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Table of contents (8 chapters)
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Front Matter
About this book
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.
Editors and Affiliations
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CNRS U.M.R. 8524, Université de Lille and IUF, Villeneuve d’Ascq Cedex, France
Valery A. Gritsenko
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National Research University Higher School of Economics, Laboratory of Mirror Symmetry and Automorphic Forms, Moscow, Russia
Vyacheslav P. Spiridonov
Bibliographic Information
Book Title: Partition Functions and Automorphic Forms
Editors: Valery A. Gritsenko, Vyacheslav P. Spiridonov
Series Title: Moscow Lectures
DOI: https://doi.org/10.1007/978-3-030-42400-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-42399-5Published: 10 July 2020
Softcover ISBN: 978-3-030-42402-2Published: 10 July 2021
eBook ISBN: 978-3-030-42400-8Published: 09 July 2020
Series ISSN: 2522-0314
Series E-ISSN: 2522-0322
Edition Number: 1
Number of Pages: XIII, 415
Number of Illustrations: 20 b/w illustrations, 11 illustrations in colour
Topics: Mathematical Applications in the Physical Sciences, Mathematical Physics, Mathematical Methods in Physics, Quantum Field Theories, String Theory, Special Functions