Elliptic Genera And Vertex Operator Super Algebras
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Elliptic Genera And Vertex Operator Super Algebras
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Author : Hirotaka Tamanoi
language : en
Publisher: Springer
Release Date : 2006-11-14
Elliptic Genera And Vertex Operator Super Algebras written by Hirotaka Tamanoi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
This monograph deals with two aspects of the theory of elliptic genus: its topological aspect involving elliptic functions, and its representation theoretic aspect involving vertex operator super-algebras. For the second aspect, elliptic genera are shown to have the structure of modules over certain vertex operator super-algebras. The vertex operators corresponding to parallel tensor fields on closed Riemannian Spin Kähler manifolds such as Riemannian tensors and Kähler forms are shown to give rise to Virasoro algebras and affine Lie algebras. This monograph is chiefly intended for topologists and it includes accounts on topics outside of topology such as vertex operator algebras.
Introduction To Vertex Operator Algebras And Their Representations
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Author : James Lepowsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To Vertex Operator Algebras And Their Representations written by James Lepowsky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
* Introduces the fundamental theory of vertex operator algebras and its basic techniques and examples. * Begins with a detailed presentation of the theoretical foundations and proceeds to a range of applications. * Includes a number of new, original results and brings fresh perspective to important works of many other researchers in algebra, lie theory, representation theory, string theory, quantum field theory, and other areas of math and physics.
Partition Functions And Automorphic Forms
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Author : Valery A. Gritsenko
language : en
Publisher: Springer Nature
Release Date : 2020-07-09
Partition Functions And Automorphic Forms written by Valery A. Gritsenko and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-09 with Mathematics categories.
This book offers an introduction to the research in several recently discovered and actively developing mathematical and mathematical physics areas. It focuses on: 1) Feynman integrals and modular functions, 2) hyperbolic and Lorentzian Kac-Moody algebras, related automorphic forms and applications to quantum gravity, 3) superconformal indices and elliptic hypergeometric integrals, related instanton partition functions, 4) moonshine, its arithmetic aspects, Jacobi forms, elliptic genus, and string theory, and 5) theory and applications of the elliptic Painleve equation, and aspects of Painleve equations in quantum field theories. All the topics covered are related to various partition functions emerging in different supersymmetric and ordinary quantum field theories in curved space-times of different (d=2,3,...,6) dimensions. Presenting multidisciplinary methods (localization, Borcherds products, theory of special functions, Cremona maps, etc) for treating a range of partition functions, the book is intended for graduate students and young postdocs interested in the interaction between quantum field theory and mathematics related to automorphic forms, representation theory, number theory and geometry, and mirror symmetry.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2007
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Progress In Algebraic Combinatorics
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Author : Eiichi Bannai
language : en
Publisher:
Release Date : 1996
Progress In Algebraic Combinatorics written by Eiichi Bannai and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
This volume consists of thirteen papers on algebraic combinatorics and related areas written by leading experts around the world. There are four survey papers illustrating the following currently active branches of algebraic combinatorics: vertex operator algebras, spherical designs, Kerdock codes and related combinatorial objects, and geometry of matrices. The remaining nine papers are original research articles covering a wide range of disciplines, from classical topics such as permutation groups and finite geometry, to modern topics such as spin models and invariants of 3-manifolds. Two papers occupy nearly half the volume and present a comprehensive account of new concepts: ``Combinatorial Cell Complexes'' by M. Aschbacher and ``Quantum Matroids'' by P. Terwilliger. Terwilliger's theory of quantum matroids unites a part of the theory of finite geometries and a part of the theory of distance-regular graphs--great progess is expected in this field. K. Nomura's paper bridges the classical and the modern by establishing a connection between certain bipartite distance-regular graphs and spin models. All contributors to this volume were invited speakers at the conference ``Algebraic Combinatorics'' in Fukuoka, Japan (1993) and participated in the Research Institute in the Mathematical Sciences (RIMS) research project on algebraic combinatorics held at Kyoto University in 1994.
Loeb Measures In Practice Recent Advances
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Author : Nigel J. Cutland
language : en
Publisher: Springer
Release Date : 2004-10-11
Loeb Measures In Practice Recent Advances written by Nigel J. Cutland and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-11 with Mathematics categories.
This expanded version of the 1997 European Mathematical Society Lectures given by the author in Helsinki, begins with a self-contained introduction to nonstandard analysis (NSA) and the construction of Loeb Measures, which are rich measures discovered in 1975 by Peter Loeb, using techniques from NSA. Subsequent chapters sketch a range of recent applications of Loeb measures due to the author and his collaborators, in such diverse fields as (stochastic) fluid mechanics, stochastic calculus of variations ("Malliavin" calculus) and the mathematical finance theory. The exposition is designed for a general audience, and no previous knowledge of either NSA or the various fields of applications is assumed.
Introduction To Symplectic Dirac Operators
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Author : Katharina Habermann
language : en
Publisher: Springer
Release Date : 2006-10-28
Introduction To Symplectic Dirac Operators written by Katharina Habermann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10-28 with Mathematics categories.
This volume is the first one that gives a systematic and self-contained introduction to the theory of symplectic Dirac operators and reflects the current state of the subject. At the same time, it is intended to establish the idea that symplectic spin geometry and symplectic Dirac operators may give valuable tools in symplectic geometry and symplectic topology, which have become important fields and very active areas of mathematical research.
Moonshine Beyond The Monster
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Author : Terry Gannon
language : en
Publisher: Cambridge University Press
Release Date : 2023-07-27
Moonshine Beyond The Monster written by Terry Gannon and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-27 with Mathematics categories.
A monograph on Moonshine, a mathematical physics topic, for graduate students and researchers.
Lie Algebras Vertex Operator Algebras And Related Topics
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Author : Katrina Barron
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-08-15
Lie Algebras Vertex Operator Algebras And Related Topics written by Katrina Barron and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-15 with Mathematics categories.
This volume contains the proceedings of the conference on Lie Algebras, Vertex Operator Algebras, and Related Topics, celebrating the 70th birthday of James Lepowsky and Robert Wilson, held from August 14–18, 2015, at the University of Notre Dame, Notre Dame, Indiana. Since their seminal work in the 1970s, Lepowsky and Wilson, their collaborators, their students, and those inspired by their work, have developed an amazing body of work intertwining the fields of Lie algebras, vertex algebras, number theory, theoretical physics, quantum groups, the representation theory of finite simple groups, and more. The papers presented here include recent results and descriptions of ongoing research initiatives representing the broad influence and deep connections brought about by the work of Lepowsky and Wilson and include a contribution by Yi-Zhi Huang summarizing some major open problems in these areas, in particular as they pertain to two-dimensional conformal field theory.
Stable Approximate Evaluation Of Unbounded Operators
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Author : C. W. Groetsch
language : en
Publisher: Springer Science & Business Media
Release Date : 2007
Stable Approximate Evaluation Of Unbounded Operators written by C. W. Groetsch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Spectral theory of bounded linear operators teams up with von Neumann’s theory of unbounded operators in this monograph to provide a general framework for the study of stable methods for the evaluation of unbounded operators. An introductory chapter provides numerous illustrations of unbounded linear operators that arise in various inverse problems of mathematical physics. Before the general theory of stabilization methods is developed, an extensive exposition of the necessary background material from the theory of operators on Hilbert space is provided. Several specific stabilization methods are studied in detail, with particular attention to the Tikhonov-Morozov method and its iterated version.