Tau Functions and their Applications

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

In this thorough and coherent introduction to tau functions, Harnad and Balogh start with the basics and extend right through to the most recent research results. This monograph is ideal for graduates or researchers in related fields unacquainted with the full range of applications of the theory of tau functions.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.