The construction of supergravity theories from the technical point of view is a non-trivial task. In particular, complications arise from the fact that fermionic representations are involved. It is therefore particularly useful to find an efficient method to deal with the technical labor in formulating supergravity theories. In these lectures, we will explore the geometric (aka rheonomic)...

The construction of supergravity theories from the technical point of view is a non-trivial task. In particular, complications arise from the fact that fermionic representations are involved. It is therefore particularly useful to find an efficient method to deal with the technical labor in formulating supergravity theories. In these lectures, we will explore the geometric (aka rheonomic)...

Cosmological observables, such as temperature fluctuations in the CMB and density fluctuations in the distribution of galaxies, can be traced back at the end of inflation where they are encoded in quantum correlations, and the wavefunction of the universe which generates them, at a space-like boundary of a quasi-dS space-time. These lectures will focus on a novel approach to construct the...

Cosmological observables, such as temperature fluctuations in the CMB and density fluctuations in the distribution of galaxies, can be traced back at the end of inflation where they are encoded in quantum correlations, and the wavefunction of the universe which generates them, at a space-like boundary of a quasi-dS space-time. These lectures will focus on a novel approach to construct the...

Supersymmetric Quantum Field Theories provide an exciting arena for exploring physics in the strong coupling regime. Supersymmetric localization has turned out to be a formidable tool for making progress in this direction. The goal of these lectures is to provide a concrete example of supersymmetric localization in the context of three-dimensional gauge theories. I will first review the basic...

Supersymmetric Quantum Field Theories provide an exciting arena for exploring physics in the strong coupling regime. Supersymmetric localization has turned out to be a formidable tool for making progress in this direction. The goal of these lectures is to provide a concrete example of supersymmetric localization in the context of three-dimensional gauge theories. I will first review the basic...

I will review some recent results on the dynamics of quantum field theories based on a renewed understanding of global symmetries and their anomalies.

I will review some recent results on the dynamics of quantum field theories based on a renewed understanding of global symmetries and their anomalies.

The general study of defects has relations with the physics of almost every field theory. Defects can be introduced into a conformal field theory as means to make contact with the real world, reducing the total amount of symmetry. The broken conformal symmetries relax some of the constraints put on the correlation functions and defects can be used as probes to study the dynamics of a theory....

The general study of defects has relations with the physics of almost every field theory. Defects can be introduced into a conformal field theory as means to make contact with the real world, reducing the total amount of symmetry. The broken conformal symmetries relax some of the constraints put on the correlation functions and defects can be used as probes to study the dynamics of a theory....

Gravitational Waves (GWs) represent a unique tool to explore the physics and the microphysics of the universe. After the GW direct detections by the LIGO/Virgo collaboration, the next target of modern cosmology is the detection of Stochastic Gravitational Wave Backgrounds (SGWB), both of cosmological and astrophysical origin. In this lectures, I will present early universe scenarios that can...

Gravitational Waves (GWs) represent a unique tool to explore the physics and the microphysics of the universe. After the GW direct detections by the LIGO/Virgo collaboration, the next target of modern cosmology is the detection of Stochastic Gravitational Wave Backgrounds (SGWB), both of cosmological and astrophysical origin. In this lectures, I will present early universe scenarios that can...

The lattice regularization of Quantum Field Theories is a first-principles approach that allows to explore their non-perturbative regime via computer simulations. Over the years, it has provided valuable inputs to experimental studies and has contributed to the understanding of some of the deepest features of strongly-interacting field theories. The constant improvement of algorithms and...

The lattice regularization of Quantum Field Theories is a first-principles approach that allows to explore their non-perturbative regime via computer simulations. Over the years, it has provided valuable inputs to experimental studies and has contributed to the understanding of some of the deepest features of strongly-interacting field theories. The constant improvement of algorithms and...

The Gauge/Gravity duality introduced a new tool for investigating QFTs in non perturbative regimes: the most phenomenologically relevant example of these theories is QCD at low energy (at the scale of nuclear physics), whose spectrum of bound states ranges from glueballs, to mesons, to complicated atomic nuclei. In these lectures we will review the Gauge/Gravity duality and discuss its...

The Gauge/Gravity duality introduced a new tool for investigating QFTs in non perturbative regimes: the most phenomenologically relevant example of these theories is QCD at low energy (at the scale of nuclear physics), whose spectrum of bound states ranges from glueballs, to mesons, to complicated atomic nuclei. In these lectures we will review the Gauge/Gravity duality and discuss its...

These lectures aim to clarify several aspects of higher-derivative quantum field theories, their issues and how to circumvent them. A special attention will be given to quantum gravity. After reviewing general definitions we discuss the role of higher derivatives in both effective field theories and fundamental ones. Focusing on the latter, we explore the class of theories suitable for quantum...

These lectures aim to clarify several aspects of higher-derivative quantum field theories, their issues and how to circumvent them. A special attention will be given to quantum gravity. After reviewing general definitions we discuss the role of higher derivatives in both effective field theories and fundamental ones. Focusing on the latter, we explore the class of theories suitable for quantum...

Reconstructing the physics of the very early universe from current observations is one of the most exciting challenges of theoretical cosmology. The main objects of interest in this context are correlation functions of perturbations on the spatial slice sitting at the end of inflation. In these lectures I will review a new approach—the "cosmological bootstrap"—that attempts to derive these...

Reconstructing the physics of the very early universe from current observations is one of the most exciting challenges of theoretical cosmology. The main objects of interest in this context are correlation functions of perturbations on the spatial slice sitting at the end of inflation. In these lectures I will review a new approach—the "cosmological bootstrap"—that attempts to derive these...

The construction of exact solutions in gravitational theories, from black holes to cosmological solutions, is of great interest. In these lectures, we will give an overview of the solution generation techniques in the realm of gravitational theories by focusing on two of them: the Ernst formalism and the inverse scattering method. In both cases, we will explicitly construct the integration...

The construction of exact solutions in gravitational theories, from black holes to cosmological solutions, is of great interest. In these lectures, we will give an overview of the solution generation techniques in the realm of gravitational theories by focusing on two of them: the Ernst formalism and the inverse scattering method. In both cases, we will explicitly construct the integration...

Upcoming surveys will probe increasingly large scales, approaching and even exceeding the Hubble scale at the survey redshifts. On these cosmological scales, surveys can in principle provide the best constraints on dark energy and modified gravity models – and will be able to test general relativity itself. In order to realise the potential of these surveys, we need to ensure that we are...