Title: Effective multifractal spectra
Speaker: Jan Reimann, Mathematics, Penn State University
Date and Time: Friday, Dec.1 1:00-2:00pm
Place: Rome 204
Multifractal measures play an important role in the study of point processes and strange attractors. A central component of the theory is the multifractal formalism, which connects local properties of a measure (pointwise dimensions) with its global properties (average scaling behavior).
In this talk I will introduce a new, effective multifractal spectrum, where we replace pointwise dimension by asymptotic compression ratio. It turns out that the underlying measure can be seen as a universal object for the multifractal analysis of computable measures. The multifractal spectrum of a computable measure can be expressed as a “deficiency of multifractality” spectrum with respect to the universal measure.
This in turn allows for developing a quantitative theory of dimension estimators based on Kolmogorov complexity. I will discuss some applications to seismological dynamics.
Short BIO: Jan Reimann is an Associate Professor in Mathematics at the Pennsylvania State University in University Park. He obtained his PhD from the University of Heidelberg in Germany and subsequently was a Morrey Assistant Professor at the University of California, Berkeley. His research focuses on computability theory and its connections to other areas, such as fractal geometry and number theory.