Higher Genus Gromov–Witten theory of Smooth Calabi–Yau Threefolds in Weighted P^4

The Yamaguchi–Yau finite generation conjecture predicts that the higher-genus Gromov–Witten potentials of compact Calabi–Yau threefolds are polynomials in a finite number of generators. In this talk, I will outline a recent approach to apply Givental’s quantization formalism to the Gromov–Witten theory of Calabi–Yau threefolds and explain a proof of this conjecture for smooth Calabi–Yau hypersurfaces in P(1, 1, 1, 1, 2), P(1, 1, 1, 1, 4), and P(1, 1, 1, 2, 5).