An Invitation to Lorentzian Geometry

An Invitation to Tame Geometry

Statistical Lorentzian geometry and the closeness of Lorentzian manifolds

I introduce a closeness function between causal Lorentzian geometries of finite volume and arbitrary underlying topology. The construction uses the fact that some information on the manifolds and metrics is encoded in the partial order that the causal structure of each metric induces among points randomly scattered in the corresponding manifold with uniform, finite density according to the volu...

Trapped submanifolds in Lorentzian geometry

In Lorentzian geometry, the concept of trapped submanifold is introduced by means of the mean curvature vector properties. Trapped submanifolds are generalizations of the standard maximal hypersurfaces and minimal surfaces, of geodesics, and also of the trapped surfaces introduced by Penrose. Selected applications to gravitational theories are mentioned.

An Invitation to Play

Parity games and their subclasses and variants pop up in various contexts: μ-calculus, tree automata, program verification [3, 1, 8]. Such games provide only binary information indicating the winning player. However, in classical games theory [12] the emphasis is rather on how much we win or lose. Can we incorporate the information about the profits and losses into parity games?

An Invitation to Topology