Concrete Mathematics: Fractals, Digital Functions, and Point Distributions (START Y96-MAT)

The START Project Y96-MAT is concerned with questions from pure mathematics which have gained new applications in various areas recently: - Diffusion on fractals: From the very beginning fractals have been used to model porous media. Consequently, diffusion and mass transport in porous media is modelled by diffusion on fractals. Physicists have found mathematical models of this type to be important aids in understanding the structure of polymers, colloids, and oil bearing rocks. The current program has achieved several results on the exact speed of this diffusion. - Digital expansions: Digital constructions present a vast number of concrete examples for dynamical systems, well-distributed sequences, and fractal phenomena. Furthermore, digital sequences and substitution automata occur in quite surprising contexts, such as mathematical physics, but also unexpectedly in number theoretical questions which have no obvious relation to digital functions. - Point distributions: "Well-distributed" point sets are commonly used for numerical integration and area measurement. In the case of high-dimensional cubes, many mostly number-theoretical constructions for such point sets are known and applied, for instance, in financial mathematics. The project intends to find number-theoretical and potential-theoretical constructions for well-distributed point sets on the sphere.