Abstract: In this talk, I'll present a recent proposal of a Fourier-Mukai kernel for VGIT problems associated to flops due to Ballard-Diemer-Favero. When the GIT problem is that of $\mathbb G_m $ acting on a smooth scheme, they check that these kernels produce the `grade-restriction windows' that have been well studied in the literature. In the non-smooth case, we show that this proposal produces windows by working on "smooth" dg-resolutions. If time permits, we will also discuss some work in progress concerning generalizations to general groups.