1, 2, log(20)/log(3): Three definitions of "dimension"

Abstract: For more than a century, mathematicians have used dimension as a way to quantify the sizes of sets, identify their regularity properties, and distinguish between "metrically distinct" sets. In this talk, we'll examine three different definitions of "dimension"—Minkowski, Hausdorff, and similarity dimensions—in order to understand what properties an adequate definition should possess and why it is desirable to work with different, non-equivalent definitions of dimension. The material we cover will provide a foundation for future talks on current developments in the theory of dimension.