Computing Node Polynomials for Plane Curves

Counting algebraic curves with certain prescribed properties is an old problem going back more than 150 years. In this talk I will describe recent progress on the following question: How many algebraic plane with a given number of nodes and given degree pass through a sufficient number of generic points? This year Fomin and Mikhalkin proved that this number is a polynomial (the node polynomial) if the degree is sufficiently large. Using tropical geometry and ``labeled floor diagrams" I will present some new node polynomials and a few other results about them.