Outer derivations on blocks of group algebras

Let G be a finite group and let k be a field whose characteristic divides the order of G. The derivation problem for group algebras asks whether HH^1(kG):=Der(kG)/Inn(kG), the space of k-linear derivations modulo inner derivations, is nonzero. Fleischmann, Janiszczak, and Lempken proved that kG always possesses a non-inner derivation in this case. Linckelmann posed a blockwise version of this result as a conjecture: if B is a non-semisimple block of the group algebra kG, then HH^1(B) is nonzero. In this talk, I will focus on recent advances on this conjecture. This is joint work with Matthew Antrobus, Benjamin Briggs and Can Wen.