Enumerative geometry is concerned with counting curves on algebraic varieties. From a slightly fancier point of view, this means doing intersection theory on moduli spaces. In this talk we will work through this in one key example: the classical 27 lines on a cubic surface. We will show how to apply Schubert calculus (the study of cohomology rings of Grassmannians) to answer enumerative questions.
Time permitting, we will sketch an alternative proof using torus localisation, a technique which can also be adapted to compute Gromov-Witten invariants.