Singularities of moduli of sheaves on K3 surfaces and formality.
Abstract: We consider the moduli space of H-semistable sheaves of a not necessarily primitive class on a projective K3 surface (X,H). Kaledin and Lehn conjectured that a certain differential graded algebra that controls the deformations of these sheaves is formal, which leads to a complete classification of the singularities of these moduli spaces. I will discuss how one can apply a technique of Kaledin to prove the conjecture in some cases. I will also mention some recent development in this direction by various authors.