On information theory in geometric measure theory: how computer science can change pure mathematics

Effective dimensions were defined by Lutz and have proven to be useful and meaningful for quantitative analysis in the contexts of algorithmic randomness, computational complexity and computable fractal geometry.

The point-to-set principle (PSP) of J. Lutz and N. Lutz is in fact a return trip from the effectivization of mathematical concepts (Hausdorff dimension) to the classical concept itself, since it fully characterizes Hausdorff and packing dimensions in terms of effective dimensions in the Euclidean space,  enabling effective dimensions to be used to answer open questions about fractal geometry, with already an interesting list of geometric measure theory results.

In this talk I will review the point-to-set principles focusing on its recent extensions to separable spaces and to Finite-State dimensions, and presenting open questions as well as further application opportunities.

About Dr. Mayordomo

Elvira Mayordomo is a Professor in the Department of Computer Science and Systems Engineering at the University of Zaragoza, Spain. She received her PhD in computer science at the Polytechnic University of Catalonia, Spain, with an emphasis on Theoretical Computer Science. She has done extensive work on algorithmic information theory, algorithmic geometric measure theory and computational complexity. She is President of the scientific association Computability in Europe (CiE).