Applications of virtual fundamental classes to enumerative geometry

The aim of this talk is to show why understanding the construction of a virtual fundamental class is useful: firstly we do this via computing these in some examples of moduli spaces of stable maps and secondly by linking these classes to Gromov-Witten invariants and thus to certain problems in enumerative geometry. I will start with a recap from the summer (17th August), when moduli spaces of stable maps were introduced, giving explicit examples along the way. Then I will follow the [BCM]-article that we have been studying to develop an obstruction theory and thus construct virtual classes for these spaces. I will end with a discussion of Gromov-Witten invariants.