Rainer Hollerbach Department of Applied Mathematics, University of Leeds Magnetorotational Instabilities in Cylindrical Taylor-Couette Flow Wednesday 27th May 14:05-14:55pm, Eastern Avenue Lecture Theatre. Taylor-Couette flow, the flow between differentially rotating cylinders, is one of the oldest problems in classical fluid dynamics, but still continues to attract considerable attention to this day. Now suppose the fluid is taken to be electrically conducting, and a magnetic field is applied. Magnetohydrodynamic effects then arise, which can yield fundamentally new results that have no analog in the nonmagnetic problem. The magnetorotational instability (MRI) is one such result, whereby magnetic effects destabilize an otherwise stable flow. In this talk I will begin by discussing the physics underlying the MRI, as well as it astrophysical significance. I will next reduce the governing equations to a linear eigenvalue problem, and show how the geometry of the externally imposed magnetic field, whether it is purely axial or also contains an azimuthal component, makes an enormous difference to the solutions. Finally, I will present a series of experimental results on the MRI in such mixed axial+azimuthal magnetic fields, and compare them with the theoretical predictions.