Topological String Theory & Gromov-Witten Invariants —
Topological A-model strings map worldsheets Σ_g (genus g) into a Calabi-Yau 3-fold X.
The Gromov-Witten invariant N_{g,d} counts (virtually) such holomorphic maps in class β∈H₂(X,ℤ) with degree d.
The partition function Z = exp(∑_{g,d} λ^{2g-2} q^d N_{g,d}) encodes all amplitudes.
Mirror symmetry (BCOV) identifies this with period integrals on the mirror CY3.
Visualized: evolving worldsheet moduli, degree-d curves, and the instanton sum structure.