Anomalies, Strings and Algebraic Geometry

Abstract

In these lectures we would like to review some of the applications of global methods in geometry and topology to the quantum theory of fields and strings. The use of the theory of characteristic classes, index theory, algebraic geometry and differential topology is becoming common place in recent theoretical physics. It seems likely that these areas of mathematics will soon become part of the mathematical background of theoretical physicists, in the same way that Riemannian geometry, group theory, and complex analysis became part of our mathematical arsenal. These new techniques provide also rather powerful tools to obtain useful qualitative (and sometimes quantitative) information in quantum field theories with gauge and/or gravitational interactions, and in string theory.