# 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

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Tagged effective dimension, geometric measure theory, projection theorem
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## 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