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Friday, January 25, 2019

**Abstract:** In 1968 Robert Kaufman introduced a potential theoretic approach to Hausdorff dimension. This approach allowed the use of Fourier analytic tools to answer questions about fractal Hausdorff dimension. In the late 90's Kenneth Falconer introduced a similar approach to packing and box counting dimensions. This allowed further developments on this area of geometric analysis such as Marstrand-Mattila type projection theorems for these different notions of fractal dimension. In this talk we will go through the development of this approach and (if time permits) go over the proof of the projection theorem for box and packing dimensions.