Seminar
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| Location: | SLMath: Online/Virtual |
Hilbert’s Tenth Problem was the only decision problem among his twenty-three problems. Precise mathematical theory of (in)computability and its interaction with number theory led to the negative solution of the problem. The seminar will focus on modern topics on computability-theoretic phenomena in number-theoretic and other algebraic and model-theoretic structures.
To participate in this seminar, please register here: https://www.msri.org/seminars/25206
Effective Hausdorff Dimension And Applications
To participate in this seminar, please register here: https://www.msri.org/seminars/25206
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.
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Effective Hausdorff Dimension And Applications
| H.264 Video | 25196_28694_8649_Effective_Hausdorff_Dimension_and_Applications.mp4 |