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I will give an introduction to the geometric aspects of Lie algebroids and show how they give the correct framework to discuss gauge theories. The analysis is solely based on geometry, and thus applies to every gauge theory, independently of their specific features and dynamics. By thoroughly re-formulating the physical content of gauge theories on Atiyah Lie algebroids, we will show that the BRST construction is part of the formalism, indicating a fascinating interplay between classical geometry and quantum physics. Time permitting, we will show how our setup encompasses gravitational theories too, once the frame bundle and solder form are added to the picture.

It is known that constraints imposed by causality and unitarity of four-particle scattering amplitudes lead to non-trivial requirements on the low energy effective field theory coefficients. We introduce families of linear and nonlinear inequalities resulting from a systematic study of positive geometry structure hidden in those constraints.

The dark photon is a well-motivated extension of the Standard Model which can mix with the regular photon. This mixing is enhanced whenever the dark photon mass matches the primordial plasma frequency, leading to resonant conversions between photons and dark photons. These conversions can produce observable cosmological signatures, including distortions to the cosmic radiation background. In this talk, I will discuss a new analytic formalism for these conversions that can account for the inhomogeneous distribution of matter in our universe, leading to new and revised limits on the mixing parameter of light dark photons derived from the COBE/FIRAS measurement of the cosmic microwave background spectrum. I will then describe some ongoing work on a dark sector model that can explain the longstanding ARCADE radio background excess through resonant conversions of dark photons.

We show that bulk operators lying between the outermost extremal surface and the asymptotic boundary admit a simple boundary reconstruction in the classical limit. This is the converse of the Python's lunch conjecture, which proposes that operators with support between the minimal and outermost (quantum) extremal surfaces - e.g. the interior Hawking partners - are highly complex. Our procedure for reconstructing this "simple wedge" is based on the HKLL construction, but uses causal bulk propagation of perturbed boundary conditions on Lorentzian timefolds to expand the causal wedge as far as the outermost extremal surface. As a corollary, we establish the Simple Entropy proposal for the holographic dual of the area of a marginally trapped surface as well as a similar holographic dual for the outermost extremal surface. We find that the simple wedge is dual to a particular coarse-grained CFT state, obtained via averaging over all possible Python's lunches. An efficient quantum circuit converts this coarse-grained state into a "simple state" that is indistinguishable in finite time from a state with a local modular Hamiltonian. Under certain circumstances, the simple state modular Hamiltonian generates an exactly local flow; we interpret this result as a holographic dual of black hole uniqueness.

The quantum gravity path integral involves a sum over topologies. Superficially, this feature is similar to Feynman diagrams of quantum field theory and the genus expansion of worldsheet string theory. There are however some key differences. While the standard construction leads to the non-abelian algebra of quantum fields, the quantum gravity path integral has been argued to define an abelian algebra associated with partition function type observables. We will discuss these issues and argue that one needs to make certain discrete choices to construct a Hilbert space from path integrals that sum over topologies. In particular, the natural choices for quantum gravity differ from those used to construct QFTs as we shall illustrate in the context of one-dimensional models.

Far-infrared spectroscopy can reveal secrets of galaxy evolution and heavy-element enrichment throughout cosmic time, and astronomers worldwide are designing cryogenic space telescopes for far-IR spectroscopy. The most challenging aspect is a far-IR detector which is both exquisitely sensitive (limited by the zodiacal-light noise in a narrow band (lambda/delta lambda ~1000)) and array able to tens of thousands of pixels. The quantum capacitance detector (QCD) being developed at MDL, is a 50mK device adapted from quantum computing applications in which photon-produced free electrons in a superconductor tunnel into a small capacitive island embedded in a resonant circuit. The QCD has optically-measured noise equivalent power (NEP) of 2x10-20 W Hz-1/2 at 1.5THz under 10-19W of optical loading, making it the most sensitive far-IR detector ever demonstrated. The QCD has further demonstrated individual far-IR photon counting, confirming the exquisite sensitivity and suitability for cryogenic space astrophysics. In this lecture, the development of the Quantum Capacitance detector will be highlighted, from inception through proof of concept devices, culminating with the demonstration of single photon detection. Current development efforts will be discussed.

In this talk I will discuss the application of the so-called “consistency relations” for large scale structures to the study of primordial non-Gaussianities of the local f_NL type. I will first introduce the consistency relations themselves, commenting on some important aspects and underlying assumptions. I will then verify them (and their violation) using N-body simulations for the matter density in the Universe. This proves consistency relations to be a promising tool to apply in the forthcoming large scale structures surveys. I will conclude describing some work in progress aimed at finding a practical recipe to constrain f_NL from these relations.

It has been proposed that microscopic black holes can catalyze decay of metastable false vacuum. The calculations of the decay rate existing in the literature make use of the Euclidean time formalism developed for equilibrium configurations. This is not the case, however, for a realistic black hole formed by gravitational collapse and emitting Hawking radiation. I will review the motivations to study black hole catalysis of vacuum decay, propose a general method to calculate the decay rate, and illustrate it on a two-dimensional toy model.