Download or read book Singular fibrations with affine fibers with applications to the regularity theory of Fourier Integral Operators written by Mikhail Vladimirovich Ruzhansky and published by . This book was released on 1998 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Regularity Theory of Fourier Integral Operators with Complex Phases and Singularities of Affine Fibrations written by Michael Ruzhansky and published by . This book was released on 2001 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hyperbolic Problems Theory Numerics Applications written by Michael Fey and published by Birkhäuser. This book was released on 2012-12-06 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: [Infotext]((Kurztext))These are the proceedings of the 7th International Conference on Hyperbolic Problems, held in Zürich in February 1998. The speakers and contributors have been rigorously selected and present the state of the art in this field. The articles, both theoretical and numerical, encompass a wide range of applications, such as nonlinear waves in solids, various computational fluid dynamics from small-scale combustion to relativistic astrophysical problems, multiphase phenomena and geometrical optics. ((Volltext))These proceedings contain, in two volumes, approximately one hundred papers presented at the conference on hyperbolic problems, which has focused to a large extent on the laws of nonlinear hyperbolic conservation. Two-fifths of the papers are devoted to mathematical aspects such as global existence, uniqueness, asymptotic behavior such as large time stability, stability and instabilities of waves and structures, various limits of the solution, the Riemann problem and so on. Roughly the same number of articles are devoted to numerical analysis, for example stability and convergence of numerical schemes, as well as schemes with special desired properties such as shock capturing, interface fitting and high-order approximations to multidimensional systems. The results in these contributions, both theoretical and numerical, encompass a wide range of applications such as nonlinear waves in solids, various computational fluid dynamics from small-scale combustion to relativistic astrophysical problems, multiphase phenomena and geometrical optics.
Download or read book Geometric Aspects of Analysis and Mechanics written by Erik P. van den Ban and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hans Duistermaat, an influential geometer-analyst, made substantial contributions to the theory of ordinary and partial differential equations, symplectic, differential, and algebraic geometry, minimal surfaces, semisimple Lie groups, mechanics, mathematical physics, and related fields. Written in his honor, the invited and refereed articles in this volume contain important new results as well as surveys in some of these areas, clearly demonstrating the impact of Duistermaat's research and, in addition, exhibiting interrelationships among many of the topics.
Download or read book Integral Fourier Operators written by Michèle Audin and published by Universitätsverlag Potsdam. This book was released on 2018-04-17 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of contributions based on lectures delivered at a school on Fourier Integral Operators held in Ouagadougou, Burkina Faso, 14–26 September 2015, provides an introduction to Fourier Integral Operators (FIO) for a readership of Master and PhD students as well as any interested layperson. Considering the wide spectrum of their applications and the richness of the mathematical tools they involve, FIOs lie the cross-road of many a field. This volume offers the necessary background, whether analytic or geometric, to get acquainted with FIOs, complemented by more advanced material presenting various aspects of active research in that area.
Download or read book Hyperbolic Problems written by Michael Fey and published by . This book was released on 1999 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Period Mappings and Period Domains written by James Carlson and published by Cambridge University Press. This book was released on 2017-08-24 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to Griffiths' theory of period maps and domains, focused on algebraic, group-theoretic and differential geometric aspects.
Download or read book Holomorphic Curves in Low Dimensions written by Chris Wendl and published by Springer. This book was released on 2018-06-28 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides an accessible introduction to the applications of pseudoholomorphic curves in symplectic and contact geometry, with emphasis on dimensions four and three. The first half of the book focuses on McDuff's characterization of symplectic rational and ruled surfaces, one of the classic early applications of holomorphic curve theory. The proof presented here uses the language of Lefschetz fibrations and pencils, thus it includes some background on these topics, in addition to a survey of the required analytical results on holomorphic curves. Emphasizing applications rather than technical results, the analytical survey mostly refers to other sources for proofs, while aiming to provide precise statements that are widely applicable, plus some informal discussion of the analytical ideas behind them. The second half of the book then extends this program in two complementary directions: (1) a gentle introduction to Gromov-Witten theory and complete proof of the classification of uniruled symplectic 4-manifolds; and (2) a survey of punctured holomorphic curves and their applications to questions from 3-dimensional contact topology, such as classifying the symplectic fillings of planar contact manifolds. This book will be particularly useful to graduate students and researchers who have basic literacy in symplectic geometry and algebraic topology, and would like to learn how to apply standard techniques from holomorphic curve theory without dwelling more than necessary on the analytical details. This book is also part of the Virtual Series on Symplectic Geometry http://www.springer.com/series/16019
Download or read book Wavelets and Their Applications written by J.S. Byrnes and published by Springer Science & Business Media. This book was released on 1994-08-31 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is probably true quite generally that in the history of human thinking the most fruitful developments frequently take place at those points where two different lines of thought meet. Hence, if they actually meet, that is, if they are at least so much related to each other that a real interaction can take place, then one may hope that new and interesting developments may follow. Werner Heisenberg This volume contains papers presented at the August 1992 NATO Advanced Study Institute on Wavelets and Their Applications. The conference was held at the beautiful Il Ciocco resort near Lucca, in the glorious Tuscany region of northern Italy. Once again we gathered at this idyllic spot to explore and extend the reciprocity between mathematics and engineering. The dynamic interaction between world-renowned scientists from the usu ally disparate communities of pure mathematicians and applied scientists, which occurred at our 1989 and 1991 ASI's, continued at this meeting. Wavelet theory and technology is in an important growth stage at which theoretical and practical results are being compared with existing methods. There have been spectacular wavelet successes and sobering comparisons with traditional ideas-but still there is a wide expanse of scientific problems to explore. Since these problems lie at the forefront of both pure mathematics and applied science, our NATO ASI was especially pertinent at this time.
Download or read book Poisson Structures written by Camille Laurent-Gengoux and published by Springer Science & Business Media. This book was released on 2012-08-27 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: Poisson structures appear in a large variety of contexts, ranging from string theory, classical/quantum mechanics and differential geometry to abstract algebra, algebraic geometry and representation theory. In each one of these contexts, it turns out that the Poisson structure is not a theoretical artifact, but a key element which, unsolicited, comes along with the problem that is investigated, and its delicate properties are decisive for the solution to the problem in nearly all cases. Poisson Structures is the first book that offers a comprehensive introduction to the theory, as well as an overview of the different aspects of Poisson structures. The first part covers solid foundations, the central part consists of a detailed exposition of the different known types of Poisson structures and of the (usually mathematical) contexts in which they appear, and the final part is devoted to the two main applications of Poisson structures (integrable systems and deformation quantization). The clear structure of the book makes it adequate for readers who come across Poisson structures in their research or for graduate students or advanced researchers who are interested in an introduction to the many facets and applications of Poisson structures.
Download or read book Applied Picard Lefschetz Theory written by V. A. Vasilʹev and published by American Mathematical Soc.. This book was released on 2002 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many important functions of mathematical physics are defined as integrals depending on parameters. The Picard-Lefschetz theory studies how analytic and qualitative properties of such integrals (regularity, algebraicity, ramification, singular points, etc.) depend on the monodromy of corresponding integration cycles. In this book, V. A. Vassiliev presents several versions of the Picard-Lefschetz theory, including the classical local monodromy theory of singularities and completeintersections, Pham's generalized Picard-Lefschetz formulas, stratified Picard-Lefschetz theory, and also twisted versions of all these theories with applications to integrals of multivalued forms. The author also shows how these versions of the Picard-Lefschetz theory are used in studying a variety ofproblems arising in many areas of mathematics and mathematical physics. In particular, he discusses the following classes of functions: volume functions arising in the Archimedes-Newton problem of integrable bodies; Newton-Coulomb potentials; fundamental solutions of hyperbolic partial differential equations; multidimensional hypergeometric functions generalizing the classical Gauss hypergeometric integral. The book is geared toward a broad audience of graduate students, research mathematiciansand mathematical physicists interested in algebraic geometry, complex analysis, singularity theory, asymptotic methods, potential theory, and hyperbolic operators.
Download or read book Zeta Integrals Schwartz Spaces and Local Functional Equations written by Wen-Wei Li and published by Springer. This book was released on 2018-11-02 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on a conjectural class of zeta integrals which arose from a program born in the work of Braverman and Kazhdan around the year 2000, the eventual goal being to prove the analytic continuation and functional equation of automorphic L-functions. Developing a general framework that could accommodate Schwartz spaces and the corresponding zeta integrals, the author establishes a formalism, states desiderata and conjectures, draws implications from these assumptions, and shows how known examples fit into this framework, supporting Sakellaridis' vision of the subject. The collected results, both old and new, and the included extensive bibliography, will be valuable to anyone who wishes to understand this program, and to those who are already working on it and want to overcome certain frequently occurring technical difficulties.
Download or read book Problems on Mapping Class Groups and Related Topics written by Benson Farb and published by American Mathematical Soc.. This book was released on 2006-09-12 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: The appearance of mapping class groups in mathematics is ubiquitous. The book presents 23 papers containing problems about mapping class groups, the moduli space of Riemann surfaces, Teichmuller geometry, and related areas. Each paper focusses completely on open problems and directions. The problems range in scope from specific computations, to broad programs. The goal is to have a rich source of problems which have been formulated explicitly and accessibly. The book is divided into four parts. Part I contains problems on the combinatorial and (co)homological group-theoretic aspects of mapping class groups, and the way in which these relate to problems in geometry and topology. Part II concentrates on connections with classification problems in 3-manifold theory, the theory of symplectic 4-manifolds, and algebraic geometry. A wide variety of problems, from understanding billiard trajectories to the classification of Kleinian groups, can be reduced to differential and synthetic geometry problems about moduli space. Such problems and connections are discussed in Part III. Mapping class groups are related, both concretely and philosophically, to a number of other groups, such as braid groups, lattices in semisimple Lie groups, and automorphism groups of free groups. Part IV concentrates on problems surrounding these relationships. This book should be of interest to anyone studying geometry, topology, algebraic geometry or infinite groups. It is meant to provide inspiration for everyone from graduate students to senior researchers.
Download or read book Noncommutative Geometry written by Alain Connes and published by Springer. This book was released on 2003-12-15 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.
Download or read book Noncommutative Geometry Quantum Fields and Motives written by Alain Connes and published by American Mathematical Soc.. This book was released on 2019-03-13 with total page 785 pages. Available in PDF, EPUB and Kindle. Book excerpt: The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. The first part of the book deals with quantum field theory and the geometric structure of renormalization as a Riemann-Hilbert correspondence. It also presents a model of elementary particle physics based on noncommutative geometry. The main result is a complete derivation of the full Standard Model Lagrangian from a very simple mathematical input. Other topics covered in the first part of the book are a noncommutative geometry model of dimensional regularization and its role in anomaly computations, and a brief introduction to motives and their conjectural relation to quantum field theory. The second part of the book gives an interpretation of the Weil explicit formula as a trace formula and a spectral realization of the zeros of the Riemann zeta function. This is based on the noncommutative geometry of the adèle class space, which is also described as the space of commensurability classes of Q-lattices, and is dual to a noncommutative motive (endomotive) whose cyclic homology provides a general setting for spectral realizations of zeros of L-functions. The quantum statistical mechanics of the space of Q-lattices, in one and two dimensions, exhibits spontaneous symmetry breaking. In the low-temperature regime, the equilibrium states of the corresponding systems are related to points of classical moduli spaces and the symmetries to the class field theory of the field of rational numbers and of imaginary quadratic fields, as well as to the automorphisms of the field of modular functions. The book ends with a set of analogies between the noncommutative geometries underlying the mathematical formulation of the Standard Model minimally coupled to gravity and the moduli spaces of Q-lattices used in the study of the zeta function.
Download or read book A Course in Abstract Harmonic Analysis written by Gerald B. Folland and published by CRC Press. This book was released on 2016-02-03 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Course in Abstract Harmonic Analysis is an introduction to that part of analysis on locally compact groups that can be done with minimal assumptions on the nature of the group. As a generalization of classical Fourier analysis, this abstract theory creates a foundation for a great deal of modern analysis, and it contains a number of elegant resul
Download or read book Elliptic Operators Topology and Asymptotic Methods written by John Roe and published by Longman Scientific and Technical. This book was released on 1988 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
