Resonant drag instabilities in fluids and plasmas

Many plasma instabilities, for instance two-stream instabilities or the magnetorotational instability, arise due to a resonance between two or more oscillation frequencies of the system. In this talk, I will introduce a general method for understanding, and calculating the properties of, such resonant instabilities. Application to dust-laden fluids and plasmas has uncovered a variety of new instabilities that occur when dust moves with a relative speed that matches the phase velocity of a fluid wave. These have interesting astrophysical applications for systems ranging from galactic winds to protoplanetary accretion disks. I will also discuss applications to other systems, for instance plasmas with a population of streaming cosmic rays, or resonant instabilities in collisionless plasmas.