Title: Bridgeland Stability and Vanishing Theorems for Surfaces

Abstract: Stability has a built-in vanishing property.  If objects A,B
are both stable and their slopes satisfy m(A) > m(B), then Hom(A,B) =
0. This suggests a strategy for proving vanishing of a cohomology
space.
Namely, identify the space with a Hom space of stable objects.  Serre
duality is one tool for doing this in the case of H^2 for surfaces,
but with Bridgeland stability we can also carry out this strategy to
prove much more delicate vanishing results for H^1.  As an example,
I'll show how to prove Reider's theorem using these ideas. This is
joint work with Daniele Arcara.