Lukas Katthän: Stanley depth, partitionable simplicial complexes and the lcm lattice

The Stanley depth is a combinatorial invariant associated to multigraded  modules over the polynomial ring. It was introduced by Apel in 2003, motivated by a famous (then) open conjecture by Stanley. Even though this conjecture was recently disproved by Duval, Goeckner, Klivans and Martin, there are still interesting (and difficult) open questions regarding this invariant. In this talk, I will review recent results in this field, in particular in connection with the lcm-lattice of monomial ideals. If time allows, I will also sketch the relation to the cone of multigraded Hilbert series of modules with a given minimal depth.