Massimo Sorella, a mathematician at Imperial College London, presents this seminar at the Institute for Advanced Study on the fast dynamo conjecture, a longstanding problem in magnetohydrodynamics asking whether magnetic field strength can grow exponentially in time under a stretching flow at a rate that does not vanish as resistivity goes to zero. Sorella proves the conjecture for the pulsed diffusion model built on a time-periodic stretch-fold-shear vector field on the 3-torus. He builds the argument using anisotropic Banach spaces matched to the flow's dynamics, first establishing a distributional eigenfunction with eigenvalue modulus greater than one in the zero-diffusivity limit, then treating resistivity as a perturbation within that functional-analytic framework. The talk is dense with functional analysis and dynamical systems machinery, aimed at researchers already fluent in PDE and ergodic theory, and runs just over an hour as part of the IAS Analysis and Mathematical Physics seminar series.