These notes are a transcript of lectures given by the author in the XVIII Modave summer
school in mathematical physics. The introduction is devoted to a detailed review of the …

In this paper we demonstrate that the exterior algebra of an Atiyah Lie algebroid generalizes
the familiar notions of the physicist's BRST complex. To reach this conclusion, we develop a …

In this paper we question the status of TEGR, the Teleparallel Equivalent of General
Relativity, as a gauge theory of translations. We observe that TEGR (in its usual translation …

In previous works, questioning the mathematical nature of the connection in the translations
gauge theory formulation of Teleparallel Equivalent to General Relativity (TEGR) Theory led …

It is well-known that principal bundles and associated bundles underlie the geometric
structure of classical gauge field theories. In this paper, we explore the reformulation of …

The first part of this thesis focuses on the Weyl-covariant nature of holography. We
generalize the Fefferman-Graham (FG) ambient construction for conformal geometry to a …

We propose a new differential geometric tool to reduce gauge symmetries: the dressing field
method. It is applied to various examples, including the electroweak sector of the standard …

This work extends both classical results on Atiyah Lie algebroids and previous
developments carried out by some of the authors on Ehresmann connections on Atiyah Lie …

Non-commutative geometry (NCG) is a mathematical discipline developed in the 1990s by
Alain Connes. It is presented as a new generalization of usual geometry, both …

In this paper, we start the investigation of a new natural approach to “unifying”
noncommutative gauge field theories (NCGFT) based on approximately finite-dimensional …