Patterns and Szemerédi phenomena in random fractals

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.

• Speaker: Pablo Shmerkin (Buenos Aires)
• Tuesday 28 January 2020, 14:00–15:00
• Venue: MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.
• Series: Probability; organiser: Perla Sousi.