Mock modularity of log Gromov-Witten invariants: the mirror to the projective plane

In joint work with Pierrick Bousseau, we established a correspondence between two seemingly different kinds of sheaf and curve counting invariants. On the sheaf theoretic side are the Vafa–Witten invariants of the projective plane, which arise from gauge theory, and on the other side are curve-counting invariants given by logarithmic Gromov–Witten theory of the mirror to the projective plane. I will describe this correspondence and show how it can be used to explain predicted mock modular behavior in the generating functions of logarithmic Gromov–Witten invariants. This is based on recent work: https://arxiv.org/abs/2602.08153