Full SYZ Conjecture for del Pezzo Surfaces and Rational Elliptic Surfaces

2021-02-22 10:00 - 11:00

CMSA-Mathematical-Physics-02.22.21

Speaker: Yu-Shen Lin (Boston University)

Title: Full SYZ Conjecture for del Pezzo Surfaces and Rational Elliptic Surfaces

Abstract: Strominger-Yau-Zaslow conjecture predicts the existence of special Lagrangian fibrations on Calabi-Yau manifolds. The conjecture inspires the development of mirror symmetry while the original conjecture has little progress. In this talk, I will confirm the conjecture for the complement of a smooth anti-canonical divisor in del Pezzo surfaces. Moreover, I will also construct the dual torus fibration on its mirror. As a consequence, the special Lagrangian fibrations detect a non-standard semi-flat metric and some Ricci-flat metrics that don’t obviously appear in the literature. This is based on a joint work with T. Collins and A. Jacob.