Junior Geometry and QFT Seminar

It is well known that the wall structure ensures certain properties of objects remain unchanged if the objects stay in the same chamber, but may vary discontinuously when crossing a wall. Thanks to Daniel’s talk last week, where the wall structure on the space of Bridgeland stability conditions was introduced by the end, we are now ready to explore its consequences. In this talk, I will first introduce DT invariants for Bridgeland semistable objects, viewed as a generalization of the DT invariants we defined last week for (semi)stable sheaves on Calabi–Yau threefolds. Then, I will develop the wall-crossing formula for these DT invariants before immediately applying that to an important case called DT/PT correspondence. Finally, I will discuss the wall-crossing behavior of BPS indices, emphasizing its connection to the wall-crossing phenomena of DT invariants.