We identify a direct correspondence between the crossed product construction which plays
a crucial role in the theory of Type III von Neumann algebras, and the extended phase space …

A universal symmetry algebra organizing the gravitational phase space has been recently
found. It corresponds to the subset of diffeomorphisms that become physical at corners …

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 a recent paper, it was shown that in diffeomorphism-invariant theories, the symplectic
vector fields induced by spacetime diffeomorphisms are integrable if one introduces an …

These notes provide a self-contained introduction to Lie algebroids, Lie-Rinehart algebras
and their universal envelopes. This review is motivated by the speculation that higher-spin …

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 …

We make a case for the unique relevance of Cartan geometry for gauge theories of gravity
and supergravity. We introduce our discussion by recapitulating historical threads, providing …

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 …