Abstract: Fast, high-accuracy algorithms for electromagnetic scattering from  axisymmetric objects are of great importance when  modeling physical  phenomena in optics, materials science (e.g. meta-materials), and  many other fields of applied science.  In this talk, we  develop an FFT-accelerated separation of variables solver that can be used  to  efficiently invert integral equation formulations of Maxwell's equations for scattering from axisymmetric  bodies. Using a standard variant of M\"uller's integral  representation of the fields, our numerical solver rapidly and directly inverts the resulting second-kind integral equation. The solver is also extended to geometries with non-smooth  generating curves and the scattering from large cavities.