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The magnetorotational instability (MRI) triggers turbulence and enablesoutward transport of angular momentum in hydrodynamically stable rotating shearflows, e.g., in accretion disks. What laws of differential rotation aresusceptible to the destabilization by axial, azimuthal, or helical magneticfield? The answer to this question, which is vital for astrophysical andexperimental applications, inevitably leads to the study of spectral andgeometrical singularities on the instability threshold. The singularitiesprovide a connection between seemingly discontinuous stability criteria andthus explain several paradoxes in the theory of MRI that were poorly understoodsince the 1950s.

Standard and helical magnetorotational instability: How singularities create paradoxal phenomena in MHD