The emergence of algebraic geometry in contemporary physics

A distinguished feature of the interplay between geometry and physics in the last, say, 20 years, is that the usual pattern of interaction between the two disciplines (mathematics provides the language to formulate the models of physical problems, and the techniques needed to solve the resulting equations) has evolved into a much more intricated web of connections. What is especially new in this fact is that physics has shown to be able to serve as a powerful source of inspiration of new mathematical ideas and techniques. In this paper we shall try to give an introduction to this beautiful circle of ideas. This paper is articulated in three sections: we rst try to give a very rough idea of what algebraic geometry is, then we discuss gauge theory, and in a nal section we talk about strings, in particular discussing how a physical theory like string theory is able to produce highly nontrivial mathematical results such as the enumeration of curves in algebraic varieties