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Sanju Velani: Diophantine approximation, fractal sets and lacunary sequences

Time: Wed 2017-09-27 15.00 - 15.50

Location: Institut Mittag-Leffler, Auravägen 17, Djursholm

Participating: Sanju Velani, University of York

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The metric theory of Diophantine approximation on fractal sets is discussed in which the denominators of the rational approximates are restricted to lacunary sequences. The case of the standard middle third Cantor set and the sequence \({3^n : n \in N}\) is the starting point of our investigation. Our metric results for this simple setup answers a problem raised by Mahler. As with all ‘good’ problems – its solution opens up a can of worms.