Three-loop QCD corrections to heavy-to-light form factors and applications to inclusive $B$ decays

We report on the calculation of heavy-to-light form factors at $\mathcal{O}(α_s^3)$ and on selected phenomenological applications in inclusive $B$-decays. After outlining the loop calculation, we extract the hard function in $\bar B \to X_s γ$, and discuss our recent progress and preliminary results