The title is a talk given by Sir M. Atiyah in a conference with the following abstract:

I will explain a deep analogy between 4-dimensional smooth geometry (Donaldson theory) and algebraic number theory. In this analogy the group of exotic 4-spheres is the counterpart of the Tate-Shafarevich group

I'm extremely curious about the analogy and I can't find a document on the subject. Would someone enlighten us about this analogy ?

Edit I found a link of the conference with many videos, and Atiyah's is now uploaded too!