Counting curves with tangency conditions: comparison of approaches -- Dan Abramovich

How many plane conics through four general points are tangent to a general line? Relative Gromov-Witten theory is devoted to "virtually" answering questions of this nature. Chuck Cadman, in his Columbia thesis, proposed an alternative approach through orbifold Gromov-Witten theory of r-th root orbifolds. I'll report on joint work with Cadman and Jonathan Wise, where we "virtually" compare the two approaches when counting genus 0 curves.