Higher genus Gromov-Witten correspondences for log Calabi-Yau surfaces

Tsinghua-BIMSA symplectic geometry seminar

Organizers：

Kenji Fukaya (YMSC), Honghao Gao (YMSC), Hang Yuan (BIMSA)

Speaker：

Ben Zhou (Tsinghua)

Time：

Wed., 14:00-15:00

Oct. 16, 2024

Venue：

C548, Shuangqing Complex Building

Title：

Higher genus Gromov-Witten correspondences for log Calabi-Yau surfaces

Abstract：

Strominger, Yau, and Zaslow (SYZ) phrased mirror symmetry as a duality between special Lagrangian fibrations over an affine manifold base. The Gross-Siebert program seeks to translate the SYZ conjecture into the language of algebraic geometry using toric degenerations and tropical geometry. From a toric log Calabi-Yau surface X with a smooth anticanonical divisor, one can construct a scattering diagram (which locally one associates a Poisson algebra) and its quantization using the Gross-Siebert program. One can then infer from the scattering diagram various kinds of Gromov-Witten invariants. I will explain the above terms, and how higher-genus correspondences between certain open, closed, and logarithmic Gromov-Witten invariants associated to the log Calabi-Yau surface X can be derived. Part of this is joint work with Tim Gr\"afnitz, Helge Ruddat, and Eric Zaslow.