Systoles, Special Lagrangians, and Bridgeland stability conditions


Yu-Wei Fan ( Harvard University, USA )
2018-05-30  15:00 - 16:00
Room 103, Mathematics Research Center Building (ori. New Math. Bldg.)

Loewner\'s torus systolic inequality states that the shortest length of a non-contractible loop (systole) on a two-torus can not be too large compare to its volume. We attempt to generalize this relation from the viewpoint of Calabi-Yau geometry. This naturally leads to the notions of systole and systolic ratio of Bridgeland stability conditions. We will first recall some backgrounds on mirror symmetry and Bridgeland stability conditions. Then we will study an example in the case of K3 surface.