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Tsinghua-BIMSA Symplectic Geometry Seminar
Higher genus Gromov-Witten correspondences for log Calabi-Yau surfaces
Higher genus Gromov-Witten correspondences for log Calabi-Yau surfaces
Organizers
Speaker
Ben Zhou
Time
Wednesday, October 16, 2024 2:00 PM - 3:00 PM
Venue
Shuangqing-C546
Online
Zoom 388 528 9728
(BIMSA)
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.