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

组织者

深谷賢治 , 高鸿灏 , 袁航

演讲者

Ben Zhou

时间

2024年10月16日 14:00 至 15:00

地点

Shuangqing-C546

线上

Zoom 388 528 9728 (BIMSA)

摘要

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.