Counting holomorphic curves in blowups of the projective plane using tropical curves.
I will explain how to compute the Gromov-Witten invariants of the complex projective plane blown up at an arbitrary number of points; these invariants count holomorphic curves, or holomorphic maps of Riemann surfaces. We will track these holomorphic curves at two different scales through an adiabatic limit, and see that when we zoom out, these holomorphic curves look like piecewise linear graphs called tropical curves. I will then describe a tropical gluing formula for our Gromov-Witten invariants, and depict how repeated application of this gluing formula allows recursive calculation of our Gromov-Witten invariants. There will be lots of pictures.
Dr Brett Parker, Monash University