The notion of causality, both local or global, is tied inextricably to the Lorentzian character of spacetime.

This is embodied by the causal structure poset which, given weak causality constriants, determines the conformal

spacetime geometry. This is the starting point for the causal set approach to quantum gravity, where the

underlying continuum is replaced by a locally finite partially...

I present a new gravitational collapse singularity theorem which improves Penrose's and which does not assume predictability (global hyperbolicity) while it is compatible with chronology violation (closed timelike curves) and black hole evaporation.

This talk illustrates a model of spacetime with closed timelike curves proposed in a recent paper (D. Fermi and L. Pizzocchero, Class. Quantum Grav. 35 (2018), 165003, 42pp). This spacetime is diﬀeomorphic to R4 and carries an ad hoc metric; it consists of a ﬂat outer region and of a “time machine”, formed by a toroidal interface and by an inner ﬂat region. The timelike geodesics of this...

In this talk I describe the mathematics required in order to provide a description of the observables for quantum fields on low-regularity spacetimes. The first step involves constructing low-regularity advanced and retarded Green operators as maps between suitable function spaces. In specifying these we need to use graph norms on Sobolev spaces to ensure that the Green operators are...