Intersection theory and the Jacobian Conjecture

Intersection theory's goal is to "count" the number of ways geometric objects intersect each other. This can be applied to enumerative geometry questions (such as "How many conics go through 4 points and are tangent to a given line?"), or more geometric enterprises (calculating the Euler characteristic of a space). In this talk I will give a brief introduction to the ideas of the subject, with a few examples (the intersection ring of projective n-space, the answer to the above conics question, and perhaps another reason why the Euler characteristic of the sphere is 2).