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Selected Topics In The Geometrical Study Of Differential Equations
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Book Synopsis Selected Topics in the Geometrical Study of Differential Equations by : Niky Kamran
Download or read book Selected Topics in the Geometrical Study of Differential Equations written by Niky Kamran and published by American Mathematical Soc.. This book was released on 2002-01-01 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Selected Topics in the Geometrical Study of Differential Equations by :
Download or read book Selected Topics in the Geometrical Study of Differential Equations written by and published by American Mathematical Soc.. This book was released on with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential Geometric Structures by : Walter A. Poor
Download or read book Differential Geometric Structures written by Walter A. Poor and published by Courier Corporation. This book was released on 2015-04-27 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory text defines geometric structure by specifying parallel transport in an appropriate fiber bundle and focusing on simplest cases of linear parallel transport in a vector bundle. 1981 edition.
Book Synopsis Analysis of Stochastic Partial Differential Equations by : Davar Khoshnevisan
Download or read book Analysis of Stochastic Partial Differential Equations written by Davar Khoshnevisan and published by American Mathematical Soc.. This book was released on 2014-06-11 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: The general area of stochastic PDEs is interesting to mathematicians because it contains an enormous number of challenging open problems. There is also a great deal of interest in this topic because it has deep applications in disciplines that range from applied mathematics, statistical mechanics, and theoretical physics, to theoretical neuroscience, theory of complex chemical reactions [including polymer science], fluid dynamics, and mathematical finance. The stochastic PDEs that are studied in this book are similar to the familiar PDE for heat in a thin rod, but with the additional restriction that the external forcing density is a two-parameter stochastic process, or what is more commonly the case, the forcing is a "random noise," also known as a "generalized random field." At several points in the lectures, there are examples that highlight the phenomenon that stochastic PDEs are not a subset of PDEs. In fact, the introduction of noise in some partial differential equations can bring about not a small perturbation, but truly fundamental changes to the system that the underlying PDE is attempting to describe. The topics covered include a brief introduction to the stochastic heat equation, structure theory for the linear stochastic heat equation, and an in-depth look at intermittency properties of the solution to semilinear stochastic heat equations. Specific topics include stochastic integrals à la Norbert Wiener, an infinite-dimensional Itô-type stochastic integral, an example of a parabolic Anderson model, and intermittency fronts. There are many possible approaches to stochastic PDEs. The selection of topics and techniques presented here are informed by the guiding example of the stochastic heat equation. A co-publication of the AMS and CBMS.
Book Synopsis Geometrical Methods in the Theory of Ordinary Differential Equations by : V.I. Arnold
Download or read book Geometrical Methods in the Theory of Ordinary Differential Equations written by V.I. Arnold and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the first edition of this book, geometrical methods in the theory of ordinary differential equations have become very popular and some progress has been made partly with the help of computers. Much of this progress is represented in this revised, expanded edition, including such topics as the Feigenbaum universality of period doubling, the Zoladec solution, the Iljashenko proof, the Ecalle and Voronin theory, the Varchenko and Hovanski theorems, and the Neistadt theory. In the selection of material for this book, the author explains basic ideas and methods applicable to the study of differential equations. Special efforts were made to keep the basic ideas free from excessive technicalities. Thus the most fundamental questions are considered in great detail, while of the more special and difficult parts of the theory have the character of a survey. Consequently, the reader needs only a general mathematical knowledge to easily follow this text. It is directed to mathematicians, as well as all users of the theory of differential equations.
Book Synopsis Special Functions, KZ Type Equations, and Representation Theory by : Aleksandr Nikolaevich Varchenko
Download or read book Special Functions, KZ Type Equations, and Representation Theory written by Aleksandr Nikolaevich Varchenko and published by American Mathematical Soc.. This book was released on with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Symmetry and Perturbation Theory by : Giuseppe Gaeta
Download or read book Symmetry and Perturbation Theory written by Giuseppe Gaeta and published by World Scientific. This book was released on 2005-01-25 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume is a collection of papers presented at the International Conference on SPT2004 focusing on symmetry, perturbation theory, and integrability. The book provides an updated overview of the recent developments in the various different fields of nonlinear dynamics, covering both theory and applications. Special emphasis is given to algebraic and geometric integrability, solutions to the N-body problem of the “choreography” type, geometry and symmetry of dynamical systems, integrable evolution equations, various different perturbation theories, and bifurcation analysis. The contributors to this volume include some of the leading scientists in the field, among them: I Anderson, D Bambusi, S Benenti, S Bolotin, M Fels, W Y Hsiang, V Matveev, A V Mikhailov, P J Olver, G Pucacco, G Sartori, M A Teixeira, S Terracini, F Verhulst and I Yehorchenko. Contents:Parametric Excitation in Nonlinear Dynamics (T Bakri)Similarity Reductions of an Optical Model (M S Bruzón & M L Gandarias)A Regularity Theory for Optimal Partition Problems (M Conti et al.)Periodic Solutions for Zero Mass Nonlinear Wave Equations (G Gentile)Renormalization Group Symmetry and Gas Dynamics (S Murata)Refined Computation of Hypernormal Forms (J Murdock)Regularity of Pseudogroup Orbits (P J Olver & J Pohjanpelto)On Birkhoff Method for Integrable Lagrangian Systems (G Pucacco)and other papers Readership: Researchers and academics. Keywords:Nonlinear Dynamics;Perturbation;Symmetry;Mathematical Physics;Integrable Systems;Dynamical Systems;Geometry;Classical MechanicsKey Features:In-depth treatment of recent advances in “choreography” solutions to the N-body problem in classical mechanicsAccount of recent advances in the geometric theory of separable and superintegrable systemsA geometric approach to symmetry of differential equations
Book Synopsis Ergodic Theory, Groups, and Geometry by : Robert J. Zimmer
Download or read book Ergodic Theory, Groups, and Geometry written by Robert J. Zimmer and published by American Mathematical Soc.. This book was released on 2008-01-01 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The study of group actions on manifolds is the meeting ground of a variety of mathematical areas. In particular, interesting geometric insights can be obtained by applying measure-theoretic techniques. This book provides an introduction to some of the important methods, major developments, and open problems in the subject. It is slightly expanded from lectures given by Zimmer at the CBMS conference at the University of Minnesota. The main text presents a perspective on the field as it was at that time. Comments at the end of each chapter provide selected suggestions for further reading, including references to recent developments."--BOOK JACKET.
Book Synopsis Tensors: Asymptotic Geometry and Developments 2016–2018 by : J.M. Landsberg
Download or read book Tensors: Asymptotic Geometry and Developments 2016–2018 written by J.M. Landsberg and published by American Mathematical Soc.. This book was released on 2019-07-05 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensors are used throughout the sciences, especially in solid state physics and quantum information theory. This book brings a geometric perspective to the use of tensors in these areas. It begins with an introduction to the geometry of tensors and provides geometric expositions of the basics of quantum information theory, Strassen's laser method for matrix multiplication, and moment maps in algebraic geometry. It also details several exciting recent developments regarding tensors in general. In particular, it discusses and explains the following material previously only available in the original research papers: (1) Shitov's 2017 refutation of longstanding conjectures of Strassen on rank additivity and Common on symmetric rank; (2) The 2017 Christandl-Vrana-Zuiddam quantum spectral points that bring together quantum information theory, the asymptotic geometry of tensors, matrix multiplication complexity, and moment polytopes in geometric invariant theory; (3) the use of representation theory in quantum information theory, including the solution of the quantum marginal problem; (4) the use of tensor network states in solid state physics, and (5) recent geometric paths towards upper bounds for the complexity of matrix multiplication. Numerous open problems appropriate for graduate students and post-docs are included throughout.
Book Synopsis Families of Riemann Surfaces and Weil-Petersson Geometry by : Scott A. Wolpert
Download or read book Families of Riemann Surfaces and Weil-Petersson Geometry written by Scott A. Wolpert and published by American Mathematical Soc.. This book was released on 2010 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a generally self-contained course for graduate students and postgraduates on deformations of hyperbolic surfaces and the geometry of the Weil-Petersson metric. It also offers an update for researchers; material not otherwise found in a single reference is included; and aunified approach is provided for an array of results.
Book Synopsis Nonlinear Dispersive Equations by : Terence Tao
Download or read book Nonlinear Dispersive Equations written by Terence Tao and published by American Mathematical Soc.. This book was released on with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Starting only with a basic knowledge of graduate real analysis and Fourier analysis, the text first presents basic nonlinear tools such as the bootstrap method and perturbation theory in the simpler context of nonlinear ODE, then introduces the harmonic analysis and geometric tools used to control linear dispersive PDE. These methods are then combined to study four model nonlinear dispersive equations. Through extensive exercises, diagrams, and informal discussion, the book gives a rigorous theoretical treatment of the material, the real-world intuition and heuristics that underlie the subject, as well as mentioning connections with other areas of PDE, harmonic analysis, and dynamical systems.".
Book Synopsis Nonlinear partial differential equations in differential geometry by : Robert Hardt
Download or read book Nonlinear partial differential equations in differential geometry written by Robert Hardt and published by American Mathematical Soc.. This book was released on 1996 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains lecture notes of minicourses at the Regional Geometry Institute at Park City, Utah, in July 1992. Presented here are surveys of breaking developments in a number of areas of nonlinear partial differential equations in differential geometry. The authors of the articles are not only excellent expositors, but are also leaders in this field of research. All of the articles provide in-depth treatment of the topics and require few prerequisites and less background than current research articles.
Book Synopsis From the Basic Homotopy Lemma to the Classification of C*-algebras by : Huaxin Lin
Download or read book From the Basic Homotopy Lemma to the Classification of C*-algebras written by Huaxin Lin and published by American Mathematical Soc.. This book was released on 2017-08-11 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines some recent developments in the theory of -algebras, which are algebras of operators on Hilbert spaces. An elementary introduction to the technical part of the theory is given via a basic homotopy lemma concerning a pair of almost commuting unitaries. The book presents an outline of the background as well as some recent results of the classification of simple amenable -algebras, otherwise known as the Elliott program. This includes some stable uniqueness theorems and a revisiting of Bott maps via stable homotopy. Furthermore, -theory related rotation maps are introduced. The book is based on lecture notes from the CBMS lecture sequence at the University of Wyoming in the summer of 2015.
Book Synopsis Harmonic Analysis: Smooth and Non-smooth by : Palle E.T. Jorgensen
Download or read book Harmonic Analysis: Smooth and Non-smooth written by Palle E.T. Jorgensen and published by American Mathematical Soc.. This book was released on 2018-10-30 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is a recent and increasing interest in harmonic analysis of non-smooth geometries. Real-world examples where these types of geometry appear include large computer networks, relationships in datasets, and fractal structures such as those found in crystalline substances, light scattering, and other natural phenomena where dynamical systems are present. Notions of harmonic analysis focus on transforms and expansions and involve dual variables. In this book on smooth and non-smooth harmonic analysis, the notion of dual variables will be adapted to fractals. In addition to harmonic analysis via Fourier duality, the author also covers multiresolution wavelet approaches as well as a third tool, namely, L2 spaces derived from appropriate Gaussian processes. The book is based on a series of ten lectures delivered in June 2018 at a CBMS conference held at Iowa State University.
Book Synopsis Wave Packet Analysis by : Christoph Thiele
Download or read book Wave Packet Analysis written by Christoph Thiele and published by American Mathematical Soc.. This book was released on with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of ''wave packet analysis'' originates in Carleson's famous proof of almost everywhere convergence of Fourier series of $L2$ functions. It was later used by Lacey and Thiele to prove bounds on the bilinear Hilbert transform. For quite some time, Carleson's wave packet analysis was thought to be an important idea, but that it had limited applications. But in recent years, it has become clear that this is an important tool for a number of other applications. This book isan introduction to these tools. It emphasizes the classical successes (Carleson's theorem and the Hilbert transform) in the main development. However, the book closes with a dedicated chapter on more recent results. Carleson's original theorem is sometimes cited as one of the most importantdevelopments of 20th century harmonic analysis. The set of ideas stemming from his proof is now seen as an essential element in modern harmonic analysis. Indeed, Thiele won the Salem prize jointly with Michael Lacey for work in this area. The book gives a nice survey of important material, such as an overview of the theory of singular integrals and wave packet analysis itself. There is a separate chapter on ''further developments'', which gives a broader view on the subject, though it does notexhaust all ongoing developments.
Book Synopsis Mathematical Biology: Modeling and Analysis by : Avner Friedman
Download or read book Mathematical Biology: Modeling and Analysis written by Avner Friedman and published by American Mathematical Soc.. This book was released on 2018-06-14 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fast growing field of mathematical biology addresses biological questions using mathematical models from areas such as dynamical systems, probability, statistics, and discrete mathematics. This book considers models that are described by systems of partial differential equations, and it focuses on modeling, rather than on numerical methods and simulations. The models studied are concerned with population dynamics, cancer, risk of plaque growth associated with high cholesterol, and wound healing. A rich variety of open problems demonstrates the exciting challenges and opportunities for research at the interface of mathematics and biology. This book primarily addresses students and researchers in mathematics who do not necessarily have any background in biology and who may have had little exposure to PDEs.
Book Synopsis Lectures on Field Theory and Topology by : Daniel S. Freed
Download or read book Lectures on Field Theory and Topology written by Daniel S. Freed and published by American Mathematical Soc.. This book was released on 2019-08-23 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.
