Is the amplituhedron a positive geometry?

I will discuss different approaches to and results about the question in the title. The main focus is on the case m=2. My goal is to discuss the strengths and technical challenges in analogy to the case of polytopes, where different approaches, based on triangulations, adjoints, or mixed Hodge theory, all work out nicely. For amplituhedra, each approach has a generalisation, yet none have lead to a proof yet.