New Publications Offered by the AMS Algebra and Algebraic Modular Calabi-Yau FIELDS INSTITUTE MONOGRAPHS Threefolds Geometry THE FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES Christian Meyer, Johannes Modular Gutenberg University, Mainz, Calabi-Yau Germany Recent Progress in Threefolds CONTEMPORARY MATHEMATICS Arithmetic and Christian Meyer This book discusses the connection 386 between Calabi-Yau threefolds and THEMAT A IC M A L N ΤΡΗΤΟΣ ΜΗ ΕΙΣΙΤΩ A S O C I C R I E E ΑΓΕΩΜΕ T M Y A FO 8 modular forms. It presents the general U 8 Recent Progress in Algebraic Geometry NDED 18 American Mathematical Society Arithmetic and theory and brings together the known Algebraic Geometry Yasuyuki Kachi, University of results. Hundreds of new examples Yasuyuki Kachi Kansas, Lawrence, KS, and S. are given of rigid and non-rigid Calabi- S. B. Mulay Pavlos Tzermias B. Mulay and Pavlos Yau threefolds, and the construction of correspondences Editors EM between them leads to conjectures about the modular forms TH AT A IC M A L N ΤΡΗΤΟΣ ΜΗ ΕΙΣΙΤΩ A S O C Tzermias, University of I C R I E E ΑΓΕΩΜΕ T M Y A F OU 88 NDED 18 Tennessee, Knoxville, TN, involved. The author has compiled tables of newforms of weight four and large levels, which are included in the American Mathematical Society Editors appendix. This proceedings volume resulted The great variety of new examples as well as the tables of from the John H. Barrett Memorial Lecture Series held at the newforms makes this volume a valuable resource for graduate University of Tennessee (Knoxville). The articles reflect recent students and researchers interested in algebraic geometry and developments in algebraic geometry. It is suitable for graduate arithmetic algebraic geometry. students and researchers interested in algebra and algebraic This item will also be of interest to those working in analysis. geometry. Contents: Arithmetic on Calabi-Yau threefolds; Fibre products Contents: F. Campana and Q. Zhang, Compact Kähler of elliptic surfaces; Quintics in P4; Double octics; Other threefolds of π1-general type; S. D. Cutkosky and L. Ghezzi, examples; Tables, correspondences, conclusions; Completions of valuation rings; A. Ebin, D. Hur, A. Katz, and Arrangements of eight planes; Modular double octics; Tables V. Shchogolev, A new construction of maximal curves; of weight two and weight four newforms; Bibliography; Index. S. J. Kovács, Strong non-isotriviality and rigidity; S. J. Kovács, Spectral sequences associated to morphisms of locally free Fields Institute Monographs, Volume 22 sheaves; T. Luo and Q. Zhang, Holomorphic forms on November 2005, 194 pages, Hardcover, ISBN 0-8218-3908-X, threefolds; K. Matsuki, A note on toroidalization: The problem 2000 Mathematics Subject Classification: 14J32, 14G10, 11G25; of resolution of singularities of morphisms in the logarithmic 14E05, 14G15, 11G40, All AMS members US$47, List US$59, category; R. J. Pries, Jacobians of quotients of Artin-Schreier Order code FIM/22 curves; K. Schwede, Gluing schemes and a scheme without closed points. Contemporary Mathematics, Volume 386 November 2005, 172 pages, Softcover, ISBN 0-8218-3401-0, LC 2005052406, 2000 Mathematics Subject Classification: 14–XX, All AMS members US$47, List US$59, Order code CONM/386 NOVEMBER 2005 NOTICES OF THE AMS 1265 New Publications Offered by the AMS Kleinian Groups groups; Banach algebras; Quantum groups; Root systems; EMOIRS Banach spaces; Convex sets; The algebra B(H); Bibliography; M of the American Mathematical Society which Are Limits of Index. Volume 177 Number 834 Geometrically Finite Translations of Mathematical Monographs, Volume 228 Kleinian Groups which Are Limits of Geometrically Groups September 2005, approximately 448 pages, Hardcover, ISBN 0- Finite Groups 8218-3731-1, 2000 Mathematics Subject Classification: 20–01, Ken’ichi Ohshika, Osaka 20Cxx; 17B10, 20G05, 20G42, All AMS members US$103, List Ken’ichi Ohshika US$129, Order code MMONO/228 THEMAT A IC University, Japan M A L N A S O C I C R I E E T M Y A F OU 88 NDED 18 This item will also be of interest to American Mathematical Society those working in geometry and topology. Contents: Preliminaries; Statements of theorems; Characteristic compression bodies; The Masur Analysis domain and Ahlfors’ conjecture; Branched covers and geometric limit; Non-realizable measured laminations; Strong convergence of function groups; Proof of the main theorem; The Second Duals of Bibliography; Index. EMOIRS M of the American Mathematical Society Beurling Algebras Memoirs of the American Mathematical Society, Volume 177, Volume 177 Number 836 Number 834 The Second Duals of H. G. Dales, University of August 2005, 116 pages, Softcover, ISBN 0-8218-3772-9, LC Beurling Algebras Leeds, England, and A. T.-M. 2005048026, 2000 Mathematics Subject Classification: 57M50, Lau, University of Alberta, 30F40, Individual member US$35, List US$58, Institutional H. G. Dales A. T.-M. Lau Edmonton, Alberta, Canada member US$46, Order code MEMO/177/834 THEMAT A IC M A L N A S O C I C R I E E T M Y A F OU 88 NDED 18 Contents: Introduction; Definitions and preliminary results; Repeated American Mathematical Society Principal Structures limit conditions; Examples; Introverted Translations of subspaces; Banach algebras of MATHEMATICAL operators; Beurling algebras; The MONOGRAPHS and Methods of second dual of 1(G, ω); Algebras on discrete, Abelian groups; Volume 228 Representation Beurling algebras on F2; Topological centres of duals of 1 Principal Theory introverted subspaces; The second dual of L (G, ω); Structures and Derivations into second duals; Open questions; Bibliography; Methods of D. Zhelobenko, Moscow, Index; Index of symbols. Representation Theory Russia Memoirs of the American Mathematical Society, Volume 177, D. Zhelobenko Number 836 The main topic of this book can be THEMAT A IC M A L N ΤΡΗΤΟΣ ΜΗ ΕΙΣΙΤΩ A S O C I C R I E E ΑΓΕΩΜΕ T Y M American Mathematical Society A F 88 OU 18 August 2005, 191 pages, Softcover, ISBN 0-8218-3774-5, LC NDED described as the theory of algebraic and topological structures admitting 2005048020, 2000 Mathematics Subject Classification: 43A10, natural representations by operators 43A20; 46J10, Individual member US$40, List US$66, in vector spaces. These structures include topological Institutional member US$53, Order code MEMO/177/836 algebras, Lie algebras, topological groups, and Lie groups. The book is divided into three parts. Part I surveys general facts for beginners, including linear algebra and functional analysis. Part II considers associative algebras, Lie algebras, topological groups, and Lie groups, along with some aspects Differential Equations of ring theory and the theory of algebraic groups. The author provides a detailed account of classical results in related branches of mathematics, such as invariant integration and Lie’s theory of connections between Lie groups and Lie American Mathematical Society Selected Papers on algebras. Part III discusses semisimple Lie algebras and Lie TRANSLATIONS groups, Banach algebras, and quantum groups. Series 2 • Volume 215 Differential Advances in the Mathematical Sciences This is a useful text for a wide range of specialists, including Selected Papers Equations and graduate students and researchers working in mathematical on Differential Analysis physics and specialists interested in modern representation Equations theory. It is suitable for independent study or supplementary and Analysis This volume contains translations of reading. papers that originally appeared in the Also available from the AMS by this acclaimed author is Japanese journal Su¯gaku. The papers Compact Lie Groups and Their Representations. range over a variety of topics, THEMAT A IC M A L N ΤΡΗΤΟΣ ΜΗ ΕΙΣΙΤΩ A S O C I C R I E E ΑΓΕΩΜΕ T American Mathematical Society Y M A including differential equations with F O 88 Contents: Introduction: Basic notions; General theory: UNDED 18 free boundary, singular integral Associative algebras; Lie algebras; Topological groups; Lie operators, operator algebras, and groups; Special topics: Semisimple Lie algebras; Semisimple Lie 1266 NOTICES OF THE AMS VOLUME 52, NUMBER 10 New Publications Offered by the AMS relations between the Brownian motion on a manifold with This item will also be of interest to those working in analysis. function theory. Contents: Part 1. Existence and uniqueness problems: First The volume is suitable for graduate students and research order systems; Scalar initial value problems; Part 2. Regular mathematicians interested in analysis and differential boundary value problems: Two-point regular boundary value equations. problems; Regular self-adjoint problems; Regular left-definite This item will also be of interest to those working in analysis. and indefinite problems; Part 3. Oscillation and singular existence problems: Oscillation; The limit-point, limit-circle Contents: G. S. Weiss, Regularity in free boundary problems; dichotomy; Singular initial value problems; Part 4. Singular S. Sakaguchi, Behavior of spatial critical points and zeros of boundary value problems: Two-point singular boundary value solutions of diffusion equations; H. Aikawa, Martin boundary problems; Singular self-adjoint problems; Singular indefinite and boundary Harnack principle for non-smooth domains; problems; Singular left-definite problems; Part 5. Examples S. Sato, Singular integrals and Littlewood-Paley functions; and other topics: Two intervals; Examples; Notation; Comments A. Kasue, Convergence of metric measure spaces and energy on some topics not covered;