Configurations, dimension, and fractal sets

Document Type

Presentation Abstract

Presentation Date

2-14-2022

Abstract

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 problems in the general area of the study of geometric configurations. A discussion of notions of size and dimension that are robust to the fractal setting will be included. As particular examples, we will 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.

Additional Details

February 14, 2022 at 3:00 p.m. Math 103 & Zoom

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