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][1] of the conference with many videos, and Atiyah's is now uploaded too!


  [1]: http://www.connes70.fudan.edu.cn/Data/View/213