A 1875 conjeture of Lord Kelvin asserts that there should be
stationary solutions to the 3D Euler equations exhibiting certain knotted
structures that are known as vortex tubes. This conjecture originated in
Kelvin's studies of the atomic structure and found applications in turbulence.
In this talk we will discuss the proof of this conjecture, which is joint work
with Daniel Peralta-Salas and involves arguments from partial differential
equations, dynamical systems and differential geometry.