Tropical computation of genus 0 characteristic numbers

From CRCG-Wiki

Let C be a generic configuration of k points and 3d-1-k lines. The characteristic number N_d(k) is the number of (complex) rational curves of degree d passing through the points and tangent to the lines. We tropicalize the problem thanks to a correspondence theorem and reduce it to the count, with multiplicities, of some bipartite graphs called floor diagrams. I will try to explain how (open) Hurwitz numbers appear naturally in the multiplicities of such graphs.

(Joint work with E.Brugallé and G. Mikhalkin)