American Mathematical Society
Advances in quantum computation; proceedings.
Editors Mahdavi and Koslover (mathematics, U. of Texas at Tyler) have collected these papers from a conference on representation theory, quantum field theory, category theory, mathematical physics and quantum information that was held in Texas in 2007. Topics for students and researchers include mathematical formulas of atom trap quantum gates, Poisson algebras and Yang-Baxter equations and topological order and entanglement. The contractions of matchgate tensor networks on non-planar graphs are also discussed. (Annotation ©2009 Book News Inc. Portland, OR)
Algebraic analysis and around in honor of Professor Masaki Kashiwara's 60th birthday; proceedings.
Nine of the 11 papers were presented by invited speakers at the conference, and the other two were invited into the volume. The topics include the Bender-Wu analysis and the Voros theory, the spherical case of local geometric Langlands correspondence, classifying spaces of degenerating mixed Hodge structures, good formal structure for meromorphic flat connections on smooth projective surfaces, and Quillen's relative Chern character. There is no index. Distributed in the US by American Mathematical Society. (Annotation ©2009 Book News Inc. Portland, OR)
Algebraic geometry; 2v.
The Institute was three weeks long, and with 513 mathematicians attending might have been the largest algebraic geometry conference in history. The first week was devoted to moduli problems and the interactions between algebraic geometry, symplectic geometry, and string theory. The topic of the second week was classical algebraic geometry with a focus on birational geometry. Arithmetic geometry and characteristic p methods took up the final week. The 28 papers in these proceedings include the plenary lectures, the Clay lectures, and several surveys related to seminar talks. Among the topics are the crepant resolution conjecture, the global geometry of the moduli space of curves, axiomatic Gromov-Witten theory and applications, a global overview of higher and derived stacks, jet schemes and similarities, the geometry and topology of symplectic varieties, a young person's guide to moduli of higher dimensional varieties, and weak approximation for hypersurfaces of low degree. The two volumes are paged together, and not indexed at all. (Annotation ©2009 Book News Inc. Portland, OR)
Algebras, representations, and applications; proceedings.
Contributions from a 2007 conference on Algebras, Representations, and Applications held in Brazil to commemorate mathematician Ivan Shestakov's 60th birthday are included in this volume for students and researchers working with the Theory of Lie, Jordan algebras, superalgebras and quantum rings. Editors Futorny (mathematics, IME-USP, Brazil), Kac (mathematics, Massachusetts Institute of Technology), Kashuba (mathematics, IME-USP, Brazil) and Zelmanov (mathematics, U. of California, San Diego) have gathered papers on such topics as derived categories for algebras with radical square zero, properties of semisimple Hopf algebras and Akivis superalgebras. A new proof of Itô's theorem in honor of Shestakov is included. (Annotation ©2009 Book News Inc. Portland, OR)
Communicating mathematics; proceedings.
This collection of 17 papers honors mathematician Joseph Gallian's work in teaching mathematics to undergraduates by collecting 14 papers that are generally expository in nature and accessible to a general mathematics audience from first-year graduate students on up. Topics include orthogonal matrices and wireless communications, probabilistic expectations on unstructured spaces, higher order necessary conditions in smooth constrained optimization, Hamiltonian paths and hyperbolic patterns, fair allocation methods for coalition games, sums-of-squares formulas, product-free subsets of groups, generalizations of product- free subsets, and vertex algebras and twisted bialgebras. (Annotation ©2009 Book News Inc. Portland, OR)
A course in approximation theory.
Written for graduate students in mathematics, physics, engineering and computer science, this textbook examines modern approximation theory and emphasizes its applications to multiple variables. Cheney (mathematics, U. of Texas, Austin) and Light (mathematics, U. of Leicester, UK) discuss the fundamentals and offer 438 practical problems in approximation theory that deal with projections, interpolation paradigms, positive definite functions, tomography, artificial neural networks and wavelets. The interpolation theorems of Schoenberg and Micchelli are also addressed. (Annotation ©2009 Book News Inc. Portland, OR)
Functional analysis and complex analysis; proceedings.
The interplay between the two methods has led to new results in a number of areas, and the mathematicians here use the new tools to describe extension properties of functions on real analytic varieties, and treat real analytic composition operations and prove the results on the non-existence of bases in spaces of real analytic functions. Among the 12 topics are Vyacheslav Zakharyuta's complex analysis, convolution operators on quasi-analytic classes of Roumieu type, connectedness in the pluri-fine topology, the analyticity and propagation of pluri-sub-harmonic singularities, and invertibility for Fréchet valued real analytic functions. No index is provided. (Annotation ©2009 Book News Inc. Portland, OR)
Groups of diffeomorphisms in honor of Shigeyuki Morita on the occasion of his 60th birthday; proceedings.
Presented by chief editor Mitsumatsu (Chuo U., Japan) and colleagues in honor of topologist Shigeyuki Morita, this volume collects six expository articles and 17 research articles concerned with the study of groups of diffeomorphisms and related topics. The expository articles discuss asymptotic geometry of foliations and pseudo-Anosov flows, Pontrjagin class and higher torsion of sphere bundles, L2-torsion invariants and the Magnus representation of the mapping class group, parameterized Gromov-Witten invariants and topology of symplectomorphism groups, mapping class actions on surface group completions, and Johnson's homomorphisms and the rational cohomology of subgroups of the mapping class groups. Among the topics discussed by the research articles are symplectic Heegaard splittings and linked abelian groups, differential characters and the Steenrod squares, relative weight filtrations on completions of mapping class groups, symplectic automorphism groups of nilpotent quotient of fundamental groups of surfaces, and new examples of elements in the kernel of the Magnus representation of the Torelli groups. Distributed in the US by the American Mathematical Society. (Annotation ©2009 Book News Inc. Portland, OR)
Introduction to fourier analysis and wavelets.
Pinsky (Northwestern U.) offers a self-contained treatment of classical Fourier analysis for upper undergraduate or beginning graduate students who are familiar with the rudiments of Lebesgue measure and integral on the real line. His approach is mostly classical and concrete, preferring explicit calculations to existential arguments. Diligent readers, he says, should be able to complete all of the 175 exercises. He explains Fourier series on the circle, Fourier transforms on the line and space, Fourier analysis in L<I>P spaces, the Poisson summation formula and multiple Fourier series, applications to probability theory, and a gentle introduction to wavelets. (Annotation ©2009 Book News Inc. Portland, OR)
Layer potential techniques in spectral analysis.
Written for researchers and students working with partial differential equations, integral equations and inverse problems, this textbook provides an asymptotic theory for eigenvalue problems that can be applied to band gap structures and the optimal design of photonic and phononic crystals. Ammari (Director of Research, CNRS, Institute Langevin, LOA), Kang (mathematics, Inha U., Korea) and Lee (mathematical sciences, Seoul National U., Korea) review the Gohberg and Sigal Theory before presenting eigenvalue perturbation problems and applications for Laplacian and Lamé systems. Engineering and physics researchers may also find these theories useful when dealing with layer potential techniques. (Annotation ©2009 Book News Inc. Portland, OR)
Lectures on quantum mechanics for mathematical students.
Faddeeva and Yakubovskii used these lectures to teach the principles of quantum mechanics to mathematics students. Now translated into English for classroom use, this text presupposes a solid math background but not extensive knowledge of mechanics or physics. Lectures include Heisenberg equations, eigenfunctions, scattering, one-dimensional particles and perturbation theory among others. (Annotation ©2009 Book News Inc. Portland, OR)
Low dimensional topology.
Mrowka (mathematics, MIT, Cambridge, MA) and Ozsváth (mathematics, Columbia U., New York, NY) present nine chapters based on lecture notes from the American Mathematical Society's Institute for Advanced Study/Park City Mathematics Institute held in summer 2006 to explore developments in low-dimensional topology, to introduce graduate students and researchers to these advances, and to foster interactions between specialists in various facets of the subject. The text includes an introduction, notes based on a special lecture by John Milnor (mathematics, Stony Brook U., NY) about the history of the topology of manifolds, and lecture notes from the seven graduate courses, taught by nine American academics, each containing five or six lectures. The lecture topics include Dehn surgery and 3-manifolds, hyperbolic geometry and 3-manifold topology, Ricci flow and Thurston's geometrization conjecture, link homology, Heegaard Floer homology, contact geometry in low dimensional typology, and four 4-manifolds. No subject index. (Annotation ©2009 Book News Inc. Portland, OR)
Malliavin calculus and its applications.
Paul Malliavin developed the stochastic calculus of variations that bears his name in 1976 primarily to establish the regularity of the probability distribution of functionals of an underlying Gaussian process. Since then it has proven to be a powerful tool for a variety of problems in stochastic analysis. Nualart has prepared this monograph from his notes for ten lectures he delivered at the conference, held at Kent State University, Ohio, in August 2008. In order to demonstrate applications, he concentrates on a Gaussian family of random variables associated with an arbitrary separable Hilbert space. Some of the examples are barely mentioned, but he provides full references for readers who want more. (Annotation ©2009 Book News Inc. Portland, OR)
Mathematical methods in quantum mechanics; with applications to Schrödinger operators.
Teschl (U. of Vienna) presents a brief, but self-contained, introduction to the mathematical methods of quantum mechanics, designed for beginning graduate students in both mathematics and physics, and suitable for use as both a textbook and for self-study. Based on several courses taught by the author at the U. of Vienna over the past decade, the text includes an introduction to spectral theory of unbounded operators, providing readers with the necessary topics for the applications in the book, followed by chapters on the free Schrödinger equation and computing the free resolvent and time evolution; discussion of position, momentum, and angular momentum via algebraic methods; development of various mathematical methods to compute the spectrum of the hydrogen atom; the nondegeneracy of the ground state; spectra of atoms; and scattering theory. (Annotation ©2009 Book News Inc. Portland, OR)
Polyhedral computation.
This volume brings together six papers based on discussions at a Workshop on Polyhedral Computation held at the Centre de Recherches Mathématiques at the U. of Montréal, Canada, in October 2006, as part of the CRM's theme semester on Combinatorial Optimization. Researchers with theoretical and computational expertise in polyhedral computation discuss combinatorial properties of linear program digraphs, combinatorial techniques for monotone generation problems, polyhedral representation conversion up to symmetries, the multi-parametric linear complementarity problem with sufficient matrices, hyperplane arrangements with large average diameter, and the Nash equilibria of rank-1 games. Also included is a previously unpublished technical report from 1980 by Norman Zadeh, who comments on what has yet to be done in the field and gives a simple pivot rule for the simplex method for which it is still unknown if it yields a polynomial time algorithm. There is no index. (Annotation ©2009 Book News Inc. Portland, OR)
Rings, modules, and representations; proceedings.
Papers from a June 2007 conference report on the latest results in current research on the theory of rings and modules, including noncommutative and commutative ring theory, module theory, representation theory, and coding theory. Papers deal with topics such as decomposition theory of modules, injectivity and generalizations, tilting theory, rings and modules with chain conditions, Leavitt path algebras, representations of finite dimensional algebras, and codes over rings. Specific paper subjects include tilting and cotilting classes over Gorenstein rings, topological representations of Von Neumann regular algebras, and Fitting's lemma for modules with well- behaved clones. While most of the papers are original research articles, some are expository surveys. There is no subject index. (Annotation ©2009 Book News Inc. Portland, OR)
Spectral analysis in geometry and number theory; proceedings.
Papers from an August 2007 conference reflect Professor Toshikazu Sunada's research interest in aspects of spectral analysis, such as interactions among geometry, number theory, dynamical systems, probability theory, and mathematical physics. Papers describe recent work in areas including trace formulae, isospectral problems, zeta functions, quantum ergodicity, random waves, discrete geometric analysis, value distribution, and semiclassical analysis. Two beginning chapters offer a brief profile of Professor Toshikazu Sunada, a pioneer in the field, and a detailed overview of his research up to age 60. There is no subject index. (Annotation ©2009 Book News Inc. Portland, OR)
