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Friday, October 19, 2018

**Abstract:** The set of particular interest will be $C(1/4) = C_{1/4} \times C_{1/4}$ where $C_{1/4}$ is the 1/4-Cantor set in $\mathbb{R}$. I will be presenting two proofs on the projections of $C(1/4)$ onto lines in $\mathbb{R}^2$. By utilizing the self-similar structure, these proofs present more detailed information on projections of $C(1/4)$ than the Marstrand projection theorem is able to. Due to time constraints, I will only go over one of the proofs in details, then sketch the proof of the sharper result by pointing out the necessary lemmas to obtain it.