This talk is based on the preprint https://arxiv.org/abs/2305.06031.
Let A be a finite-dimensional algebra and T(A) the lattice of torsion classes of finitely-generated A-modules. We use the theory of stability conditions to define a partial order (the "facial semistable order") on a set of intervals in T(A). By restricting to functorially finite torsion classes, this yields a partial order on the set of all 2-term presilting complexes. This then further restricts to the oriented mutation graph on 2-term silting complexes. In this talk, we discuss the construction, cover relations, and lattice properties of the facial semistable order.