Fractality, Self-Similarity and Complex Dimensions
  We present an overview of a theory of complex dimensions of self-similar fractal strings, and compare this theory to the theory of varieties over a finite field from the geometric and the dynamical point of view. Then we combine the several strands to discuss a possible approach to establishing a cohomological interpretation of the complex dimensions. 
Michel L. Lapidus and Machiel van Frankenhuijsen