Lectures on quantum geometry

Abstract

In these lectures we discuss the way in which N = 2 superconformal field theory, in the context of string theory, gives rise to geometrical models of spacetime whose quantitative and qualitative properties differ significantly from their classical (General Relativistic) counterparts. After an overview of some general consequences of N = 2 superconformal symmetry, we specialize to concrete field theoretic representations of this algebra. We indicate how a number of familiar constructs from classical geometry naturally arise in these theories, but in a modified form giving rise to what is called “stringy” or “quantum” geometry. Our main focus is on mirror symmetry and spacetime topology change.