Talks

The aim of this talk is to construct quantum states, satisfying the Hadamard

condition, for Maxwell's theory on generic globally-hyperbolic Lorentzian manifolds. The novelty of our approach is a new gauge fixing at the level of initial data that allows us to suppress all the unphysical degrees of freedom. This gauge will be achieved by introducing a new Hodge decomposition for differential k-forms in Sobolev spaces on complete (possibly non-compact)

Riemannian manifolds. The key ingredient for our construction of states is a microlocal factorization of the Cauchy evolution operator that will guarantee the physical relevance of our quantum state. (joint work with Simone Murro;

based on arXiv:2401.08403) 

We propose a novel approach for constructing Hadamard states for Maxwell's theory on globally-hyperbolic spacetimes, based on a new gauge fixing condition, the Cauchy radiation gauge, that allows to suppress all the unphysical degrees of freedom. The key ingredient for achieving this gauge is a new Hodge decomposition for differential k-forms in Sobolev spaces on complete (possibly non-compact) Riemannian manifolds. Hadamard states are then constructed via a microlocal factorization of the wave equation. (joint work with Simone Murro; based on arXiv:2401.08403) 

We propose a novel approach for constructing Hadamard states for Maxwell's theory on globally-hyperbolic spacetimes. The key idea is to fix the gauge degrees of freedom completely via a pseudodifferential projection and to construct Hadamard projectors for the gauge-fixed theory satisfying the positivity condition. A quasi-free and gauge-invariant Hadamard state for Maxwell's theory is then obtained by pulling back the Hadamard projection to the space of gauge-invariant on-shell observables. (Joint work with Simone Murro)

We consider transition amplitudes in the coloured simplicial Boulatov model. The starting point of this discussion is the construction of suitable boundary observables from spin-network states living on the dual 1-skeleton of some fixed boundary topology. The transition amplitudes defined using these observables are then given by a sum over all possible bulk topologies with our fixed boundary, each weighted by their corresponding Ponzano-Regge spin foam amplitude. Afterwards, we discuss the transition amplitudes for two explicit choices of boundary topologies, namely the 2-sphere and 2-torus, and show that they factorize into a sum entirely given by the combinatorics of the boundary spin-network state. This can be seen as the first step towards a more detailed study of quasi-local holographic dualities in the context of coloured Boulatov-Ooguri type GFT models. 

The aim of this talk is to construct quantum states, satisfying the Hadamard condition, for Maxwell's theory on generic globally-hyperbolic Lorentzian manifolds. The novelty of our approach is a new gauge fixing at the level of initial data that allows us to suppress all the unphysical degrees of freedom. This gauge will be achieved by introducing a new Hodge decomposition for differential k-forms in Sobolev spaces on complete (possibly non-compact) Riemannian manifolds. The key ingredient for our construction of states is a microlocal factorization of the Cauchy evolution operator that will guarantee the physical relevance of our quantum state. (joint work with Simone Murro; based on arXiv:2401.08403)

The aim of this talk is to construct quantum states, satisfying the Hadamard condition, for Maxwell's theory on generic globally-hyperbolic Lorentzian manifolds. The novelty of our approach is a new gauge fixing at the level of initial data that allows us to suppress all the unphysical degrees of freedom. This gauge will be achieved by introducing a new Hodge decomposition for differential k-forms in Sobolev spaces on complete (possibly non-compact) Riemannian manifolds. The key ingredient for our construction of states is a microlocal factorization of the Cauchy evolution operator that will guarantee the physical relevance of our quantum state. (joint work with Simone Murro; based on arXiv:2401.08403)

Einstein's general theory of relativity is one of the cornerstones of modern physics and of our understanding of the structure of space and time. In this seminar talk, we will give a general introduction and overview of Einstein's theory, with an eye towards mathematical relativity, which is the branch of pure mathematics studying problems arising from general relativity. We will start by reviewing some historical and physical aspects of the theory. Afterwards, we will give a brief introduction to Lorentzian geometry, the language in which general relativity is written. The rest of the talk will center on various aspects of general and mathematical relativity, including the Cauchy problem, black holes and singularity theorems, as well as some real life applications. 

We will start by reviewing physical aspects of classical three-dimensional general relativity, focusing on its topological nature, and by giving an overview of various approaches to the corresponding quantum theory, with an eye on the spin foam and group field theory (GFT) approach. The main goal of this talk is to set up a formalism to calculate transition amplitudes of three-dimensional quantum gravity in the GFT formalism. To do so, we will give a brief introduction to crystallization theory, a branch of geometric topology, in which one represents simplicial complexes as edge-coloured graphs, allowing to represent topological operations in a purely graph-theoretic way. As a main result, we will show that the transition amplitude for a spherical boundary factorizes into a sum entirely given by the combinatorics of the boundary state, which can be seen as the first step towards a more detailed study of holographic dualities in the context of GFT models for topological field theories and quantum gravity. We will also briefly give an outlook to more complicated boundary topologies and their topological obstructions.