Bridgeland stability conditions under the Fourier-Mukai transforms on abelian threefolds
The notion of Fourier-Mukai transform for abelian varieties was introduced by Mukai in the early 1980s. Since then Fourier-Mukai theory turned out to be extremely successful in studying stable sheaves and complexes of them, and also their moduli spaces. I will discuss how the Fourier-Mukai techniques are useful to show that the conjectural construction proposed by Bayer, Macri and Toda gives rise to Bridgeland stability conditions on any abelian threefold. Part of this is a joint work with Antony Maciocia.