Abstract: In General Relativity, an impulsive gravitational wave is a localized and singular solution of the Einstein equations modeling the spacetime distortions created by a strongly gravitating source.

I will present a local theory of the Cauchy problem in U(1)-symmetry for rough data evolving towards a ternary collision of such impulsive gravitational waves, which, unlike binary ones, may create an anomalous singularity. Joint work with Jonathan Luk.