Title: Deformations of stability conditions with applications to Hilbert schemes of points and very general abelian varieties

Abstract: The construction of stability conditions on the bounded derived category of coherent sheaves on smooth projective varieties is a notoriously difficult problem, especially when the canonical bundle is trivial. In this talk, I will illustrate a new and very effective technique based on deformations. A key ingredient is a general result about deformations of bounded t-structures (and with some additional and mild assumptions). Two remarkable applications are the construction of stability conditions for very general abelian varieties in any dimension and for irreducible holomorphic symplectic manifolds of Hilb^n-type, again in all possible dimensions. This is joint work (in progress) with C. Li, E. Macri', A. Perry and X. Zhao.