In symplectic manifolds, isotropic, coisotropic, and lagrangian submanifolds play a central role, and their study leads to deep problems in symplectic geometry and topology. It turns out that the linearized version of this study is already quite non-trivial. The classification of pairs of isotropic subspaces in a symplectic vector space turns out to be rather simple, but for isotropic triples, it is much more complicated. In particular, there are families of inequivalent indecomposable isotropic triples depending on one parameter (but no more). In these talks, I will report on progress on this problem in ongoing work with Christian Herrmann (University of Dartmstadt) and Jonathan Lorand (University of Z\"urich).