Tag Archives: effective dimension
Pinned distance sets using effective dimension
I have just uploaded a paper on the Hausdorff dimension of pinned distance sets. For a given set , the distance set of E is If , the pinned distance set of E with respect to x is An important … Continue reading
Projection theorems using effective dimension
In this post I will describe how to use effective dimension to investigate how the fractal dimension of a set changes when projected onto a linear subspace. The first theorem investigating this behavior is the celebrated Marstrand projection theorem. Theorem … Continue reading
Posted in Uncategorized
Tagged effective dimension, geometric measure theory, projection theorem
Leave a comment
The dimension spectra of planar lines
I recently uploaded a paper solving the dimension spectrum conjecture. I wanted to write a post explaining some of the intuition behind the proof. The theme of the conjecture is to better understand the randomness of points on a line. … Continue reading