Algorithmic fractal dimensions were first developed at the beginning of the current century. As the name suggests, they are algorithmic versions of classical fractal dimensions. These are obtained by imposing various computability and complexity constraints on the functions that characterize Hausdorff dimension and its dual, packing dimension. Various choices of these constraints have already given algorithmic fractal dimensions applications in computability theory, computational complexity, information theory, and number theory. Most strikingly, algorithmic fractal dimensions are being used with increasing frequency to prove new theorems — some answering long-standing open problems — in classical fractal geometry, theorems whose statements do not involve computability or related aspects of mathematical logic.
The lecturer for the conference will be Dr. Jack Lutz, Professor of Computer Science at Iowa State University. Dr. Lutz is a distinguished American theoretical computer scientist, renowned for his contributions to the fields of resource-bounded measure and effective dimension. His work extends to research in DNA computing and self-assembly. Lutz pursued his education at the University of Kansas, earning master’s degrees in mathematics and computer science, and completed his Ph.D. at the California Institute of Technology. He has spent a majority of his career at Iowa State University, serving as a professor of computer science and mathematics and directing the Laboratory for Molecular Programming.