{"product_id":"tau-functions-and-their-applications-hardback-9781108492683","title":"Tau Functions and their Applications (Hardback) 9781108492683","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eTau Functions and their Applications\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eA thorough introduction to tau functions, from the basics through to the most recent results, with applications in mathematical physics.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eJohn Harnad (Author), Ferenc Balogh (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781108492683, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 4 February 2021\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e520 pages, 17 b\/w illus.\u003cbr\u003e25.1 x 17.6 x 3.4 cm, 1.114 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e'This book is a magnificent handbook on the applications of the ? -functions.' Dimitar A. Kolev, zbMATH\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eTau 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.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface\u003cbr\u003e List of symbols\u003cbr\u003e 1. Examples\u003cbr\u003e 2. KP flows and the Sato-Segal-Wilson Grassmannian\u003cbr\u003e 3. The KP hierarchy and its standard reductions\u003cbr\u003e 4. Infinite dimensional Grassmannians\u003cbr\u003e 5. Fermionic representation of tau functions and Baker functions\u003cbr\u003e 6. Finite dimensional reductions of the infinite Grassmannian and their associated tau functions\u003cbr\u003e 7. Other related integrable hierarchies\u003cbr\u003e 8. Convolution symmetries\u003cbr\u003e 9. Isomonodromic deformations\u003cbr\u003e 10. Integrable integral operators and dual isomonodromic deformations\u003cbr\u003e 11. Random matrix models I. Partition functions and correlators\u003cbr\u003e 12. Random matrix models II. Level spacings\u003cbr\u003e 13. Generating functions for characters, intersection indices and Brézin-Hikami matrix models\u003cbr\u003e 14. Generating functions for weighted Hurwitz numbers: enumeration of branched coverings\u003cbr\u003e Appendix A. Integer partitions\u003cbr\u003e Appendix B. Determinantal and Pfaffian identities\u003cbr\u003e Appendix C. Grassmann manifolds and flag manifolds\u003cbr\u003e Appendix D. Symmetric functions\u003cbr\u003e Appendix E. Finite dimensional fermions: Clifford and Grassmann algebras, spinors, isotropic Grassmannians\u003cbr\u003e Appendix F. Riemann surfaces, holomorphic differentials and theta functions\u003cbr\u003e Appendix G. Orthogonal polynomials\u003cbr\u003e Appendix H. Solutions of selected exercises\u003cbr\u003e References\u003cbr\u003e Alphabetical Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematical physics [\u003ca title=\"See our other books on Mathematical physics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20physics%20%5BPHU%5D%22\"\u003ePHU\u003c\/a\u003e], Relativity physics [\u003ca title=\"See our other books on Relativity physics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Relativity%20physics%20%5BPHR%5D%22\"\u003ePHR\u003c\/a\u003e], Quantum physics [\u003ca title=\"See our other books on Quantum physics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Quantum%20physics%20%5Bquantum%20mechanics%20\u0026amp;%20quantum%20field%20theory%5D%20%5BPHQ%5D%22\"\u003equantum mechanics \u0026amp; quantum field theory PHQ\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46004629897496,"sku":"9781108492683","price":149.89,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9781108492683i.jpg?v=1696706724","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/tau-functions-and-their-applications-hardback-9781108492683","provider":"Freshly Printed Books","version":"1.0","type":"link"}