Mathematical Conversations

I've been working a lot on "random surfaces" in recent years.  These are "canonical" random fractal Riemannian manifolds (just as Brownian motion is a canonical random fractal curve) and they come up in many areas of physics and mathematics.  In a recent lCM lecture (with notes), I tried to give a proper general audience overview of the subject.  In the outdoor session on Wednesday I will speculate about what random surfaces might have to do with the Clay Institute's Millennium Prize Problem about Yang-Mills theory.  I have been instructed to talk about my dreams.  But time permitting, I may mix in a touch of reality as well.