Mirror Symmetry of Abelian Fibered Calabi-Yau Manifolds with ρ = 2

Explore mirror symmetry concepts in this 49-minute lecture from the Workshop on Representation Theory, Calabi-Yau Manifolds, and Mirror Symmetry, where Professor Shinobu Hosono from Gakushuin University examines Calabi-Yau manifolds fibered by (1,8)-polarized abelian surfaces with Picard number two. Discover how mirror symmetry emerges from boundary points in the explicitly constructed mirror family over a toric variety, and learn about Gromov-Witten invariants calculations up to genus 2, revealing generating functions expressed in elliptic (quasi-)modular forms reminiscent of modular anomaly equations found in elliptic surfaces. Based on collaborative research with Hiromichi Takaki, this mathematical exploration delves deep into advanced geometric concepts and their symmetrical properties.