Abstract
The construction of stability conditions on the bounded derived
category of coherent sheaves on smooth projective varieties is
notoriously a difficult problem, especially when the canonical bundle
is trivial. In this talk, I will review some results and techniques
related to the latter setting. I will specifically concentrate on the
case of Hilbert scheme of points on K3 surfaces and (as a work in
progress) on generic abelian varieties of any dimension. This is joint
work in progress with C. Li, E. Macri' and X. Zhao.