Xander Faber will give the talk on Monday, December 6 at 4:15 in Math 528. This lecture will be open to all.
Abstract:
How does one measure the dimension of subsets of
R^n which aren't smooth manifolds? For example, the standard
middle-thirds Cantor set has Lebesgue measure zero, but it's
uncountable. Consequently, it seems a bit harsh to label it
as a set of dimension zero. Hausdorff invented a particularly
nice notion of dimension which agrees with the usual sense of
dimension when the subset is a submanifold, but it's far more
general. The Cantor set has Hausdorff dimension log 2 / log 3.
In this talk we'll define the Hausdorff dimension, give some of
its properties, and then look at a very small list of interesting
applications of the theory.
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