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UID:node-3036675@mathematics.huji.ac.il
DTSTAMP:20210615T110000Z
DTSTART:20210615T110000Z
DTEND:20210615T120000Z
SUMMARY:Manuel Luethi (TAU) Random walks on homogeneous spaces, SpectralGaps, and Khintchine's theorem on fractals
DESCRIPTION:*Abstract:* Khintchine's theorem in Diophantine approximation gives a zero \none law describing the approximability of typical points by rational points. \nIn 1984, Mahler asked how well points on the middle third Cantor set can be \napproximated. His question fits into an attempt to determine conditions under \nwhich subsets of Euclidean space inherit the Diophantine properties of the \nambient space.\nIn this talk, we discuss a complete analogue of Khintchineâ€™s theorem for \ncertain fractal measures. Our results hold for fractals generated by rational \nsimilarities of Euclidean space that have sufficiently small Hausdorff \nco-dimension. The main ingredient to the proof is an effective \nequidistribution theorem for associated fractal measures on the space of \nunimodular lattices. The latter is established using a spectral gap property \nof a type of Markov operators associated with a random walk related to the \ngenerating similarities. This is joint work with Osama Khalil.\n*Zoom details:*\nJoin Zoom Meeting [1]\nMe...
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