### On the dimension of sets that avoid approximate arithmetic progressions

Ergodic Theory and Dynamical Systems Seminar

23rd April 2020, 2:00 pm – 3:00 pm

Online, https://bluejeans.com/729781245

I will present quantitative estimates for the supremum of the Hausdorff dimension of sets in the real line which avoid epsilon-approximations of arithmetic progressions. These estimates improve considerably the bounds given by Fraser, Saito and Yu (IMRN, 2019), in particular answering a question left open in that paper. I will also show that for this problem, Hausdorff dimension is equivalent to box or Assouad dimension. Joint work with J. Fraser and P. Shmerkin.

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