Alexia Yavicoli

On the dimension of sets that avoid approximate arithmetic progressions

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.