Bertrand Rémy: Simple and non-simple groups acting on buildings, overview and open questions

We will review results on simplicity for groups acting on buildings; we will also mention some yet unsolved problems, in particular dealing with the case of trees. Surprisingly, this is the case (with the simplest possible buildings) where the situation is not fully understood for Kac-Moody lattices. This is joint work with Pierre-Emmanuel Caprace.