The quasicentral modulus is a numerical invariant associated with a n-tuple of Hilbert space operators and a normed ideal of compact operators. It plays a key role in perturbations of n-tuples of operators and invariance of absolutely continuous spectra results. The talk will be about new results on the quasicentral modulus and commutants mod normed ideals. This will include exact formulas for the quasicentral modulus in fractional dimension and for hybrid perturbations. I will then talk about commutants mod normed ideals for compact differentiable manifolds with boundary and the K-theory exact sequence for their Calkin algebras for connected sums of manifolds.