Category Archives: Uncategorized
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
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
Effective dimension of points on a line
The purpose of this post is to describe the strategy Neil Lutz and I used to prove lower bounds on the effective dimension of points on a line in . This strategy seems quite general, and has been the basis … Continue reading
Welcome to my Math + CS blog! I plan on using this blog to talk about my research and to post lecture notes. Quick test of Latex functionality: .