Notices of the American Mathematical Society ISSN 0002-9920 ABCD springer.com New and Noteworthy from Springer Quadratic Diophantine Equations Fibonacci’s De Practica T. Andreescu , University of Dallas, Dallas, TX, USA; D. Andrica , Geometrie University Cluj-Napoca, Romania B. Hughes , Sherman Oaks, CA, USA This text treats the classical theory of quadratic diophantine Leonardo da Pisa, better known as of the American Mathematical Society equations and guides the reader through the last two decades of Fibonacci, selected the most useful parts December 2007 Volume 54, Number 11 computational techniques and progress in the area. The of Greco-Arabic geometry for the book De presentation features two basic methods to investigate and Practica Geometrie. This translation is a motivate the study of quadratic diophantine equations: the theories reconstruction of the book as the author of continued fractions and quadratic fi elds. 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Softcover ISBN 978-0-387-74646-3 7 $19.95 Easy Ways to Order for the Americas 7 Write: Springer Order Department, PO Box 2485, Secaucus, NJ 07096-2485, USA 7 Call: (toll free) 1-800-SPRINGER 7 Fax: +1(201)348-4505 7 Email: [email protected] or for outside the Americas 7 Write: Springer Distribution Center GmbH, Haberstrasse 7, 69126 Heidelberg, Germany 7 Call: +49 (0) 6221-345-4301 7 Fax : +49 (0) 6221-345-4229 Email: [email protected] Prices are subject to change without notice. All prices are net prices. 7 7 013369x From the Museum of Associahedra (see page 1516) Trim: 8.25" x 10.75" 144 pages on 40 lb Cougar Opaque • Spine: 1/4" • Print Cover on 9pt Carolina ,!4%8 ,!4%8 ,!4%8 Pro New & Forthcoming from Birkhäuser Winner of the Ferran Sunyer i Balaguer Prize 2007 Spectral Theory of Infi nite- The Theory of the Top Area Hyperbolic Surfaces Volume I: Introduction to the Kinematics Determinantal Ideals DAVID BORTHWICK, Emory University, Atlanta, GA, USA and Kinetics of the Top ROSA M. MIRÓ-ROIG, Universitat de Barcelona, Spain FELIX KLEIN; ARNOLD SOMMERFELD This book introduces geometric spectral theory This comprehensive overview of determinantal ideals in the context of infi nite-area Riemann surfaces, Translated by RAYMOND J. NAGEM and GUIDO SANDRI, both Boston University, MA, USA includes an analysis of the latest results in the fi eld. providing a comprehensive account of dramatic The author develops new insights into addressing and recent developments in the fi eld. The spectral theory The lecture series on The Theory of the Top was solving open problems in liaison theory and Hilbert of hyperbolic surfaces is a point of intersection for originally given as a dedication to Göttingen University schemes. Three principal problems are addressed a great variety of areas, including quantum physics, by Felix Klein in 1895, but has since found broader in the book: CI-liaison class and G-liaison class discrete groups, differential geometry, number theory, appeal. This volume is the fi rst of a series of four self- of standard determinantal ideals; the multiplicity complex analysis, spectral theory, and ergodic theory. contained English translations that provide insights conjecture for standard determinantal ideals; and The book highlights these connections, at a level into kinetic theory and kinematics, with a focus on unobstructedness and dimension of families of accessible to graduate students and researchers from providing background material and basic theoretical standard determinantal ideals. a wide range of fi elds. concepts. 2008/APPROX. 155 PP./HARDCOVER Topics covered include an introduction to the 2008/APPROX. 315 PP., 159 ILLUS./HARDCOVER ISBN 9783764385347/$54.95 geometry of hyperbolic surfaces, analysis of the ISBN 9780817647209/$59.95 TENT. PROGRESS IN MATHEMATICS, VOL. 264 resolvent of the Laplacian, characterization of the spectrum, scattering theory, resonances and scattering Winner of the Ferran Sunyer i poles, the Selberg zeta function, the Poisson formula, The Maximum Principle Balaguer Prize 2006 distribution of resonances, the inverse scattering PATRIZIA PUCCI, Università degli Studi di Perugia, Italy; problem, Patterson–Sullivan theory, and the dynamical JAMES SERRIN, University of Minnesota, MN, USA Holomorphic Morse Inequalities approach to the zeta function. Maximum principles are fundamental results in and Bergman Kernels 2008/XII, 356 PP., 10 ILLUS./HARDCOVER the theory of second order elliptic equations. This XIAONAN MA, Ecole Polytechnique, Paris, France; ISBN 9780817645243/$59.95 principle lends itself to a quite remarkable number GEORGE MARINESCU, University of Köln, Germany PROGRESS IN MATHEMATICS, VOL. 256 of subtle uses when combined appropriately with other notions. Intended for a wide audience, this book This book is a self-contained and unifi ed approach to provides a clear and comprehensive explanation of the holomorphic Morse inequalities and the asymptotic Nonlinear Oscillations of various maximum principles available in elliptic theory, expansion of the Bergman kernel on manifolds utilizing Hamiltonian PDEs beginning for linear equations and progressing to the heat kernel. The main tool used in the work is the MASSIMILIANO BERTI, Università degli Studi di Napoli recent work on nonlinear and singular equations. analytic localization technique in local index theory ‘Federico II’, Italia developed by Bismut–Lebeau. Highlighting the most 2007/X, 234 PP./HARDCOVER recent results in the fi eld for the fi rst time, the author This monograph presents recent existence results ISBN 9783764381448/$64.95 presents various applications and provides new of nonlinear oscillations of Hamiltonian PDEs, PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS perspectives on several active areas of research in particularly of periodic solutions for completely AND THEIR APPLICATIONS, VOL. 73 complex, Kähler and symplectic geometry. resonant nonlinear wave equations. After introducing the reader to classical fi nite- 2007/XIII, 422 PP./HARDCOVER Walks on Ordinals and Their ISBN 9783764380960/$79.95 dimensional dynamical system theory, including the Characteristics Weinstein–Moser and Fadell–Rabinowitz bifurcation PROGRESS IN MATHEMATICS, VOL. 254 STEVO TODORCEVIC, Université Paris VII - CNRS, Paris, results, the author develops an analogous theory for France and University of Toronto,