Many invariants in symplectic geometry and low dimensional topology are defined by "counting" points of moduli spaces (of solutions to suitable nonlinear elliptic equations). To make sense of "counting" when the moduli spaces are not manifolds of the expected dimension, one needs a technical device called the virtual fundamental class (VFC).

In this talk, we will try to explain the basic idea behind VFCs and illustrate how this works in some model cases.