Arithmetic progressions in sets of fractional dimension
Izabella Laba (UBC)

Let $E\subset {\bf R}$ be a closed set of Hausdorff dimension $\alpha$. We prove that if $\alpha$ is sufficiently close to 1, and if $E$ supports a probability measure obeying appropriate dimensionality and Fourier decay conditions, then $E$ contains non-trivial 3-term arithmetic progressions. (Joint work with Malabika Pramanik.)

Colloquium, Department of Mathematics, Rice University
December 4, 2008 4-5PM, HB 227

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