Geometry Seminar

Enumerative mirror symmetry is the computation of Gromov-Witten invariants via integrals of the holomorphic volume form in a mirror Calabi-Yau geometry. This prediction along with the period computation for the mirror quintic threefold by Candelas, de la Ossa, Green and Parkes here at UT in 1991 started the field. We report on a recent breakthrough - a proof of enumerative mirror symmetry within the intrinsic mirror symmetry framework for the crucial test case \(K_{\mathbb{P}^2}\), the local projective plane. This opens the way to finally proving enumerative mirror symmetry in a completely tautological and structural fashion, without "miracles" or ad hoc choices. This is joint work with Michel van Garrel and in part with Helge Ruddat.