Invariants from the Topological String/Spectral Theory correspondence

Building on the seminal paper by Candelas, De La Ossa, Green, and Parkes, topological string
theory on Calabi–Yau threefolds has been a source of inspiration for enumerative geometers.
While mirror symmetry has been extensively studied in all its aspects, the so-called Topological
String/Spectral Theory (TS/ST) correspondence of Grassi–Hatsuda-Mariño has been recently
attracting more attention. Indeed, it predicts a new source of (resurgent) invariants, which
should be conjecturally related to enumerative invariants. In this talk, I will introduce these new
resurgent invariants and discuss their expected connection with Gromov–Witten invariants,
focusing on the examples of local P2.