UBC Mathematics Department
Enumerative geometry is a very old subject. It attempts to answer questions such as: How many members of a pencil of cubics through 8 points are singular? Our first task will be to explain what this means and how to answer such questions. In recent years new insights in enumerative geometry have been gained by the techniques of quantum cohomology. In fact, we only now understand even the proper questions enumerative geometry should ask. We will explain this new point of view.