  The magnetorotational instability (MRI) triggers turbulence and enables
outward transport of angular momentum in hydrodynamically stable rotating shear
flows, e.g., in accretion disks. What laws of differential rotation are
susceptible to the destabilization by axial, azimuthal, or helical magnetic
field? The answer to this question, which is vital for astrophysical and
experimental applications, inevitably leads to the study of spectral and
geometrical singularities on the instability threshold. The singularities
provide a connection between seemingly discontinuous stability criteria and
thus explain several paradoxes in the theory of MRI that were poorly understood
since the 1950s.
