Seminar series
Date
Mon, 09 Nov 2026
Time
16:30 -
17:30
Location
L4
Speaker
Michele Coti-Zelati
Organisation
Imperial College
The fast dynamo conjecture, posed by Zeldovich and Sakharov and later recorded in Arnold’s book of problems, asks whether a smooth, autonomous, divergence-free flow on the three-torus can amplify magnetic fields exponentially at a rate bounded uniformly away from zero as the magnetic resistivity vanishes. In this talk, we resolve the conjecture by constructing a flow based on the classical stretch–fold–shear (SFS) mechanism. The proof uses anisotropic Banach spaces adapted to the ideal dynamics to obtain an isolated unstable eigenmode with a distributional eigenfunction. A singular spectral perturbation argument then shows that this instability persists for small positive resistivity. The construction is robust and yields an open set of smooth autonomous fast dynamos.