In these lecture notes we give an introduction to Bridgeland stability conditions on smooth
complex projective varieties with a particular focus on the case of surfaces. This includes …

We introduce a general method to induce Bridgeland stability conditions on semiorthogonal
components of triangulated categories. In particular, we prove the existence of Bridgeland …

We show that a purely algebraic structure, a two-dimensional scattering diagram, describes
a large part of the wall-crossing behavior of moduli spaces of Bridgeland semistable objects …

We survey some recent results concerning the so called Categorical Torelli problem. This is
to say how one can reconstruct a smooth projective variety up to isomorphism, by using the …

We prove that ideal sheaves of lines in a Fano three-fold of Picard rank one and index two
are stable objects in the Kuznetsov component, with respect to the stability conditions …

We give an interpretation of the Fano variety of lines on a cubic fourfold and of the
hyperkahler eightfold, constructed by Lehn, Lehn, Sorger and van Straten from twisted cubic …

We show that the stability conditions on the Kuznetsov component of a Gushel–Mukai
threefold, constructed by Bayer, Lahoz, Macrì and Stellari, are preserved by the Serre …

The spectrum of BPS states in type IIA string theory compactified on a Calabi–Yau threefold
famously jumps across codimension-one walls in complexified Kähler moduli space, leading …

The key result in the theory of Bridgeland stability conditions is the property that they form a
complex manifold. This comes from the fact that given any small deformation of the central …

We give an interpretation of the Fano variety of lines on a cubic fourfold and of the
hyperkähler eightfold, constructed by Lehn, Lehn, Sorger and van Straten from twisted cubic …