Computability Seminar MSRI program on DDC-Effective Hausdorff dimension and applications

Organizer: V. Harizanov

For link contact [email protected]

Thursday, November 19, 12:00-1:00 ET on Zoom

Speaker: : Ted Slaman, UC California, Berkeley

Title: Effective Hausdorff dimension and applications

Abstract: The Hausdorff Dimension of a set of real numbers A is a numerical indication of the geometric fullness of A. Sets of positive measure have dimension 1, but there are null sets of every possible dimension between 0 and 1.  For example, the Cantor middle third set has dimension log(2)/log(3). Effective Hausdorff Dimension is a variant which incorporates computability-theoretic considerations. By work of Jack and Neil Lutz, Elvira Mayordomo, and others, there is a direct connection between the Hausdorff dimension of A and the effective Hausdorff dimensions of its elements. We will describe how this “point-to-set” principle allows for novel approaches to classical problems in Geometric Measure Theory.