softcover; ISBN: 978- member US$46.20; Order code: 8218-4914-9; List US$66; Individual 0-8218-5240-8; List US$77; Individual MEMO/212/999 member US$39.60; Order code: member US$46.20; Order code: MEMO/211/991 MEMO/210/990 Analysis Logic and Foundations Iwasawa Theory, Projective Limit Operators, Collective Modules, and Modular Compactness, and the Definable Additive Representations Spectral Theory of Infinite Categories: Purity and Ralph Greenberg, University of Matrices Model Theory Washington, Seattle, WA Volume 211, Number 992 Simon N. Chandler-Wilde, Mike Prest, University of 2011; 185 pp.; softcover; ISBN: 978- University of Reading, England, Manchester, England 0-8218-4931-6; List US$83; Individual and Marko Lindner, Technical Volume 210, Number 987 member US$49.80; Order code: University of Chemnitz, Germany 2011; 109 pp.; softcover; ISBN: 978- MEMO/211/992 Volume 210, Number 989 0-8218-4767-1; List US$70; Individual 2011; 111 pp.; softcover; ISBN: 978- member US$42; Order code: 0-8218-5243-9; List US$70; Individual MEMO/210/987 Fonction Zêta des Hauteurs member US$42; Order code: des Variétés Toriques non MEMO/210/989 Déployées Mathematical Physics David Bourqui, I.R.M.A.R., Differential Forms on Rearranging Dyson- Rennes, France Wasserstein Space and Schwinger Equations Volume 211, Number 994 Infinite-Dimensional 2011; 151 pp.; softcover; ISBN: 978- Karen Yeats, Simon Fraser 0-8218-4936-1; List US$77; Individual Hamiltonian Systems University, Burnaby, BC, Canada member US$46.20; Order code: Wilfrid Gangbo and Hwa Memoirs of the American MEMO/211/994 Kil Kim, Georgia Institute Mathematical Society, Volume 211, of Technology, Atlanta, GA, Number 995 2011; 82 pp.; softcover; ISBN: 978-0- and Tommaso Pacini, Scuola Valuations and Differential 8218-5306-1; List US$66; Individual Normale Superiore, Pisa, Italy Galois Groups member US$39.60; Order code: Volume 211, Number 993 MEMO/211/995 Guillaume Duval 2011; 77 pp.; softcover; ISBN: 978-0- 8218-4939-2; List US$66; Individual Volume 212, Number 998 member US$39.60; Order code: 2011; 68 pp.; softcover; ISBN: 978-0- MEMO/211/993 8218-4906-4; List US$60; Individual member US$36; Order code: MEMO/212/998

Order by Phone | 1-401-455-4000 or 1-800-321-4267 AMS-DisAMS-Ditributedstributed Publications Entropy of Meromorphic Publications Maps and Dynamics of Birational Maps Topological Properties of Henry De Thélin, Université Rauzy Fractals Paris 13, Villetaneuse, France, and Gabriel Vigny, Laboratoire Anne Siegel, Université de Rennes, Amiénois de Mathématique France, and Jörg M. Thuswaldner, Fondamentale et Appliquée, University of Leoben, Austria Amiens, France Mémoires de la Société Mémoires de la Société Mathématique de France, Number Mathématique de France, Number 118 122 2009; 144 pp.; softcover; ISBN: 978- 2011; 98 pp.; softcover; ISBN: 978-2-85629- 2-85629-290-7; List US$42; Individual European Hindustan Book 302-7; List US$42; Individual member member US$37.80; Order code: US$37.80; Order code: SMFMEM/122 Mathematical Agency SMFMEM/118 Society A publication of Hindustan Book A Fundamental Domain Uncertainty Principles Agency. Distributed on an exclusive A publication of the European for V3 Associated to Non- Mathematical Society (EMS). basis by the AMS in North Distributed within the Americas America. Online bookstore rights Mary Rees, University of Liverpool, Degenerate Quadratic by the American Mathematical worldwide. England Forms Society. Mémoires de la Société Tantrasan ˙graha of Mathématique de France, Number Bruno Demange, Institut Fourier, 121 St. Martin d’Heres, France Classification of Algebraic Nıˉlakantha Somaya ˉ jı ˉ 2010; 139 pp.; softcover; ISBN: 978- Mémoires de la Société 2-85629-301-0; List US$42; Individual Mathématique de France, Number Varieties K. Ramasubramanian, ITT member US$37.80; Order code: 119 Bombay, Powai, India Carel Faber, Royal Institute of , and M. SMFMEM/121 2009; 102 pp.; softcover; ISBN: 978- S. Sriram, University of Madras, 2-85629-297-6; List US$42; Individual Technology, Stockholm, Sweden, member US$37.80; Order code: University Chennai, India Gerard van der Geer, Hindustan Book Agency La Droite de Berkovich SMFMEM/119 of Amsterdam, The Netherlands, 2011; 642 pp.; hardcover; ISBN: 978-93- Sur Z and Eduard Looijenga, Utrecht 80250-09-0; List US$82; AMS members University, The Netherlands, US$65.60; Order code: HIN/48 Jérôme Poineau, Institut de Editors Recherche Mathématique Avancée, Vieweg Verlag EMS Series of Congress Reports, Strasbourg, France A publication of Vieweg Verlag. Volume 3 Astérisque, Number 334 The AMS is exclusive distributor 2011; 346 pp.; hardcover; ISBN: 978-3- Société 2010; 284 pp.; softcover; ISBN: 978-2- in North America. Vieweg 03719-007-4; List US$98; AMS members Mathématique de 85629-294-5; List US$105; Individual Verlag Publications are available US$78.40; Order code: EMSSCR/3 member US$94.50; Order code: AST/334 worldwide from the AMS outside France of Germany, Switzerland, Austria, Efficient Numerical A publication of the Société Multiplicative Properties and Japan. Mathématique de France, Methods for Non-local Marseilles (SMF), distributed by of the Slice Filtration Operators the AMS in the U.S., Canada, Algebraic Geometry I 2 Pablo Pelaez, Universitaet -Matrix Compression, and Mexico. Orders from other Duisburg-Essen, Germany Schemes. With Examples and HAlgorithms and Analysis countries should be sent to the Astérisque, Number 335 Exercises SMF. Members of the SMF receive 2011; 291 pp.; softcover; ISBN: 978- Steffen Börm, Kiel University, a 30% discount from list. 2-85629-305-8; List US$90; Individual Ulrich Görtz, University of Bonn, Germany member US$81; Order code: AST/335 Germany, and Torsten Wedhorn, EMS Tracts in Mathematics, Volume Convergence des University of Paderborn, Germany 14 Neumann and Dirichlet Vieweg Advanced Lectures in 2010; 441 pp.; hardcover; ISBN: 978-3- Polygones de Harder- Mathematics 03719-091-3; List US$78; AMS members Narasimhan Heat Kernels in Inner 2010; 615 pp.; softcover; ISBN: 978-3- US$62.40; Order code: EMSTM/14 Uniform Domains 8348-0676-5; List US$91; AMS members Huayi Chen, Université Paris US$81.90; Order code: VWALM/12 Lectures on Gaussian Diderot, France Pavel Gyrya and Laurent Saloff- Mémoires de la Société Coste, Cornell University, Ithaca, Quantum Groups and Integral Operators and Mathématique de France, Number NY Classical Groups 120 Astérisque, Number 336 Noncommutative Spaces 2010; 120 pp.; softcover; ISBN: 978- 2011; 145 pp.; softcover; ISBN: 978- Perspectives on Quantum Yurii A. Neretin, University of 2-85629-296-9; List US$42; Individual 2-85629-306-5; List US$45; Individual Vienna, Austria member US$37.80; Order code: member US$40.50; Order code: AST/336 Geometry SMFMEM/120 EMS Series of Lectures in California Mathematics, Volume 13 Matilde Marcolli, Projections in Several Institute of Technology, Pasadena, 2011; 571 pp.; softcover; ISBN: 978-3- Creation of Fermions by 03719-080-7; List US$78; AMS members Complex Variables CA, and Deepak Parashar, US$62.40; Order code: EMSSERLEC/13 Rotating Charged Black University of Cambridge, UK, Holes Chin-Yu Hsiao, University of Editors Nikolai I. Lobachevsky, Cologne, Germany Vieweg Aspects of Mathematics, Dietrich Häfner, Université Mémoires de la Société Volume 40 Pangeometry Bordeaux 1, Talence, France Mathématique de France, Number 2010; 240 pp.; hardcover; ISBN: 978-3- Mémoires de la Société 123 8348-1442-5; List US$75; AMS members Athanase Papadopoulos, Mathématique de France, Number 2011; 136 pp.; softcover; ISBN: 978- US$67.50; Order code: VWAM/40 Université de Strasbourg, France, 117 2-85629-304-1; List US$42; Individual Editor 158 pp.; softcover; ISBN: 978-2-85629- member US$37.80; Order code: 284-6; List US$42; Individual member SMFMEM/123 Translated by Athanase US$37.80; Order code: SMFMEM/117 Papadopoulos Heritage of European Mathematics, Volume 4 2010; 322 pp.; hardcover; ISBN: 978-3- 03719-087-6; List US$98; AMS members US$78.40; Order code: EMSHEM/4 25

Order Online | www.ams.org/bookstore index by Title and Author Index by Title and Author

A Cojocaru, Alina-Carmen��21 Eisenstein Series Hajto, Zbigniew��5 and Automorphic Algebra: Chapter 0��14 Colding, Tobias Holck��4 Han, Qing��3, 4 L-Functions��14 Algebraic Geometry I��25 Combinatorial Problems Har-Peled, Sariel��11 Elliptic Curves, Modular Forms, and Exercises��17 Algebraic Groups and and Their L-functions ��8 Harmonic Analysis on Differential Galois Combinatorics and Graphs ��17 Reductive, p-adic Elliptic Partial Differential Theory��5 Groups��13 Combinatorics and Physics��20 Equations ��3 Algebra��14 Harmonic Maps and Concentration, Ellwood, David A. ��18 Differential Geometry ��19 Aluffi, Paolo��14 Functional Inequalities Entropy and the Quantum��20 and Isoperimetry��15 Hedayat, Samad��17 Ara, Pere ��15 Entropy of Meromorphic Maps Convergence des Polygones de Hensel, Sebastian��8 Arthur, James��21 and Dynamics of Birational Harder-Narasimhan��25 Maps��25 Hereditary Noetherian Prime Aschbacher, Michael��14 Costello, Kevin��10 Rings and Idealizers ��13 The Erdo ˝s Distance Aspects of Operator Algebras A Course in Convexity��17 Problem��17 Hironaka, Eriko��18 and Applications��15 A Course in Eskin, Gregory��5 Houdré, Christian ��15 B Minimal Surfaces ��4 Etingof, Pavel��8 Hsiao, Chin-Yu��25 Babinkostova, L.��19 Cox, David A. ��6 F I Barvinok, Alexander��17 Cozzens, Margaret B.��12 Faber, Carel��25 Inevitable Randomness in A Basic Course in Partial Creation of Fermions by Discrete Mathematics��17 Differential Equations��4 Rotating Charged Black Faddeev, L. D.��20 Interactions Between Hyperbolic Beck, József��17 Holes��25 Farina, Alberto��16 Geometry, Quantum Topology Berberian, Sterling K.��11 Crespo, Teresa��5 Flatto, Leopold��19 and Number Theory��18 Bergelson, Vitaly��19 Cross Disciplinary Advances in Folland, Gerald B. ��20 Introduction to Representation Quantum Computing ��16 Theory��8 Bewersdorff, Jörg��14 Fonction Zêta des Hauteurs Cuesta, Mabel ��16 des Variétés Toriques non An Introduction to the History BioMath in the Schools��12 D Déployées��24 of Algebra��14 Blass, Andreas��19 Friedlander, Leonid ��15 Iosevich, Alex��17 Dasbach, Oliver ��18 Bonheure, Denis��16 A Fundamental Iwasawa Theory, Projective De Lellis, Camillo��24 Börm, Steffen��25 Domain for V3��25 Modules, and Modular De Thélin, Henry��25 Representations��24 Bourqui, David��24 G Definable Additive Boyallian, Carina ��13 J Categories: Purity and Galina, Esther��13 Jin, Renling ��19 Braverman, Maxim��15 Model Theory��24 Galois Theory Brown, Leonard L., III��16 Deift, Percy ��14 for Beginners��14 K Brualdi, Richard A.��17 Demange, Bruno��25 Gangbo, Wilfrid��24 Kalfagianni, Efstratia��18 C Di Nasso, Mauro ��19 Garibaldi, Julia��17 Kappeler, Thomas��15 Gelbart, Steve��21 Caicedo, A. E. ��19 Differential Forms on Kazachkov, Ilya��24 Wasserstein Space and Geometric Approximation Casals-Ruiz, Montserrat��24 Kharaghani, Hadi��17 Infinite-Dimensional Algorithms��11 Castaño-Bernard, Ricardo��20 Hamiltonian Systems��24 Khosrovshahi, Geometry ��7 Gholamreza B. ��17 Centres of Centralizers of Differential Topology��19 Geschke, S.��19 Kim, Hwa Kil��24 Unipotent Elements in Simple A Discrete Transition to Algebraic Groups��24 Advanced Mathematics ��17 Gioev, Dimitri ��14 Kofman, Ilya��18 Champanerkar, Abhijit��18 Doran, Robert S.��13 Golberg, Oleg ��8 Kolyada, Sergiy��16 Chandler-Wilde, Duval, Guillaume��24 Goldberg, David��21 Kosaki, Hideki��24 Simon N��24 Dynamical Numbers: Interplay Görtz, Ulrich��25 Koslover, Deborah��16 Chen, Huayi��25 between Dynamical Systems Grassmannians, Moduli Spaces Kuchment, Peter��15 Chung, Fan R. K.��17 and Number Theory��16 and Vector Bundles ��18 L Classification of Algebraic E Greenberg, Ralph��24 Varieties ��25 La Droite de Ebrahimi-Fard, Kurusch��20 Groups, Algebras and Berkovich Sur Z��25 The Classification of Finite Applications��13 Efficient Numerical Methods Simple Groups��14 Lagarias, Jeffrey C.��21 for Non-local Operators��25 Guillemin, Victor��19 Cogdell, James W. ��21 Lami Dozo, Enrique J.��16 Eigenvalue Distribution Gyrya, Pavel��25 Cogolludo-Agustín, José of Large Random Lauter, Kristin ��21 H Ignacio��18 Matrices ��10 Lawther, R. ��24 Häfner, Dietrich��25 26

Order by Phone | 1-401-455-4000 or 1-800-321-4267 Index by Title and Author

Lectures on Gaussian Integral New Developments Richmond, Bettina�� 17 Topological Properties of Operators and Classical in Lie Theory and Its Rauzy Fractals �� 25 Richmond, Thomas �� 17 Groups�� 25 Applications�� 13 Topology of Algebraic Varieties Roberts, Fred S.�� 12 Lectures on Linear Partial Nikolai I. Lobachevsky, and Singularities�� 18 Differential Equations�� 5 Pangeometry�� 25 Robson, J. Chris�� 13 Toric Varieties�� 6 Lectures on Quantum Nonlinear Elliptic Partial S Towards Non-Abelian p-adic Mechanics for Mathematics Differential Equations�� 16 Saal, Linda�� 13 Hodge Theory in the Good Students�� 20 Reduction Case�� 24 O Sally, Judith D �� 7 Ledoux, Michel �� 15 Olsson, Martin C.�� 24 Two Kinds of Derived Sally, Paul J, Jr�� 7, 13 Lee, Kyung Bai�� 19 Categories, Koszul On Certain -Functions�� 21 L Saloff-Coste, Laurent�� 25 Duality, and Comodule- Levy, Lawrence S.�� 13 On Systems of Equations over Contramodule Scheepers, M.�� 19 Limit Operators, Collective Free Partially Commutative Correspondence �� 24 Compactness, and the Groups�� 24 Scheidler, Renate �� 21 Spectral Theory of Infinite U Schenck, Henry K.�� 6 Matrices �� 24 P Ueltschi, Daniel�� 20 Schwartz, Richard Evan�� 9 Lin, Fanghua �� 3 Pacini, Tommaso �� 24 The Ultimate Challenge�� 21 Schwendner, Alex�� 8 Lindner, Marko �� 24 Papadopoulos, Athanase�� 25 Ultrafilters across Seifert Fiberings �� 19 Little, John B. �� 6 Parashar, Deepak �� 25 Mathematics �� 19 Senger, Steven �� 17 Liu, Tiankai �� 8 Pastur, Leonid �� 10 Uncertainty Principles Associated to Pelaez, Pablo �� 25 Sepanski, Mark R.�� 14 Lledó, Fernando�� 15 Non-Degenerate Quadratic Sesiano, Jacques�� 14 Looijenga, Eduard�� 25 Perera, Francesc�� 15 Forms �� 25 Set Theory and Its Loubeau, E.�� 19 Poineau, Jérôme�� 25 Understanding Numbers Applications�� 19 in Elementary School Lovász, László �� 17 Pollack, Alan�� 19 Shahidi, Freydoon �� 14 Mathematics �� 7 Lozano-Robledo, Álvaro�� 8 Poncelet’s Theorem�� 19 Shahriari, Shahriar �� 17 v Lyons, Richard�� 14 Positive Definiteness of Functions with Applications Shcherbina, Mariya�� 10 Vaintrob, Dmitry�� 8 M to Operator Norm Siegel, Anne�� 25 Valdinoci, Enrico �� 16 Inequalities�� 24 Mahdavi, Kazem�� 16 Sims, Robert�� 20 Valuations and Differential Positselski, Leonid �� 24 Galois Groups �� 24 Manin, Yuri �� 16 Smith, Stephen D. �� 14 Prest, Mike�� 24 van der Geer, Gerard �� 25 Marchenko, Soibelman, Yan�� 20 Vladimir A.�� 12 Previato, Emma �� 18 Van Schaftingen, Jean�� 16 Solomon, Ronald�� 14 Marcolli, Matilde �� 20, 25 Pries, Rachel�� 21 van Suijlekom, Walter D. � 20 Spadaro, Matous ˇ ek, Jir ˇ í�� 17 Projections in Several Emanuele Nunzio�� 24 Vigny, Gabriel�� 25 Complex Variables�� 25 Measure and Integration�� 11 Spectral Graph Theory�� 17 W Q Milies, César Polcino �� 13 Spectral Theory and Geometric Ward, Thomas �� 16 Q-Valued Functions Milman, Emanuel�� 15 Analysis�� 15 Wedhorn, Torsten�� 25 Revisited�� 24 Milman, Mario�� 15 Spice, Loren�� 13 Weitsman, Jonathan�� 15 Quantum Field Theory �� 20 Minicozzi, William P., II�� 4 Sriram, M. S. �� 25 Willem, Michel�� 16 Quantum Groups and Mirror Symmetry and Noncommutative Stoltzfus, Neal �� 18 WIN—Women Tropical Geometry�� 20 Spaces �� 25 Sturm-Liouville Operators in Numbers�� 21 Möller, Martin�� 16 Quantum Mechanics for and Applications�� 12 Wu, Hung-Hsi�� 7 Mathematicians�� 20 Montaldo, S. �� 19 Symmetry for Y R Elliptic PDEs�� 16 Moree, Pieter�� 16 Yakubovskiı ˘, O. A. �� 20 Ramakrishnan, Dinakar�� 21 T Mostly Surfaces �� 9 Yeats, Karen�� 24 Ramasubramanian, K.�� 25 Takácˇ, Peter �� 16 Multiplicative Properties of the Yu, Jiu-Kang�� 21 Slice Filtration�� 25 Random Matrix Theory: Takhtajan, Leon A.�� 20 Yudovina, Elena�� 8 N Invariant Ensembles and Tantrasan ˙ graha of Universality�� 14 Nıˉlakantha Somayaˉjı ˉ�� 25 Z Neretin, Yurii A.�� 25 Raymond, Frank�� 19 Testerman, D. M.�� 24 Zharkov, Ilia�� 20 Neumann and Dirichlet Heat Kernels in Inner Uniform Rearranging Dyson-Schwinger Thirty-three Miniatures�� 17 Equations �� 24 Domains�� 25 Thuswaldner, Jörg M.�� 25 Rees, Mary�� 25 Neumann, Walter�� 18 Topalov, Peter �� 15 Renormalization and Effective Field Theory�� 10 27

Order Online | www.ams.org/bookstore index by Series

Poncelet's Theorem ��19 13 On Certain L-Functions ��21 DIMACS: Series in Discrete EMS Tracts in Mathematics Understanding Numbers in Elementary Mathematics and Theoretical (EMSTM) Colloquium Publications (COLL) School Mathematics ��7 Computer Science (DIMACS) This series includes advanced texts The Ultimate Challenge ��21 Each volume in the Colloquium This series includes conference and and monographs covering all fields in Publications series contains enduring workshop proceedings and volumes pure and applied mathematics. Tracts AMS Chelsea Publishing (CHEL) and important results from outstanding on education in discrete mathematics will give a reliable introduction and mathematicians worldwide, offering reference to special fields of current Following a centuries-old tradition and theoretical computer science. the finest in scholarly mathematical research. The books in the series will, of building on what has gone before, Volumes are derived from programs at publishing. These incomparable works, in most cases, be authored mono- mathematicians continue to mine and the Center for Discrete Mathematics from the turn of the century to the graphs, although edited volumes may utilize insights and results from the and Theoretical Computer Science, present, provide definitive treatment of be published if appropriate. They are classical literature. The mission of the a consortium of Rutgers University, some of mathematics’ most significant addressed to graduate students seeking AMS-Chelsea book series is to make Princeton University, AT&T results. (ISSN 0065-9258) Hardcover; access to research topics as well as to some of the most important classics Labs—Research, Alcatel-Lucent Bell reprints in softcover. the experts in the field working at the that were once out of print available to Laboratories, Cancer Institute of frontier of research. new generations of mathematicians and VOL. TITLE PAGE New Jersey (CINJ), NEC Laboratories America, and Telcordia Technologies graduate students. The series continues 58 Eisenstein Series and VOL. TITLE PAGE (with partners at Avaya Labs, HP Labs, the tradition of the original Chelsea Automorphic L-Functions ��14 14 Efficient Numerical Methods Publishing Company, founded by Aaron IBM Research, Microsoft Research, Georgia Institute of Technology, for 2Non-local Operators: Galuten, and contains many of its most Contemporary Mathematics -Matrix Compression, successful and recognized titles. Rensselaer Polytechnic Institute, and H (CONM) Stevens Institute of Technology). Algorithms and Analysis ��25 VOL. TITLE PAGE This series of high-quality, refereed Research at DIMACS includes discrete 373 Sturm-Liouville Operators Fields Institute Communications proceedings written by recognized and computational geometry, discrete (FIC) and Applications: Revised experts in their fields maintains high optimization, data structures and algo- Edition ��12 scientific standards. Volumes draw rithms, computational intractability, This series features proceedings and 370 Differential Topology ��19 from worldwide conferences and massive data sets, networks, graph lecture notes from the activities at 361 Combinatorial Problems and symposia sponsored by the American theory, combinatorics, computa- the Fields Institute for Research in Exercises: Second Edition ��17 Mathematical Society and other organi- tional number theory and cryptology, Mathematical Sciences in Toronto, zations. (ISSN 0271-4132) Softcover. discrete probability, recursive func- Ontario, Canada. The publications 241 Measure and Integration ��11 tion theory and mathematical logic, evolve from each year’s main program. VOL. TITLE PAGE Boolean functions, computational and Interdisciplinary titles emerge from Astérisque (AST) 545 Concentration, Functional mathematical biology, and compu- programs and workshops that discuss Astérisque, published by the Société Inequalities and Isoperimetry 15 tational algebra. Titles in this series applications of the mathematical Mathématique de France, consists of 544 New Developments in Lie are co-published with the Center for sciences in science, engineering, long papers of high quality, lecture Theory and Its Applications ��13 Discrete Mathematics and Theoretical industry, and business. (ISSN 1069- notes, and conference or seminar 543 Harmonic Analysis on Computer Science beginning with 5265) Hardcover. proceedings. It is sold in the current Reductive, p-adic Groups ��13 Volume 8. (ISSN 1052-1798) Hardcover; reprints VOL. TITLE PAGE year as separate issues or as a journal 542 Harmonic Maps and Differential subscription. The AMS distributes in softcover. 60 WIN—Women in Numbers: Geometry ��19 Research Directions in Number Astérisque in the U.S., Canada, and VOL. TITLE PAGE Mexico. Orders from other countries 541 Interactions Between Hyperbolic Theory ��21 should be sent to the SMF, Maison Geometry, Quantum Topology 76 BioMath in the Schools ��12 de la SMF, case 916-Luminy-F-13288 and Number Theory ��18 Graduate Studies in Mathematics Marseille cedex 09, France, or to 540 Nonlinear Elliptic Partial EMS Series of Congress Reports (GSM) Differential Equations ��16 (EMSSCR) Institut Henri Poincaré, 11 rue Pierre The volumes in this series are specifi- et Marie Curie, 75231 Paris cedex 05, 539 Combinatorics and Physics ��20 EMS Series of Congress Reports cally designed as graduate studies texts, France. Individual AMS member price 538 Topology of Algebraic Varieties publishes volumes originating from but are also suitable for recommended is listed. Members of SMF in North and Singularities ��18 conferences or seminars focusing on and/or supplemental course reading. America may purchase single back any field of pure or applied math- With appeal to both students and issues at a 30% discount from list price. 537 Groups, Algebras and Applications ��13 ematics. The individual volumes professors, these texts make ideal inde- (ISSN 0303-1179) Softcover. include an introduction to their subject pendent study resources. The breadth 536 Cross Disciplinary Advances in NO. TITLE PAGE and a review of the contributions in and depth of the series’ coverage make Quantum Computing ��16 336 Neumann and Dirichlet Heat this context. Articles are required to it an ideal acquisition for all academic 535 Spectral Theory and Geometric Kernels in Inner Uniform undergo a refereeing process and are libraries that support mathematics Analysis ��15 Domains ��25 accepted only if they contain a survey programs. (ISSN 1065-7338) Hardcover. 534 Aspects of Operator Algebras or significant results not published else- 335 Multiplicative Properties of the VOL. TITLE PAGE and Applications ��15 where in the literature. Slice Filtration ��25 124 Toric Varieties ��6 533 Set Theory and Its Applications 334 La Droite de VOL. TITLE PAGE ��19 123 Lectures on Linear Partial Berkovich Sur Z ��25 3 Classification of Algebraic Differential Equations ��5 532 Dynamical Numbers: Interplay Varieties ��25 between Dynamical Systems and 122 Algebraic Groups and CBMS Regional Conference Series Differential Galois Theory ��5 in Mathematics (CBMS) Number Theory ��16 EMS Series of Lectures in 531 Combinatorics and Graphs ��17 Mathematics (EMSSERLEC) 121 A Course in Minimal Surfaces ��4 Each monograph offers a written 530 Ultrafilters across Mathematics 120 A Basic Course in Partial account of lectures given by the This book series is aimed at students, Differential Equations ��4 author as principal speaker at a ��19 professional mathematicians and scien- 104 Algebra: Chapter 0 ��14 regional conference sponsored by the 529 Entropy and the Quantum ��20 tists. It publishes polished notes arising Conference Board of the Mathematical 528 Symmetry for Elliptic PDEs ��16 from seminars or lecture series in all 95 Quantum Mechanics for fields of pure and applied mathematics. Mathematicians ��20 Sciences and supported by the National 527 Mirror Symmetry and Tropical The individual volumes are intended to Science Foundation. The material in Geometry ��20 54 A Course in Convexity ��17 these lectures is accessible to nonspe- give a rapid and accessible introduction cialists. All individuals receive the Courant Lecture Notes (CLN) into their particular subject, guiding the Heritage of European individual member price. (ISSN 0160- audience to topics of current research Mathematics (EMSHEM) 7642) Softcover. This important series, co-published and the more advanced and specialized by the AMS and the Courant Institute literature. This series published by the European NO. TITLE PAGE of Mathematical Sciences at New Mathematical Society (EMS) features VOL. TITLE PAGE 92 Spectral Graph Theory ��17 York University, offers cutting-edge the selected or collected works research in mathematics and theo- 13 Lectures on Gaussian Integral of distinguished mathematicians. Clay Mathematics Proceedings retical computer science. NYU faculty Operators and Classical Groups Biographies of and correspondence (CMIP) and visitors have written most of the ��25 between outstanding mathematicians, volumes, which are primarily based as well as other texts of historic math- Each volume in this series is derived on graduate courses and minicourses ematical interest are also included. from lectures given at the annual Clay offered at the Institute. (ISSN 1529- VOL. TITLE PAGE Mathematics Institute summer schools 9031) Softcover. or other CMI conferences. The volumes 4 Nikolai I. Lobachevsky, offer clear, accessible introductions to VOL. TITLE PAGE Pangeometry ��25 areas of current research. This series 18 Random Matrix Theory: is co-published by the AMS and CMI. Invariant Ensembles and (ISSN 1534-6455) Softcover. Universality ��14 VOL. TITLE PAGE 1 Elliptic Partial Differential 14 Grassmannians, Moduli Spaces Equations: Second Edition ��3 28 and Vector Bundles ��18

Order by Phone | 1-401-455-4000 or 1-800-321-4267 Index by Series

Hindustan Book Agency (HIN) a 30% discount from list. (ISSN 0249- MSRI Mathematical Circles 56 The Erdo ˝ s Distance Problem �� 17 Titles published by Hindustan Book 633X) Softcover. Library (MCL) 53 Thirty-three Miniatures: Agency (New Delhi, India) include NO. TITLE PAGE Mathematical circles originated in Mathematical and Algorithmic Applications studies in advanced mathematics, in 123 Projections in Several Complex Eastern Europe in the 1930s, spreading of Linear Algebra �� 17 monographs, lecture notes, and/or Variables �� 25 to Western Europe, Aisa, and, even- conference proceedings, on current 47 Lectures on Quantum 122 Entropy of Meromorphic Maps tually, to North America. They are topics of interest. The books are distrib- Mechanics for Mathematics and Dynamics of Birational gatherings of motivated students uted worldwide except in India by the Students �� 20 Maps �� 25 looking for new challenges in math- AMS. Hardcover and softcover. ematics as well a deeper understanding 35 Galois Theory for Beginners: 121 A Fundamental Domain NO. TITLE PAGE V of the subject. Student circles are A Historical Perspective �� 14 for 3 �� 25 usually run by college professors, 48 Tantrasan ˙graha of Nı ˉ lakantha 120 Convergence des Polygones de schoolteachers, or even enthusiastic University Lecture Series (ULECT) Somaya ˉjı ˉ �� 25 Harder-Narasimhan �� 25 parents wishing to share their apprecia- Each book in this series focuses on an 119 Uncertainty Principles tion of and love for mathematics. While Mathematical Surveys and important and rapidly developing topic, Associated to Non-Degenerate solving problems is emphasized, the and is designed to give readers the most Monographs (SURV) Quadratic Forms �� 25 circles also pay considerable attention to mathematical ideas and techniques that current information on the subject area. This series of high-level monographs is 118 Topological Properties of Rauzy are broadly helpful. Some books in the series originated designed to meet the need for careful Fractals �� 25 from important lecture series given by expositions in research fields of current 117 Creation of Fermions by The idea of teacher mathematical circles outstanding mathematicians worldwide. interest. Each volume gives a survey Rotating Charged Black Holes 25 is more recent. Such circles are gather- (ISSN 1047-3998) Softcover. of the subject, along with a brief intro- ings for elementary and secondary duction to recent developments and Memoirs of the American school teachers where they may develop VOL. TITLE PAGE unsolved problems. (ISSN 0076-5376) effective approaches to teaching math- Mathematical Society (MEMO) 49 Inevitable Randomness in Hardcover; reprints in softcover. ematics, with a particular emphasis on Discrete Mathematics �� 17 problem solving. VOL. TITLE PAGE This series is devoted to the publication of research in all areas of pure The books in the series are suitable for Vieweg Advanced Lectures in 174 Hereditary Noetherian Prime and applied mathematics. Manuscripts leaders and participants in mathemat- Rings and Idealizers �� 13 Mathematics (VWALM) accepted for publication are similar ical circles. Parents of the participants 173 Geometric Approximation to those published in Transactions of in the student circles will also find the Vieweg Advanced Lectures in Algorithms �� 11 the American Mathematical Society books quite useful. The books come Mathematics is a softcover series repre- 172 The Classification of Finite and meet the same editorial require- from several sources: translations of senting notes from advanced graduate Simple Groups: Groups of ments. To qualify for publication, the suitable books from Russian or Eastern courses on current topics of interest. Characteristic 2 Type �� 14 manuscripts must be correct, new, European sources, books written in The AMS is exclusive distributor significant, well-written, and of interest English for this audience, and practical in North America. Vieweg Verlag 171 Eigenvalue Distribution of Large Publications are available worldwide Random Matrices �� 10 to a substantial number of mathemati- books for and written by organizers cians. Each issue contains either a of mathematical circles. The series from the AMS outside of Germany, 170 Renormalization and Effective single monograph or a group of related is copublished by the Mathematical Switzerland, Austria, and Japan. (ISSN Field Theory �� 10 papers. The series is also available by Sciences Research Institute and the 0932-7134). Softcover. 166 Seifert Fiberings �� 19 subscription. (Nos. 1-122: LC 52-42839) American Mathematical Society. (ISSN NO. TITLE PAGE (ISSN 0065-9266) Softcover. 149 Quantum Field Theory: 1944-8074) Softcover. 12 Algebraic Geometry I: A Tourist Guide for NO. TITLE PAGE VOL. TITLE PAGE Schemes. With Examples and Mathematicians �� 20 999 On Systems of Equations over 3 Geometry: A Guide Exercises �� 25 Mathematical World (MAWRLD) Free Partially Commutative for Teachers �� 7 Groups �� 24 Vieweg Aspects of Mathematics This accessible series brings the beauty 998 Valuations and Differential Pure and Applied Undergraduate (VWAM) and wonder of mathematics to the Galois Groups �� 24 Texts (AMSTEXT) The texts published in this series are advanced high school student, the 997 Positive Definiteness of intended for graduate students and all mathematics teacher, the scientist Intended for undergraduate post- Functions with Applications to mathematicians who wish to broaden or engineer, and the lay reader with calculus courses, the textbooks in this Operator Norm Inequalities �� 24 their research horizons or who simply a strong interest in mathematics. series, founded by the highly respected want to get a better idea of what is Mathematical World features well- 996 Two Kinds of Derived mathematician and educator, Paul J. going on in a given field. They are written, challenging expository works Categories, Koszul Duality, Sally, Jr., maintain the highest standards introductions to areas close to modern that illustrate the fascination and and Comodule-Contramodule of scholarship while being taught at research and prepare the reader for usefulness of mathematics. (ISSN Correspondence �� 24 universities throughout the US and a better understanding of research 1055-9426) 995 Rearranging Dyson-Schwinger abroad. papers. Many of the books can also be Equations �� 24 VOL. TITLE PAGE VOL. TITLE PAGE used to supplement graduate course 994 Fonction Zêta des Hauteurs des 27 An Introduction to the History 11 Algebra �� 14 programs. Editor for Vieweg’s Aspects Variétés Toriques non Déployées of Algebra: Solving Equations of Mathematics series is Klas Diedrich. �� 24 3 A Discrete Transition to from Mesopotamian Times to Advanced Mathematics �� 17 The AMS is exclusive distributor the Renaissance �� 14 993 Differential Forms on in North America. Vieweg Verlag Wasserstein Space and Infinite- Student Mathematical Library Publications are available worldwide from the AMS outside of Germany, Mémoires de la Société Dimensional Hamiltonian (STML) Mathématique de France Systems �� 24 Switzerland, Austria, and Japan. (ISSN 0179-2156). Hardcover. (SMFMEM) 992 Iwasawa Theory, Projective The AMS undergraduate series, the Modules, and Modular Student Mathematical Library, is for VOL. TITLE PAGE The Mémoires de la Société books that will spark students’ interests Representations �� 24 40 Quantum Groups and Mathématique de France is approxi- 991 Q-Valued Functions Revisited 24 in modern mathematics and increase their appreciation for research. Books Noncommutative Spaces: mately 450 pages in length per year p and is divided into 5 numbers. Each 990 Towards Non-Abelian -adic published in the series emphasize Perspectives on Quantum number is a monograph or a series Hodge Theory in the Good original topics and approaches. The Geometry �� 25 of articles on a single subject. The Reduction Case �� 24 step from mathematical coursework editorial committee has brought this 989 Limit Operators, Collective to mathematical research is one of the publication to the forefront in scien- Compactness, and the Spectral most important developments in a tific quality. Mémoires de la Société Theory of Infinite Matrices �� 24 mathematician’s career. To make the Mathématique de France is sold in the 988 Centres of Centralizers of transition successfully, the student current year as separate issues or as a Unipotent Elements in Simple must be motivated and interested in journal subscription. Distributed by the Algebraic Groups �� 24 doing mathematics rather than merely AMS in the U.S., Canada, and Mexico. learning it. They are suitable for honors 987 Definable Additive Categories: Orders from other countries should courses, upper-division seminars, Purity and Model Theory �� 24 be sent to the SMF, Maison de la SMF, reading courses, or self-study. (ISSN case 916-Luminy-F-13288 Marseille 1520-9121) cedex 09, France, or to Institut Henri VOL. TITLE PAGE Poincaré, 11 rue Pierre et Marie Curie, 75231 Paris cedex 05, France. Individual 60 Mostly Surfaces �� 9 AMS member price is listed. Members 59 Introduction to Representation of the SMF in North America receive Theory �� 8 58 Elliptic Curves, Modular Forms, and Their L-functions �� 8

Order Online | www.ams.org/bookstore ordering Information

ORDER ONLINE: member discount up to Email Notification of New AMS Publications www.ams.org/bookstore All AMS individual members 20% ORDER BY Mail: throughout the world and AMS Bookstore New Title Notification institutional members in North is a service made available by the AMS Download an order form at America are eligible for discounted for those who wish to receive email www.ams.org/bookstore/pspdf/orderform.pdf membership pricing on all AMS books. announcing new titles or AMS cata- and send with payment enclosed to: logs as soon as they become available booksTORe Plans American Mathematical Society on the AMS Bookstore. Sign up at P. O. Box 845904 The AMS offers a comprehensive www.ams.org/bookstore-email. Boston, MA 02284-5904 USA discount and stocking plan for quali- If using a credit card, please include fied retail bookstores in the U.S. and AMS Textbooks the name, number, and expiration date of Canada. For further details, contact the AND EXAM COPIES the card. AMS Commercial Accounts Group at 1-800-321-4AMS or send email to Find the right textbook for your course! ORDER BY Phone: [email protected]. The AMS publishes many high-quality For callers in the United States and Library Approval Plans books for use in the classroom. To Canada, the Society’s toll-free number view a comprehensive list of our AMS library approval plans are is 1-800-321-4AMS (4267). Callers best-selling textbooks, please visit currently offered by Blackwell’s Book outside the U.S. and Canada, please call www.ams.org/bookstore/textbooks. Services and Yankee Book Peddler. 1-401-455-4000. Business hours are Most of the titles are specifically designed 8:00 a.m. to 5:00 p.m., Eastern Time, Standing Orders as undergraduate or graduate texts but Monday through Friday, except on U.S. are also suitable for recommended holidays. Standing orders are accepted for most and/or supplemental course reading. When ordering by phone, book series offered by the Society. Pro Request a desk or exam copy by visiting forma invoices are sent to standing please use code UP71 www.ams.org/bookstore/exam-desk- order customers prior to the publica- request. tion of each new volume. Shipment is ORDER BY Fax: made upon receipt of payment. A new Pricing and Payment standing order at list or institutional Download an order form at • All pricing in U.S. dollars—please www.ams.org/bookstore/pspdf/orderform.pdf member price entitles the purchaser to acquire back volumes at a discount. remit in U.S. currency. Worldwide Fax: 1-401-455-4046 This discount will apply to a one- • Prices and publication dates are time purchase of ten or more back correct as of April 2011. Bank Transfers volumes in the book series if the order • Prices, special offers, and publication is placed within six months from the Citizens Bank dates are subject to change without date of the new standing order. Contact 1 Citizens Drive notice. the Member and Customer Services Riverside, RI 02915-4996 USA Department to begin a new standing • We accept orders by check, credit Bank ABA, Swift code, and Account order. card, or bank transfer. numbers or other inquiries and notifications about wire transfers should be directed to the Member and Customer ORDERS FROM OUTSIDE THE UNITED STATES Services Department at: macs-com@ Orders worldwide are accepted online at www.ams.org/bookstore ams.org. Automated Clearing House or through the following exclusive agents: (ACH) inquiries, authorization requests and notifications should be sent to: • Europe, Middle East, Africa: Eurospan Group [email protected]. • Japan: Maruzen Co. Ltd. (Tokyo), Neutrino Inc. (Tokyo) Transfers should contain name of payer • India: Hindustan Book Agency (New Delhi), India Book House (New Delhi), (no titles please) and reason for payment Segment Book Distributors (New Delhi) (pro forma number, membership dues, For book orders in SE Asia, China, South America, or other regions, etc.). Fax copy of transfer and order to: please contact the Member and Customer Services Department at 1-401-455-4046, Attn: Member and 1-401-455-4000 or send an email to [email protected] Customer Services Department; or send details of payment by email to: cust- [email protected]; or mail to Member and Customer Services Department, AMS, Change of Address? 201 Charles Street, Providence, RI Send an email to [email protected] 02904-2294 USA.

Need an order form? Visit www.ams.org/bookstore/pspdf/orderform.pdf 30

Order by Phone | 1-401-455-4000 or 1-800-321-4267 AMS on Social Networks

“Like” us—and As part of the Society’s commitment find others who to the open flow of communication “Like” the AMS—at and community engagement, the AMS our AMS Facebook uses several social networking tools page. to supplement the channels currently in place for members, press, and the general public. We invite you to follow and share content of interest. We invite you to use these networks to Follow us on Twitter. find news, updates on AMS programs, commentary, and contests; to connect with others who have similar interests; and to communicate with each other and the AMS. Link from www.ams.org.

Set up an RSS feed to receive content electronically when- ever it is updated on the ams.org website. www.ams.org/about-us/social

Subscribe to our videos, share them, comment on them and embed them in your own sites from the AMS YouTube channel.