Tuesday 24 March 2026, 16:00 - 17:00 in HG01.028
Romeo Troubat (IHES)
Global hyperbolicity in higher signature
Global hyperbolicity is the strongest causality condition in Lorentzian geometry. It encapsulates both the non-existence of causal loops and of causal paths going to the edge of the spacetime in finite time and is of interest to both physicists and mathematicians. In non-Lorentzian pseudo-Riemannian geometry of signature (p,q), i.e such that p and q are greater than 1, there does not exist any obvious generalization of global hyperbolicity as there does not exist any notion of causality for causal paths. This stems for the connectedness of the space of negative vectors in $R^{p,q}$ when q is greater than 1. My goal in this talk will be to introduce a possible generalization of the notions of causality and of Cauchy time functions in higher signatures as well as to generalize a number of results by Geroch in this new setting.