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Nonlinear Partial Fourier–Mukai and Nahm Stable Homotopy Around the Diff erential Equations Transforms in Geometry and Arf-Kervaire Invariant Asymptotic Behavior of Solutions and Mathematical Physics VICTOR P. SNAITH, University of Sheffi eld, UK Self-Similar Solutions CLAUDIO BARTOCCI, Università degli Studi di Genova, This monograph describes important techniques MI-HO GIGA; YOSHIKAZU GIGA, both Giga Laboratory, Italy; UGO BRUZZO, SISSA, Trieste, Italy; DANIEL of stable homotopy theory, both classical and new, HERNANDEZ RUIPEREZ, Universidad de Salamanca, Spain University of Tokyo, Japan; JÜRGEN SAAL, University of applying them to the long-standing unsolved problem Konstanz, Germany This book examines the differential-geometric of the existence of framed manifolds with odd This work will serve as an excellent fi rst course constructions of (Nahm) as well as the algebro- Arf-Kervaire invariant. Opening with an account of the in modern analysis. Key topics in nonlinear PDEs geometric approach to (Fourier–Mukai functors) necessary algebraic topology background, the book as well as several fundamental tools and methods transforms in geometry and math physics. Also proceeds in a quasi-historical manner drawing from are presented; few prerequisites are required of included is a considerable amount of material the author’s contributions over several decades. A new the reader. Challenging exercises, examples, and scattered in the literature and not systematically technique entitled “upper triangular technology” is illustrations help explain the rigorous analytic basis organized in any existing textbook or monograph. introduced, which enables the author to relate Adams for the Navier–Stokes equations, mean curvature fl ow operations to Steenrod operations and thereby to equations, and other important equations describing 2009/APPROX. 300 PP./HARDCOVER recover most of the important classical Arf-Kervaire real phenomena. The main focus of the text is on ISBN 9780817632465/$74.95 TENT. invariant results. The fi nal chapter briefl y relates the PROGRESS IN MATHEMATICS showing how self-similar solutions are useful in book to the contemporary motivic stable homotopy studying the behavior of solutions of nonlinear PDEs, theory of Morel-Voevodsky. especially those of parabolic type. Number Theory 2009/APPROX. 250 PP./HARDCOVER 2009/APPROX. 350 PP., 20 ILLUS./HARDCOVER Structures, Examples, and Problems ISBN 9783764399030/$79.95 TENT. ISBN 9780817641733/$99.00 TENT. TITU ANDREESCU, The University of Texas at Dallas, PROGRESS IN MATHEMATICS Richardson, TX, USA; DORIN ANDRICA, ‘Babes-Bolyai’ Spectral Methods in University, Cluj-Napoca, Romania Representation Theory This introductory textbook takes a problem-solving Surface Superconductivity approach to number theory, situating each concept of Algebraic Groups and SØREN FOURNAIS, University of Aarhus, Denmark; within the framework of an example or a problem for Quantum Groups BERNARD HELFFER, Université Paris-Sud and CNRS, solving. Starting with the essentials, the text covers France AKIHIKO GYOJA, Nagoya University, Nagoya, Japan; divisibility, unique factorization, modular arithmetic HIRAKU NAKAJIMA, Kyoto University, Kyoto, Japan; These two expert researchers in the fi eld present a and the Chinese Remainder Theorem, Diophantine KEN-ICHI SHINODA, Sophia University, Tokyo, Japan; comprehensive treatment of key results concerning equations, binomial coeffi cients, Fermat and Mersenne TOSHIAKI SHOJI, Nagoya University, Nagoya, Japan; primes and other special numbers, special sequences, TOSHIYUKI TANISAKI, Osaka City University, Osaka, the Ginzburg-Landau (GL) functional. Spectral Methods Japan (Eds.) in Surface Superconductivity examines in detail the and problems of density. Included are sections on two- and three-dimensional cases of the GL functional mathematical induction and the pigeonhole principle, This volume contains invited articles by top notch as they pertain to superconductivity. Also, instances of as well as a discussion of other number systems. experts who focus on such topics as modular large GL parameter kappa are covered, and a variety of representations of algebraic groups, representations 2009/APPROX. 370 PP., 150 ILLUS./HARDCOVER of quantum groups and crystal bases, representations exercises and open problems are discussed to further ISBN 9780817632458/$59.95 TENT. the reader’s understanding of the material. of affi ne Lie algebras, representations of affi ne Hecke algebras, modular or ordinary representations of fi nite 2009/APPROX. 300 PP./HARDCOVER A Lost Mathematician, reductive groups, and representations of complex ISBN 9780817647964/$79.95 TENT. refl ection groups and associated Hecke algebras. PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS Takeo Nakasawa Invited contributors include: H.H. Andersen; AND THEIR APPLICATIONS, VOL. 77 The Forgotten Father of Matroid Theory T. Arakawa; S. Ariki; J. Du; M. Geck; V. Ginzburg; HIROKAZU NISHIMURA, Tsukuba University, Japan; J.C. Jantzen; S;J. Kang; M. Kashiwara; S. Kato; SUSUMU KURODA, Passau, Germany (Eds.) Advances in Phase G.I. Lehrer; G. Lusztig; I. Mirkovic; H. Miyachi; Space Analysis of Partial Matroid theory was invented independently by two H. Nakajima; T. Nakashima; R. Rouquier; D. Sagaki; mathematicians in the 1930s, namely, Hassler Whitney Y. Saito; O. Schiffmann; T. Suzuki; T. Tanisaki; and Diff erential Equations in USA and Takeo Nakasawa in Japan. The former is J. Xiao. In Honor of Ferruccio Colombini’s well known, but unfortunately the latter had remained anonymous until a decade or two ago. 2009/APPROX. 450 PP./HARDCOVER 60th Birthday ISBN 9780817646967/$99.00 TENT. ANTONIO BOVE, University of Bologna, Italy; This book is structured in four parts: the fi rst part PROGRESS IN MATHEMATICS DANIELE DEL SANTO, University of Trieste, Italy; consists of Nakasawa’s four German papers and the M.K. VENKATESHA MURTHY, University of Pisa, Italy second part contains their English translations. The (Eds.) third part is devoted to an explanation of Nakasawa’s 2009/APPROX. 400 PP./HARDCOVER life and his times, and the fourth part deals with the ISBN 9780817648602/$119.00 TENT. comparison between the two fathers of matroid theory. PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS 2009/APPROX. 150 PP./HARDCOVER AND THEIR APPLICATIONS ISBN 9783764385729/$69.95

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