Abstract: Enumerative geometry deals with counting geometric objects (lines, curves, planes) subject to certain restrictions (passing through a collection of points, tangent to a curve, etc.).

I will discuss a wide class of such problems on a crossroads of a real enumerative geometry and smooth topology and explain its relation to the theory of finite type invariants. I will also present a simple approach to such problems using maps of configuration spaces and intersections.

The talk does not assume any preliminary knowledge of the subject and should be easily accessible to students.