Gravity without coordinates? - Some Mathematics


The metric formulation of general relativity has a huge gauge symmetry group: the same spacetime geometry can be described by many different metrics associated to different choices of coordinates on spacetime. Since the physics is in the geometry and not in the coordinates, it is beneficial, especially en route to quantum gravity, to be able to work on Moduli spaces of geometries, i.e. the spaces of metrics modulo changes of coordinates. In general these are very complicated mathematical objects to analyze or calculate with, but I will highlight some mathematical advances in lower-dimensional geometry, that follow the bijective approach of encoding all information about a geometry in simpler objects (like trees). Along the way I will mention some ongoing activities in my group aiming to extend this to settings more relevant to gravity.

HEP seminar
Radboud University