CMSA Mathematical Physics Seminar: Full SYZ Conjecture for del Pezzo Surfaces and Rational Elliptic Surfaces


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February 22, 2021 10:00 am - 11:00 am
via Zoom Video Conferencing

Yu-Shen Lin - Boston University

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.