I review some of my recent work on non-lorentzian geometry. the classification kinematical Lie algebras and their associated Klein geometries. then describe Cartan geometries modelled them characterisation in terms intrinsic torsion.

{We consider neural units whose response functions are Lorentzians rather than the usual sigmoids or steps. This consideration is justiied by the fact that neurons can be paired and that a suitable diierence of the sigmoids of the paired neurons can create a window response function. Lorentzians are special cases of such windows and we take advantage of their simplicity to generate polynomial e...

A formulation of the non-commutative geometry for the standard model of particle physics with a Lorentzian signature metric is presented. The elimination of the fermion doubling in the Lorentzian

We show that the normalized Lorentzian state sum is finite on any triangulation. It thus provides a candidate for a perturbatively finite quantum theory of general relativity in four dimensions with Lorentzian signature.

In this note a proof is given for global existence and uniqueness of minimal surfaces of Lorentzian type from a cylinder into certain Lorentzian manifolds for given initial values up to the first derivatives.

We develop a supervised dimensionality reduction method, called Lorentzian discriminant projection (LDP), for feature extraction and classification. Our method represents the structures of sample data by a manifold, which is furnished with a Lorentzian metric tensor. Different from classic discriminant analysis techniques, LDP uses distances from points to their within-class neighbors and globa...