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SUMMARY:Computability and Set Theoretic Aspects of Hausdorff Dimension - T
 heodore Slaman (University of California\, Berkeley)
DTSTART:20220608T101500Z
DTEND:20220608T111500Z
UID:TALK174818@talks.cam.ac.uk
DESCRIPTION:The Hausdorff Dimension of a set of real numbers A is a numeri
 cal indication of the geometricfullness of A. Sets of positive measure hav
 e dimension 1\, but there are null sets of every possibledimension between
  0 and 1. &nbsp\;\nEffective Hausdorff Dimension is a variant which incorp
 orates computability-theoreticconsiderations. By work of Jack and Neil Lut
 z\, Elvira Mayordomo\, and others\, there is a directconnection between th
 e the effective Hausdorff dimensions of the elements of a set A and theHau
 sdorff dimension of A itself. We will describe how this point-to-set princ
 iple works\, how allowsfor novel approaches to classical problems and furt
 her lines of investigation in Geometric MeasureTheory.
LOCATION:Seminar Room 1\, Newton Institute
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