学术报告（周雁 2024.12.20）

Abstract: The Mirror Symmetry Program for log Calabi-Yau varieties proposed by Gross-Hacking-Keel predicts that for a large class of Calabi-Yau (resp. log Calabi-Yau) varieties, their homogeneous coordinate (resp.coordinate) rings have canonical bases of theta functions analogous to the classical theta functions of abelian varieties. We prove this conjecture for a smooth log Calabi-Yau surfaces with maximal boundary. The key ingredient of our proof is identification of the compactified mirror family of a positive Looijenga pair constructed by Gross-Hacking-Keel with the universal family of log Calabi-Yau surface pairs deformation equivalent to the original Looijenga pair. The talk is based on joint work with Jonathan Lai.