Rigid Singularity Theorem in Globally Hyperbolic Spacetimes
  We show the rigid singularity theorem, that is, a globally hyperbolic spacetime satisfying the strong energy condition and containing past trapped sets, either is timelike geodesically incomplete or splits isometrically as space $\times$ time. This result is related to Yau's Lorentzian splitting conjecture. 
Makoto Narita (Rikkyo University)