Brownian motions and Dirichlet forms on self-similar fractals

In this talk, we will briefly review the process on the constructions of Brownian motions and Dirichlet forms on self-similar fractals. We will start with the constructions on the classical Sierpinski gasket and Sierpinski carpet, and include some recent progress on the unconstrained Sierpinski carpets. The talk is based on joint work with Shiping Cao.