Configurations, Dimensions, and Fractal Sets

A vibrant and classic area of research is that of relating the size of a set to the finite point configurations that it contains.  Here, size may refer to cardinality, dimension, or measure.  In this talk, we give an introduction to some notions of size and dimension that are robust to the fractal setting.  

As particular examples, we consider two notions of size- Hausdorff dimension and Newhouse thickness- that can be used to guarantee the existence of arbitrarily long paths within fractal subsets of Euclidean space.