Differential Geometry Geometry In Mathematical Physics And Related Topics

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The second of three parts comprising Volume 54, the proceedings of the Summer Research Institute on Differential Geometry, held at the University of California, Los Angeles, July 1990 (ISBN for the set is 0-8218-1493-1). Among the subjects of Part 2 are gauge theory, symplectic geometry, complex ge

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Genre : Mathematics
Author : Robert Everist Greene
Publisher : American Mathematical Soc.
Release : 1993
File : 681 Pages
ISBN-13 : 9780821814956


Differential Geometry And Mathematical Physics

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Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact.

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Genre : Science
Author : Gerd Rudolph
Publisher : Springer Science & Business Media
Release : 2012-11-09
File : 766 Pages
ISBN-13 : 9789400753457


Geometry In Mathematical Physics And Related Topics

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Genre : Complex manifolds
Author : Robert Everist Greene
Publisher :
Release : 1993
File : 655 Pages
ISBN-13 : LCCN:92032831


Topics In Contemporary Differential Geometry Complex Analysis And Mathematical Physics

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This volume contains the contributions by the participants in the eight of a series workshops in complex analysis, differential geometry and mathematical physics and related areas.Active specialists in mathematical physics contribute to the volume, providing not only significant information for researchers in the area but also interesting mathematics for non-specialists and a broader audience. The contributions treat topics including differential geometry, partial differential equations, integrable systems and mathematical physics.

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Genre : Mathematics
Author : Stancho Dimiev
Publisher : World Scientific
Release : 2007
File : 350 Pages
ISBN-13 : 9789812707901


Perspectives Of Complex Analysis Differential Geometry And Mathematical Physics Proceedings Of The 5th International Workshop On Complex Structures And Vector Fields

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This workshop brought together specialists in complex analysis, differential geometry, mathematical physics and applications for stimulating cross-disciplinary discussions. The lectures presented ranged over various current topics in those fields. The proceedings will be of value to graduate students and researchers in complex analysis, differential geometry and theoretical physics, and also related fields.

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Genre : Mathematics
Author : Stancho Dimiev
Publisher : World Scientific
Release : 2001-08-02
File : 220 Pages
ISBN-13 : 9789814491211


Global Differential Geometry

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This volume contains a collection of well-written surveys provided by experts in Global Differential Geometry to give an overview over recent developments in Riemannian Geometry, Geometric Analysis and Symplectic Geometry. The papers are written for graduate students and researchers with a general interest in geometry, who want to get acquainted with the current trends in these central fields of modern mathematics.

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Genre : Mathematics
Author : Christian Bär
Publisher : Springer Science & Business Media
Release : 2011-12-18
File : 520 Pages
ISBN-13 : 9783642228421


Advances In Differential Equations And Mathematical Physics

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The text offers a combination of certain emerging topics and important research advances in the area of differential equations. The topics range widely and include magnetic Schroedinger operators, the Boltzmann equations, nonlinear variational problems and noncommutative probability theory. The text is suitable for graduate and advanced graduate courses and seminars on the topic, as well as research mathematicians and physicists working in mathematical physics, applied mathematics, analysis and differential equations.

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Genre : Mathematics
Author : Eric Carlen
Publisher : American Mathematical Soc.
Release : 1998
File : 234 Pages
ISBN-13 : 9780821808610


Stochastic Geometric Mechanics

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Collecting together contributed lectures and mini-courses, this book details the research presented in a special semester titled “Geometric mechanics – variational and stochastic methods” run in the first half of 2015 at the Centre Interfacultaire Bernoulli (CIB) of the Ecole Polytechnique Fédérale de Lausanne. The aim of the semester was to develop a common language needed to handle the wide variety of problems and phenomena occurring in stochastic geometric mechanics. It gathered mathematicians and scientists from several different areas of mathematics (from analysis, probability, numerical analysis and statistics, to algebra, geometry, topology, representation theory, and dynamical systems theory) and also areas of mathematical physics, control theory, robotics, and the life sciences, with the aim of developing the new research area in a concentrated joint effort, both from the theoretical and applied points of view. The lectures were given by leading specialists in different areas of mathematics and its applications, building bridges among the various communities involved and working jointly on developing the envisaged new interdisciplinary subject of stochastic geometric mechanics.

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Genre : Mathematics
Author : Sergio Albeverio
Publisher : Springer
Release : 2017-11-17
File : 275 Pages
ISBN-13 : 9783319634531


Weyl And The Problem Of Space

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This book investigates Hermann Weyl’s work on the problem of space from the early 1920s onwards. It presents new material and opens the philosophical problem of space anew, crossing the disciplines of mathematics, history of science and philosophy. With a Kantian starting point Weyl asks: among all the infinitely many conceivable metrical spaces, which one applies to the physical world? In agreement with general relativity, Weyl acknowledges that the metric can quantitatively vary with the physical situation. Despite this freedom, Weyl “deduces”, with group-theoretical technicalities, that there is only one “kind” of legitimate metric. This construction was then decisive for the development of gauge theories. Nevertheless, the question of the foundations of the metric of physical theories is only a piece of a wider epistemological problem. Contributing authors mark out the double trajectory that goes through Weyl’s texts, from natural science to philosophy and conversely, always through the mediation of mathematics. Readers may trace the philosophical tradition to which Weyl refers and by which he is inspired (Kant, Husserl, Fichte, Leibniz, Becker etc.), and explore the mathematical tradition (Riemann, Helmholtz, Lie, Klein) that permitted Weyl to elaborate and solve his mathematical problem of space. Furthermore, this volume analyzes the role of the interlocutors with whom Weyl discussed the nature of physical space (Einstein, Cartan, De Sitter, Schrödinger, Eddington). This volume features the work of top specialists and will appeal to postgraduates and scholars in philosophy, the history of science, mathematics, or physics.

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Genre : Science
Author : Julien Bernard
Publisher : Springer Nature
Release : 2019-10-09
File : 433 Pages
ISBN-13 : 9783030115272


Symmetries And Overdetermined Systems Of Partial Differential Equations

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This three-week summer program considered the symmetries preserving various natural geometric structures. There are two parts to the proceedings. The articles in the first part are expository but all contain significant new material. The articles in the second part are concerned with original research. All articles were thoroughly refereed and the range of interrelated work ensures that this will be an extremely useful collection.

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Genre : Mathematics
Author : Michael Eastwood
Publisher : Springer Science & Business Media
Release : 2009-04-23
File : 565 Pages
ISBN-13 : 9780387738314