I'm a mathematician studying Schubert calculus, and I'm out to compute the Gromov-Witten invariants of the complete flag manifold. Well, I actually already know how to compute them, but only in a way that involves cancellation, and the goal is to masterfully cancel everything and have only a formula that describes what's left.
I've heard this has some relationship to quantum field theory. I know very little physics other than what an enthusiast would read in a popular science book, but I do have some interest in the relationship of the problem I will spend my life failing to solve (far easier problems have been unsolved for 136 years) to reality. If anyone could give a brief overview of why physicists care about Gromov-Witten invariants I would appreciate it.