In the first part we discuss the holographic entanglement entropy in
AdS4/CFT3 for finite domains with generic shapes. For smooth shapes the
constant term can be evaluated by employing a generalisation of the Willmore
functional for two dimensional surfaces. Explicit examples are given for
asymptotically AdS4 black holes, domain wall geometries and time dependent
backgrounds.
The second part is focused on the entanglement negativity in CFT.
In 2+1 dimensions we present some numerical results for two adjacent regions
in a two dimensional harmonic lattice, discussing the area law behaviour and
the corner contributions. In 1+1 dimensions and for two disjoint intervals
in the Ising and the Dirac fermion models, we show that the contribution of
a given spin structure to the moments of the partial transpose is obtained
as the scaling limit of a specific lattice term. This analysis provides also
the moments of the partial transpose for the free fermion.