Northern California Symplectic Geometry Seminar: Systoles, Special Lagrangians, and Bridgeland stability conditions

Seminar | November 4 | 4-5 p.m. | 748 Evans Hall

 Yu-Wei Fan, UC Berkeley

 Department of Mathematics

We propose a question that naturally generalizes Loewner’s torus systolic inequality from the perspective of Calabi-Yau geometry: Is the square of the minimum volume of special Lagrangians in a Calabi-Yau manifold bounded above by the total vol- ume of the Calabi-Yau? We introduce the categorical analogues of systole and volume in terms of Bridgeland stability conditions, which enables us to formulate its mirror question under mirror symmetry. Finally, we give an affirmative answer to the mirror question for K3 surfaces of Picard rank one.