Recent advances and open questions on the susy structure of the chiral de Rham Complex
  We review different constructions of the supersymmetry subalgebras of the
chiral de Rham complex on special holonomy manifolds. We describe the
difference between the holomorphic-anti-holomorphic sectors based on a local
free ghost system vs the decomposition in left-right sectors from a local
Boson-Fermion system. We describe the topological twist in the case of $G_2$
and $Spin_7$ manifolds. We describe the construction of these algebras as
quantum Hamiltonian reduction of Lie superalgebras at the minimal or
superprincipal nilpotent.
