Résume | The so-called RoCK (or Rouquier) blocks play an important role in representation theory of symmetric groups over a finite field of characteristic $p$, as well as of Hecke algebras at roots of unity. Turner has conjectured that a certain idempotent truncation of a RoCK block is Morita equivalent to the principal block $B_0$ of the wreath product $S_p\wr S_w$, where $w$ is the ``weight'' of the block. More precisely (and more simply), the conjecture states that the idempotent truncation in question is isomorphic to a tensor product of $B_0$ and a certain matrix algebra. The talk will outline a proof of this conjecture, which uses an isomorphism between the group algebra of a symmetric group and a cyclotomic Khovanov-Lauda-Rouquier algebra and the resulting grading on the group algebra of the symmetric group. This result generalizes a theorem of Chuang-Kessar, which applies to the case $w |