Regularisation by fractional noise and the zero noise limit

In the talk, I will present the results from my thesis on the limit of zero noise for the singular SDEs driven by the fractional Brownian motion. I will present the proof of convergence towards the extremal solutions in the Peano example in the full Catellier-Gubinelli regime (which is to say we can consider arbitrarily singular power-law function), along with the upper bound for the convergence rate. The proof uses techniques from regularisation by noise and the study of ergodicity of fractional SDEs, established by Hairer and Panloup-Richard. Time permitting, I will discuss ongoing work on the multidimensional case and remaining open problems, along with some possible ideas on how to solve them.