Instanton Counting, Quantum Geometry and Algebra

This book pedagogically describes recent developments in gauge theory, in particular four—dimensional N = 2 supersymmetric gauge theory, in relation to various fields in mathematics, including algebraic geometry, geometric representation theory, vertex operator algebras. The key concept is the instanton, which is a solution to the anti—self—dual Yang–Mills equation in four dimensions.

In the first part of the book, starting with the systematic description of the instanton, how to integrate...