# Undergraduate companion to the minicourse on Tuesday April 18 and Thursday April 19, 2017, 8-9:15am, SMLC 356

### Event Description:

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*Title: **The Hausdorff dimension *

#### Speaker: Ricardo A. Sáenz (Universidad de Colima, Mexico)

Abstract: There exist subsets in the plane that lead to nonsense when we try to measure them, like curves with “infinite length” or sets with “zero area”. In order to avoid such situations, we have to find the “right exponent” to measure them. This exponent is called the Hausdorff dimension of the set, discovered by Felix Hausdorff at the start of the XX century. In these lectures we define the Hausdorff dimension of a subset of , and we review its basic properties. We calculate explicitly the Hausdorff dimension of some examples, and state and prove Hutchinson’s theorem on the dimension of self-similar sets under certain conditions.