On January 20, I will give a 4 hours mini course on the Dirichlet forms at the NYU campus of Abu Dhabi. Lectures will be posted on this blog and I will prepare an extended set of lecture notes. This visit to Abu Dhabi will also be the occasion to push further a long-term project on stochastic areas with my friend and collaborator Nizar Demni.
Abstract: Dirichlet forms theory allow us to define Laplacians, PDEs and boundary conditions in very general frameworks which do not require any kind of smooth structures including metric spaces like fractals. In this mini-course, we will cover the following topics:
1) Contraction semigroups, quadratic forms and generators in Hilbert spaces;
2) Dirichlet forms;
3) Examples of Dirichlet spaces: Riemannian manifolds, Fractals, Metric spaces;
4) The Gagliardo-Nirenberg interpolation theory in Dirichlet spaces.
Research and Lecture notes 
Thank you I would very much like to have access to these notes and to recordings of the mini course On Dirichlet forms , PDE and Probability. At NYU Abu Dhabi.
Sincerely Dennis Sullivan ( needing help online )
Dear Denis, Thanks for the interest. I will make those notes available and keep you updated.