Algebraic, Analytic and Geometric Aspects of Complex Differential Equations and Their Deformations
Author:
Publisher:
Published: 2007
Total Pages: 269
ISBN-13:
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Space – Time – Matter
Author: Jochen Brüning
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2018-04-09
Total Pages: 590
ISBN-13: 3110451530
DOWNLOAD EBOOKThis monograph describes some of the most interesting results obtained by the mathematicians and physicists collaborating in the CRC 647 "Space – Time – Matter", in the years 2005 - 2016. The work presented concerns the mathematical and physical foundations of string and quantum field theory as well as cosmology. Important topics are the spaces and metrics modelling the geometry of matter, and the evolution of these geometries. The partial differential equations governing such structures and their singularities, special solutions and stability properties are discussed in detail. Contents Introduction Algebraic K-theory, assembly maps, controlled algebra, and trace methods Lorentzian manifolds with special holonomy – Constructions and global properties Contributions to the spectral geometry of locally homogeneous spaces On conformally covariant differential operators and spectral theory of the holographic Laplacian Moduli and deformations Vector bundles in algebraic geometry and mathematical physics Dyson–Schwinger equations: Fix-point equations for quantum fields Hidden structure in the form factors ofN = 4 SYM On regulating the AdS superstring Constraints on CFT observables from the bootstrap program Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities Yangian symmetry in maximally supersymmetric Yang-Mills theory Wave and Dirac equations on manifolds Geometric analysis on singular spaces Singularities and long-time behavior in nonlinear evolution equations and general relativity
Analytic, Algebraic and Geometric Aspects of Differential Equations
Author: Galina Filipuk
Publisher: Birkhäuser
Published: 2018-08-01
Total Pages: 471
ISBN-13: 9783319849997
DOWNLOAD EBOOKThis volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in Będlewo, Poland in September 2015. The contributions provide an overview of the current level of interaction between algebra, geometry and analysis and demonstrate the manifold aspects of the theory of ordinary and partial differential equations, while also pointing out the highly fruitful interrelations between those aspects. These interactions continue to yield new developments, not only in the theory of differential equations but also in several related areas of mathematics and physics such as differential geometry, representation theory, number theory and mathematical physics. The main goal of the volume is to introduce basic concepts, techniques, detailed and illustrative examples and theorems (in a manner suitable for non-specialists), and to present recent developments in the field, together with open problems for more advanced and experienced readers. It will be of interest to graduate students, early-career researchers and specialists in analysis, geometry, algebra and related areas, as well as anyone interested in learning new methods and techniques.
Algebraic and Analytic Aspects of Integrable Systems and Painleve Equations
Author: Anton Dzhamay
Publisher: American Mathematical Soc.
Published: 2015-10-28
Total Pages: 210
ISBN-13: 1470416549
DOWNLOAD EBOOKThis volume contains the proceedings of the AMS Special Session on Algebraic and Analytic Aspects of Integrable Systems and Painlevé Equations, held on January 18, 2014, at the Joint Mathematics Meetings in Baltimore, MD. The theory of integrable systems has been at the forefront of some of the most important developments in mathematical physics in the last 50 years. The techniques to study such systems have solid foundations in algebraic geometry, differential geometry, and group representation theory. Many important special solutions of continuous and discrete integrable systems can be written in terms of special functions such as hypergeometric and basic hypergeometric functions. The analytic tools developed to study integrable systems have numerous applications in random matrix theory, statistical mechanics and quantum gravity. One of the most exciting recent developments has been the emergence of good and interesting discrete and quantum analogues of classical integrable differential equations, such as the Painlevé equations and soliton equations. Many algebraic and analytic ideas developed in the continuous case generalize in a beautifully natural manner to discrete integrable systems. The editors have sought to bring together a collection of expository and research articles that represent a good cross section of ideas and methods in these active areas of research within integrable systems and their applications.
Algebraic and Geometric Aspects of Integrable Systems and Random Matrices
Author: Anton Dzhamay
Publisher: American Mathematical Soc.
Published: 2013-06-26
Total Pages: 363
ISBN-13: 0821887475
DOWNLOAD EBOOKThis volume contains the proceedings of the AMS Special Session on Algebraic and Geometric Aspects of Integrable Systems and Random Matrices, held from January 6-7, 2012, in Boston, MA. The very wide range of topics represented in this volume illustrates
Geometric and Algebraic Structures in Differential Equations
Author: P.H. Kersten
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 346
ISBN-13: 9400901798
DOWNLOAD EBOOKThe geometrical theory of nonlinear differential equations originates from classical works by S. Lie and A. Bäcklund. It obtained a new impulse in the sixties when the complete integrability of the Korteweg-de Vries equation was found and it became clear that some basic and quite general geometrical and algebraic structures govern this property of integrability. Nowadays the geometrical and algebraic approach to partial differential equations constitutes a special branch of modern mathematics. In 1993, a workshop on algebra and geometry of differential equations took place at the University of Twente (The Netherlands), where the state-of-the-art of the main problems was fixed. This book contains a collection of invited lectures presented at this workshop. The material presented is of interest to those who work in pure and applied mathematics and especially in mathematical physics.
Differential Algebra, Complex Analysis and Orthogonal Polynomials
Author: Primitivo B. Acosta Humanez
Publisher: American Mathematical Soc.
Published: 2010
Total Pages: 241
ISBN-13: 0821848860
DOWNLOAD EBOOKPresents the 2007-2008 Jairo Charris Seminar in Algebra and Analysis on Differential Algebra, Complex Analysis and Orthogonal Polynomials, which was held at the Universidad Sergio Arboleda in Bogota, Colombia.
Linear Differential Equations in the Complex Domain
Author: Yoshishige Haraoka
Publisher: Springer Nature
Published: 2020-11-16
Total Pages: 396
ISBN-13: 3030546632
DOWNLOAD EBOOKThis book provides a detailed introduction to recent developments in the theory of linear differential systems and integrable total differential systems. Starting from the basic theory of linear ordinary differential equations and integrable systems, it proceeds to describe Katz theory and its applications, extending it to the case of several variables. In addition, connection problems, deformation theory, and the theory of integral representations are comprehensively covered. Complete proofs are given, offering the reader a precise account of the classical and modern theory of linear differential equations in the complex domain, including an exposition of Pfaffian systems and their monodromy problems. The prerequisites are a course in complex analysis and the basics of differential equations, topology and differential geometry. This book will be useful for graduate students, specialists in differential equations, and for non-specialists who want to use differential equations.
Algebraic Geometry and Complex Analysis
Author: Enrique Ramirez de Arellano
Publisher: Lecture Notes in Mathematics
Published: 1989-12-20
Total Pages: 204
ISBN-13:
DOWNLOAD EBOOKFrom the contents: G.R. Kempf: The addition theorem for abstract Theta functions.- L. Brambila: Existence of certain universal extensions.- A. Del Centina, S. Recillas: On a property of the Kummer variety and a relation between two moduli spaces of curves.- C. Gomez-Mont: On closed leaves of holomorphic foliations by curves (38 pp.).- G.R. Kempf: Fay's trisecant formula.- D. Mond, R. Pelikaan: Fitting ideals and multiple points of analytic mappings (55 pp.).- F.O. Schreyer: Certain Weierstrass points occurr at most once on a curve.- R. Smith, H. Tapia-Recillas: The Gauss map on subvarieties of Jacobians of curves with gd2's.
Isomonodromic Deformations and Frobenius Manifolds
Author: Claude Sabbah
Publisher: Springer Science & Business Media
Published: 2007-12-20
Total Pages: 290
ISBN-13: 1848000545
DOWNLOAD EBOOKBased on a series of graduate lectures, this book provides an introduction to algebraic geometric methods in the theory of complex linear differential equations. Starting from basic notions in complex algebraic geometry, it develops some of the classical problems of linear differential equations. It ends with applications to recent research questions related to mirror symmetry. The fundamental tool used is that of a vector bundle with connection. The book includes complete proofs, and applications to recent research questions. Aimed at graduate students and researchers, the book assumes some familiarity with basic complex algebraic geometry.
