Title: Wall crossing from tilt stability and its applications
I will first quickly review slope stability on sheaves with some examples. Then I will introduce Bridgeland's tilt stability with a focus on the description of nested walls and ways to determine different types of walls. I will also give an explicit computation showing how to use wall crossing to determine the sheaf structure. Some applications such as describing the moduli of sheaves of a given Chern character and Castelnuovo bounds will be discussed in the end of the talk.