Benjamin Sung: Stability Manifolds and Applications

The theory of Bridgeland stability conditions assigns a complex manifold to the derived category of coherent sheaves on a smooth projective variety. The structure of this complex manifold is central for applications to algebraic geometry and mathematical physics, but describing even a connected component is often a difficult, open problem. In this talk, I will survey recent progress on describing the complete stability manifolds for a wide class of varieties, including abelian threefolds and general products of varieties with elliptic curves. I will describe applications to mirror symmetry for abelian varieties as well as to establishing higher Chern character inequalities. This is based partly on works in progress, one with Fabian Haiden, and the other with Chunyi Li, Zhiyu Liu, and Xiaolei Zhao.