Symmetries and their Holographic Aspects in Quantum Field Theory

In this thesis we study generalized global symmetries in Quantum Field Theory. In the modern definition, symmetries are viewed as extended topological operators. On the one hand this new paradigm efficiently encodes all the information a symmetry usually comes with (e.g. 't Hooft anomalies) and on the other it allows for many interesting generalizations. After the Introduction, the first chapter is a brief review of basic concepts used throughout the thesis. The rest of this work is conceptua...

Topological Aspects of Quantum Field Theory

Quantum Field Theories (QFTs) have a universal protected sector provided by topological operators. They generalize the ordinary notion of symmetry in various directions, allowing to transport many familiar concepts (symmetry breaking, anomalies, gauging, etc...) in a much more general framework. This thesis is devoted to the study of several aspects of these topological properties, and their interplay with the dynamics. A central tool is provided by a Topological Quantum Field Theory (TQF...

Formulae of Jeffrey-Kirwan type in enumerative geometry

This thesis explores various aspects of the Jeffrey-Kirwan localisation formula, a powerful tool in computing integrals on quotients of smooth varieties by reductive group actions. Initially developed by Jeffrey and Kirwan in the symplectic context, this formula has seen various adaptations and extensions scattered throughout the literature. The primary goal of this thesis is to provide a fully algebraic proof of the Jeffrey-Kirwan localisation formula, building on the work of Lerman, Guillem...

Exploring phases of non-abelian gauge theories with perturbation theory

Ultrarelativistic Phase Transition in the early Universe: The faster the better

Geometric analysis and measure theory in general ambient spaces.

In this thesis we deal with several questions concerning measure theory and geometric analysis. In the first chapter we deal with two questions: the first one is a problem proposed by David H. Frelmin concerning Hausdorff measures on $\mathbb{R}^n$ built with a distance inducing the Euclidean topology. The second question we answer is about the absolute continuity of the pushforward measure via suitable charts in metric measure spaces. Then, we study the asymptotics as $s\to o^+$ of the $s$-f...

Dissipative solutions to Hamiltonian system, and one conjecture for non autonomous viscous conservation laws and one in measure theory

Hybrid reduced-order methods for segregated fluid-structure interaction solvers in an ALE approach using the Finite Volume Method.

This dissertation intends to construct hybrid reduced-order models (ROMs) for segregated Fluid-structure interactions solvers in an Arbitrary Lagrangian-Eulerian (ALE) framework both in laminar and turbulent regime. The ROM methodology developed is based on full order solvers which make use of the Finite Volume Discretization method. The hybrid ROMs are built by combining data-driven techniques and classic model reduction approaches, such as proper orthogonal decomposition combined with Ga...

Quantum Effects in Cosmology: Unveiling the Quantum Nature of the Primordial Fluctuations

It is commonly accepted in cosmology that a period of inflation took place in the Early Universe. This period of accelerated expansion provides the seeds for structure formation through vacuum fluctuations of the inflaton scalar field. These fluctuations get stretched by the quasi-exponential expansion of the Universe and become squeezed. The generation of perturbations out of the vacuum is a purely quantum phenomenon, however the Cosmological Microwave Background (CMB) measurements are analy...