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Distributions D-Modules, Perverse Sheaves, Partial Diff erential Equations Theory and Applications and Representation Theory Second Edition EMMANUELE DIBENEDETTO, Vanderbilt University, JOHANNES J. DUISTERMAAT; JOHAN A.C. KOLK, RYOSHI HOTTA,Okayama University of Science, Japan; Nashville, TN, USA both Universiteit Utrecht, The Netherlands KIYOSHI TAKEUCHI, University of Tsukuba, Japan; TOSHIYUKI TANISAKI, Osaka City University, Japan This text is a concise, application-oriented “The author’s intent is to present an elementary introduction to the theory of distributions. It D-modules continues to be an active area of introduction to pdes... In contrast to other elementary presents distributions as a natural method of stimulating research in such mathematical areas textbooks on pdes...much more material is presented analysis from both a mathematical and physical as algebra, analysis, differential equations, and on the three basic equations: Laplace’s equation, the point of view. The discussion emphasizes representation theory. Key to D-modules, Perverse heat and wave equations... The text is complemented applications to the general study of linear partial Sheaves, and Representation Theory is the authors’ by numerous exercises and hints to proofs.” differential equations. essential algebraic-analytic approach to the theory, —MATHEMATICAL REVIEWS which connects D-modules to representation theory The topics include an introduction to distributions, and other areas of mathematics. Signifi cant concepts Large parts of this revised second edition have been differentiation, convergence, and convolution of and topics that have emerged over the last few streamlined and rewritten to incorporate years of distributions, as well as Fourier transformations decades are presented, including a treatment of the classroom feedback, correct errors, and improve and spaces of distributions having special theory of holonomic D-modules, perverse sheaves, clarity. properties. The applications relate the theory to the all-important Riemann-Hilbert correspondence, 2ND ED. 2008/APPROX. 340 PP., 10 ILLUS./HARDCOVER solutions of partial differential equations occurring Hodge modules, and the solution to the Kazhdan- ISBN 9780817645519/$59.95 TENT. in physics, for instance, in mechanics, optics, Lusztig conjecture using D-module theory. 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Main can serve as a text for advanced undergraduates JOACHIM KOCK, Universitat Autònoma de Barcelona, Spain; ISRAEL VAINSENCHER, Universidade Federal de statistical concepts considered are point and interval and graduate students in mathematics, physics, Minas Gerais, Pampulha - Belo Horizonte, Brazil estimates, hypothesis testing, power function, various engineering, and the natural sciences, as well as an statistical tests: z, t, chi-square and Kolmogorov- excellent reference for applied mathematicians and “The book seems to be ideally designed for a semester Smirnov. mathematical physicists. course or ambitious self-study.” —MATHSCINET 2007/X, 318 PP., 44 ILLUS./SOFTCOVER 2008/APPROX. 350 PP. 50 ILLUS./HARDCOVER ISBN 9780817644970/$39.95 ISBN 9780817645267/$59.95 TENT. This book is an elementary introduction to stable maps and quantum cohomology, starting with an introduction Knot Theory and Its to stable pointed curves, and culminating with a proof New Edition of the associativity of the quantum product. 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