Bogomolov-Gieseker type inequality and OSV Conjecture, I

The conjectural Bogomolov-Gieseker (BG) type inequality among Chern characters of certain semistable objects in the derived category of coherent sheaves on projective 3-folds was proposed by Bayer, Macri and myself. Originally it was proposed in order to construct a Bridgeland stability condition on projective 3-folds, while it turned out that our conjecture has applications to the study of Fujita conjecture on 3-folds. (Bayer-Bertram-Macri-T.)
In this talk, I explain that our BG inequality conjecture is also related to Denef-Moore's approach towards Ooguri-Strominger-Vafa conjecture predicted in string theory. I will try to include both math and physics aspects of this subject in two talks, as far as possible.