Abstract: In 1858, Helmholtz predicted that two ring-formed filaments in

fluids will pass through each other and become leapfrogging. In this

talk I will give a rigorous justification of Helmholtz's conjecture for

3D Euler flow, and also discuss the dynamical desingularization of

vortices for 2D Euler flows. The key ingredients are new gluing methods

for Euler flows. (Joint work with Juan Davila, Manuel del Pino and

Monica Musso.)