This is the first talk for a reading seminar in Bridgeland stability. I will not attempt to give an overview of this topic and will only mention briefly what my goals of this seminar are. Instead, I will discuss stability conditions on abelian categories and provide some examples. This will provide motivation for the more sophisticated concept of Bridgeland stability conditions on triangulated categories.
For the first talk, very little background is required. For the subsequent talks, a basic understanding of triangulated or derived categories will likely be assumed; if you are keen on joining this seminar and don't have this background but are willing to do some outside reading and accept some results on faith, it is possible that you could still follow. At the end of the talk, we can discuss the details of this seminar and, in particular, decide on a meeting time.