Notes for a lecture at the Mostow conference

Author's comments: I took the occasion of the Mostow conference in New Haven on Oct. 23 to discuss my still provisional reflections on the geometric theory, thus for the second part of the Prologue. The best I can offer in the way of a geometric theory with which I would be pleased is a sketch of the principal difficulties to be overcome. There are many. The importance for me is the very strong analytic flavour of the theory I hope to construct or see constructed.

Video of lecture: https://www.youtube.com/watch?v=pfpzET8UkF4