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Patterns and Szemerédi phenomena in random fractals

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If you have a question about this talk, please contact Perla Sousi .

I will talk about a joint work with Ville Suomala in which we find sharp dimension thresholds for the existence of various patterns in fractal percolation sets. Some of the configurations we study are homothetic copies of finite sets, angles and volumes of simplices. In the spirit of Szemeréti-type results in random discrete sets, we also study the corresponding problems in sets of positive natural measure.

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