[PDF] Tau Functions And Their Applications eBook

Author : John Harnad
Publisher : Cambridge University Press
Page : 549 pages
File Size : 47,41 MB
Release : 2021-02-04
Category : Mathematics
ISBN : 1108492681

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A thorough introduction to tau functions, from the basics through to the most recent results, with applications in mathematical physics.

Author : John Harnad
Publisher : Cambridge University Press
Page : 549 pages
File Size : 36,17 MB
Release : 2021-02-04
Category : Science
ISBN : 1108637213

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Tau functions are a central tool in the modern theory of integrable systems. This volume provides a thorough introduction, starting from the basics and extending to recent research results. It covers a wide range of applications, including generating functions for solutions of integrable hierarchies, correlation functions in the spectral theory of random matrices and combinatorial generating functions for enumerative geometrical and topological invariants. A self-contained summary of more advanced topics needed to understand the material is provided, as are solutions and hints for the various exercises and problems that are included throughout the text to enrich the subject matter and engage the reader. Building on knowledge of standard topics in undergraduate mathematics and basic concepts and methods of classical and quantum mechanics, this monograph is ideal for graduate students and researchers who wish to become acquainted with the full range of applications of the theory of tau functions.

Author : Pavel Bleher
Publisher : Cambridge University Press
Page : 454 pages
File Size : 44,24 MB
Release : 2001-06-04
Category : Mathematics
ISBN : 9780521802093

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Expository articles on random matrix theory emphasizing the exchange of ideas between the physical and mathematical communities.

Author : Lubjana Beshaj
Publisher : American Mathematical Soc.
Page : 344 pages
File Size : 37,97 MB
Release : 2019-02-26
Category : Curves, Algebraic
ISBN : 1470442477

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This volume contains a collection of papers on algebraic curves and their applications. While algebraic curves traditionally have provided a path toward modern algebraic geometry, they also provide many applications in number theory, computer security and cryptography, coding theory, differential equations, and more. Papers cover topics such as the rational torsion points of elliptic curves, arithmetic statistics in the moduli space of curves, combinatorial descriptions of semistable hyperelliptic curves over local fields, heights on weighted projective spaces, automorphism groups of curves, hyperelliptic curves, dessins d'enfants, applications to Painlevé equations, descent on real algebraic varieties, quadratic residue codes based on hyperelliptic curves, and Abelian varieties and cryptography. This book will be a valuable resource for people interested in algebraic curves and their connections to other branches of mathematics.

Author : Joseph A. Ball
Publisher : Birkhäuser
Page : 604 pages
File Size : 31,7 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3034878818

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Many developments on the cutting edge of research in operator theory and its applications are reflected in this collection of original and review articles. Particular emphasis lies on highlighting the interplay between operator theory and applications from other areas, such as multi-dimensional systems and function theory of several complex variables, distributed parameter systems and control theory, mathematical physics, wavelets, and numerical analysis.

Author : Leonardo Castellani
Publisher : IOS Press
Page : 950 pages
File Size : 27,33 MB
Release : 1996
Category : Science
ISBN : 9789051992472

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This book focuses on quantum groups, i.e., continuous deformations of Lie groups, and their applications in physics. These algebraic structures have been studied in the last decade by a growing number of mathematicians and physicists, and are found to underlie many physical systems of interest. They do provide, in fact, a sort of common algebraic ground for seemingly very different physical problems. As it has happened for supersymmetry, the q-group symmetries are bound to play a vital role in physics, even in fundamental theories like gauge theory or gravity. In fact q-symmetry can be considered itself as a generalization of supersymmetry, evident in the q-commutator formulation. The hope that field theories on q-groups are naturally reguralized begins to appear founded, and opens new perspectives for quantum gravity. The topics covered in this book include: conformal field theories and quantum groups, gauge theories of quantum groups, anyons, differential calculus on quantum groups and non-commutative geometry, poisson algebras, 2-dimensional statistical models, (2+1) quantum gravity, quantum groups and lattice physics, inhomogeneous q-groups, q-Poincaregroup and deformed gravity and gauging of W-algebras.

Author : M. Amélia Bastos
Publisher : Springer Nature
Page : 654 pages
File Size : 45,60 MB
Release : 2021-03-31
Category : Mathematics
ISBN : 3030519457

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This book presents 30 articles on the topic areas discussed at the 30th “International Workshop on Operator Theory and its Applications”, held in Lisbon in July 2019. The contributions include both expository essays and original research papers reflecting recent advances in the traditional IWOTA areas and emerging adjacent fields, as well as the applications of Operator Theory and Functional Analysis. The topics range from C*–algebras and Banach *–algebras, Sturm-Liouville theory, integrable systems, dilation theory, frame theory, Toeplitz, Hankel, and singular integral operators, to questions from lattice, group and matrix theories, complex analysis, harmonic analysis, and function spaces. Given its scope, the book is chiefly intended for researchers and graduate students in the areas of Operator Theory, Functional Analysis, their applications and adjacent fields.