Counting curves with tangency conditions
Charles Cadman, University of Michigan


Gromov-Witten theory has been used to tackle problems in enumerative geometry ever since Kontsevich found a nice recursion computing the number of rational degree d plane curves passing through 3d-1 general points. The Gromov-Witten theory of stacks is a recent development, and I used it to count rational plane curves which are tangent to a smooth cubic at a specified number of points. More precisely, there are explicit recursions which generalize Kontsevich's recursion and reduce everything to how many lines pass through two general points. It is possible to combine this with a technique used by Caporaso and Harris to generalize and simplify the result. I will state the result and give an outline of the proof.