While the issue of boundedness of singular integral operators (SIO) is reasonably understood, the specific manner in which the geometry impacts the size of the SIO remains a source of fascinating questions. After the initial breakthrough by S. Hofmann, M. Mitrea, and M. Taylor in 2010, significant progress has been made by D. Mitrea, I. Mitrea, and the present speaker in their series Geometric Harmonic Analysis, vols. I-V, 2022-2023, in the realm of boundary layer potentials associated with elliptic PDE’s. Here, I will report on recent progress aimed at taking the next steps in the direction of accommodating boundary layer potentials associated with parabolic PDE’s. The main tools and techniques originate in Harmonic Analysis and Geometric Measure Theory.