Seminar in Number Theory and Algebraic Geometry

Abstract: General relativity is conventionally described as a field theory in a pseudo-Riemannian set up in four dimensions. In particular the Levi-Civita connection is used in its formulation which means that torsion is vanishing and that the covariant derivative of the metric vanishes as well. The first part of this talk will focus on the conventional theory of general relativity. This will include some historical aspects, including alternative formulations considered by Albert Einstein where torsion or non-metricity do not vanish. In a modern perspective, this is noted as teleparallel theories of gravity, which provides an arena of geometrical reformulations of general relativity as well as going beyond general relativity. The latter is related to breaking diffeomorphism and/or Lorentz symmetries. The remainder of the talk is committed to why the teleparallel gravity can be useful to address problems in general relativity (including the variational principle of the action, notion of energy, and numerical relativity), and theories beyond general relativity.