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Isomonodromic Deformations and Frobenius Manifolds

2007-12-20 Mathematics
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Release : 2007-12-20
Genre : Mathematics
Kind : eBook
Book Rating : 545/5 ( reviews)

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Book Synopsis Isomonodromic Deformations and Frobenius Manifolds by : Claude Sabbah

Download or read book Isomonodromic Deformations and Frobenius Manifolds written by Claude Sabbah. This book was released on 2007-12-20. Available in PDF, EPUB and Kindle. Book excerpt: Based 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.

Isomonodromic Deformations and Applications in Physics

2002 Mathematics
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Release : 2002
Genre : Mathematics
Kind : eBook
Book Rating : 045/5 ( reviews)

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Book Synopsis Isomonodromic Deformations and Applications in Physics by : John P. Harnad

Download or read book Isomonodromic Deformations and Applications in Physics written by John P. Harnad. This book was released on 2002. Available in PDF, EPUB and Kindle. Book excerpt: The area of inverse scattering transform method or soliton theory has evolved over the past two decades in a vast variety of exciting new algebraic and analytic directions and has found numerous new applications. Methods and applications range from quantum group theory and exactly solvable statistical models to random matrices, random permutations, and number theory. The theory of isomonodromic deformations of systems of differential equations with rational coefficents, and mostnotably, the related apparatus of the Riemann-Hilbert problem, underlie the analytic side of this striking development. The contributions in this volume are based on lectures given by leading experts at the CRM workshop (Montreal, Canada). Included are both survey articles and more detailed expositionsrelating to the theory of isomonodromic deformations, the Riemann-Hilbert problem, and modern applications. The first part of the book represents the mathematical aspects of isomonodromic deformations; the second part deals mostly with the various appearances of isomonodromic deformations and Riemann-Hilbert methods in the theory of exactly solvable quantum field theory and statistical mechanical models, and related issues. The book elucidates for the first time in the current literature theimportant role that isomonodromic deformations play in the theory of integrable systems and their applications to physics.

Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces

1999 Mathematics
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Release : 1999
Genre : Mathematics
Kind : eBook
Book Rating : 178/5 ( reviews)

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Book Synopsis Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces by : I︠U︡. I. Manin

Download or read book Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces written by I︠U︡. I. Manin. This book was released on 1999. Available in PDF, EPUB and Kindle. Book excerpt: This is the first monograph dedicated to the systematic exposition of the whole variety of topics related to quantum cohomology. The subject first originated in theoretical physics (quantum string theory) and has continued to develop extensively over the last decade. The author's approach to quantum cohomology is based on the notion of the Frobenius manifold. The first part of the book is devoted to this notion and its extensive interconnections with algebraic formalism of operads, differential equations, perturbations, and geometry. In the second part of the book, the author describes the construction of quantum cohomology and reviews the algebraic geometry mechanisms involved in this construction (intersection and deformation theory of Deligne-Artin and Mumford stacks). Yuri Manin is currently the director of the Max-Planck-Institut für Mathematik in Bonn, Germany. He has authored and coauthored 10 monographs and almost 200 research articles in algebraic geometry, number theory, mathematical physics, history of culture, and psycholinguistics. Manin's books, such as Cubic Forms: Algebra, Geometry, and Arithmetic (1974), A Course in Mathematical Logic (1977), Gauge Field Theory and Complex Geometry (1988), Elementary Particles: Mathematics, Physics and Philosophy (1989, with I. Yu. Kobzarev), Topics in Non-commutative Geometry (1991), and Methods of Homological Algebra (1996, with S. I. Gelfand), secured for him solid recognition as an excellent expositor. Undoubtedly the present book will serve mathematicians for many years to come.

Complex Differential and Difference Equations

2019-11-18 Mathematics
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Release : 2019-11-18
Genre : Mathematics
Kind : eBook
Book Rating : 614/5 ( reviews)

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Book Synopsis Complex Differential and Difference Equations by : Galina Filipuk

Download or read book Complex Differential and Difference Equations written by Galina Filipuk. This book was released on 2019-11-18. Available in PDF, EPUB and Kindle. Book excerpt: The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

Frobenius Manifolds

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 361/5 ( reviews)

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Book Synopsis Frobenius Manifolds by : Claus Hertling

Download or read book Frobenius Manifolds written by Claus Hertling. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: Quantum cohomology, the theory of Frobenius manifolds and the relations to integrable systems are flourishing areas since the early 90's. An activity was organized at the Max-Planck-Institute for Mathematics in Bonn, with the purpose of bringing together the main experts in these areas. This volume originates from this activity and presents the state of the art in the subject.

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