Dimension bounds for singular affine forms

in this talk, I will establish upper bounds on the dimension of sets of singular affine forms in singly metric settings, where either the matrix or the shift is fixed. The results will be derived in a generalized weighted setup and for points sampled from fractals. This partially answers the questions posed by Das, Fishman, Simmons, Urbański, as well as by Kleinbock and Wadleigh.

 This talk is based on https://arxiv.org/pdf/2501.01713