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PubblicazioneRelative Quot schemes over families of smooth and nodal curves(SISSA, 2025-12-19)The present work studies relative Quot schemes parameterizing locally free sheaf quotients with zero--dimensional support on the fibers of a morphism. We focus on families of smooth curves with at most nodal singularities, as well as families of smooth, higher dimensional varieties. The thesis is organized around three projects, which explore both geometric and combinatorial aspects of these relative Quot schemes. The first project, carried out in collaboration with Barbara Fantechi and Ajay Gautam, provides an explicit geometric description of Quot schemes of families of smooth projective curves. We show that the Quot scheme of a locally free sheaf filtered by line bundles admits a finite locally closed stratification, each stratum being isomorphic to an affine vector bundle over products of symmetric powers of the family, with rank given by an explicit formula. Our result generalizes an existing description by Bifet via an independent approach, which does not rely on Białynicki--Birula decompositions. In addition, it determines the class of the relative Quot scheme in the Grothendieck ring of varieties. Further applications concern nested Quot schemes and Quot schemes of positive rank quotients on a smooth projective curve. The second project addresses Quot schemes of smooth morphisms of arbitrary relative dimension. By analyzing the Quot--to--Sym morphism and its behavior under the natural stratification by integer partitions, we show that its restriction to each stratum is {\'e}tale–locally trivial. Combined with the language of power structures on the Grothendieck ring, this result yields two formulas for Quot schemes of smooth morphisms. The third project concerns Quot schemes over families of nodal curves, with emphasis on Losev--Manin spaces. We first study the geometry of Hilbert schemes over Losev--Manin spaces, showing that they are smooth, irreducible of known dimension. Moreover, by combining existing formulas for smooth curves and nodal singularities, we derive an explicit identity for generating functions of the corresponding Quot scheme classes in the Grothendieck ring. The chapter concludes by addressing some open questions and possible further research directions.
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PubblicazioneAb initio design of 2D spintronic materials: engineering magnetism and ferroelectricity through defects and doping(SISSA, 2025-12-19)Two-dimensional (2D) materials and their van der Waals (vdW) heterostructures offer unprecedented opportunities for engineering magnetic and ferroelectric properties at the atomic scale. Reduced dimensionality enhances interlayer interactions, symmetry breaking, and spin-orbit coupling (SOC), making these systems promising platforms for next-generation spintronic and multiferroic devices. Achieving robust and tunable ferroic behavior in the 2D limit requires a microscopic understanding of how defects, interlayer structure, charge redistribution, and carrier doping influence magnetic and ferroelectric responses. This thesis investigates the key mechanisms governing magnetism and ferroelectricity in representative 2D materials and heterostructures, using first-principles density functional theory (DFT) calculations to examine atomic-scale effects such as Gr defects and Fe clustering in Fe/Gr/Co stacks, interlayer sliding and charge redistribution in bilayer VTe2, and spin–orbit-driven magnetic anisotropy in hole-doped monolayer VS2, thereby identifying principles for tailoring ferroic properties in ultrathin systems. In Fe/Gr/Co synthetic antiferromagnets (SAFs), graphene (Gr) vacancy defects and Fe clustering modulate the interlayer magnetic coupling. Motivated by experimental observations, DFT calculations show that these structural features weaken antiferromagnetic (AFM) superexchange and promote ferromagnetic (FM) alignment. Spectromicroscopy measurements at the Nanospectroscopy and VUV beamlines at Elettra confirm these effects, and both theory and experiment demonstrate that passivating defect sites with Ag atoms or carbon-based molecules restores AFM coupling. In metallic bilayer VTe2, sliding-induced ferroelectricity arises from charge redistribution across the vdW gap during interlayer sliding, breaking inversion symmetry. The out-of-plane (OOP) polarization depends sensitively on interlayer spacing, Te corrugation, magnetic configuration, and external perturbations such as strain, Janus substitution, and point defects, which can selectively enhance or suppress the polarization. In hole-doped monolayer VS2, the switch from in-plane (IP) to OOP magnetization is driven by larger spin–orbit–induced splittings and energy shifts that favor the perpendicular orientation. Hole doping depletes the higher-energy valence states most affected by these splittings, lowering the energy more strongly for the OOP configuration and enabling perpendicular magnetic anisotropy at realistic doping levels. This mechanism provides general strategies for tuning magnetic anisotropy in 2D semiconductors. Collectively, these studies reveal how interlayer coupling, defect chemistry, charge redistribution, and spin–orbit interactions govern ferroic responses in 2D materials. The results provide a unified microscopic framework and actionable strategies for engineering magnetic and ferroelectric functionalities in ultrathin systems, advancing the design of energy-efficient, multifunctional spintronic and multiferroic devices.
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PubblicazioneThe SAFE Labs Handbook as a tool for improving lab culture( 2025)Creating positive and equitable lab environments has become a growing priority for the scientific community and funders of scientific research. Research institutions typically respond to this need by providing mandatory or optional training opportunities for their staff. However, there are limited resources for group leaders to improve the culture in their labs. Here, we introduce the SAFE Labs Handbook: a collection of 30 "commitments" that can be implemented by individual group leaders to improve research culture in the life sciences. The commitments were collaboratively developed by 13 group leaders working in eight different European countries. We also report the results of a survey in which we asked more than 200 researchers, at various career stages, about the commitments. Even though all 30 commitments were rated as significantly important by respondents, implementation rates were notably low (<25%). However, more than 95% of group leaders said they would consider implementing them. The SAFE Labs Handbook therefore represents a unique, community-driven tool with the potential to improve lab culture on a global scale.
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PubblicazioneQuantum black holes: from regularization to information paradoxes(Springer, 2025)Quantum black holes, a broad class of objects that refine the solutions of general relativity by incorporating semiclassical and/or quantum gravitational effects, have recently attracted renewed attention within the scientific community. This resurgence of interest is largely driven by advances in gravitational wave astronomy, which have opened the possibility of testing some of these models in the near future. In this essay, we provide a concise overview of the key discussions that emerged during the “Black Hole Inside/Out" meeting, held in August 2024 in Copenhagen. We report these ideas, their connections to the information paradox, and the potential use of analogue gravity as a test bed for these concepts.
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PubblicazioneEntanglement and Asymmetry in Quantum Field Theory(SISSA, 2025-12-18)This thesis investigates the use of concepts from quantum information theory to analyze and quantify symmetry breaking in extended quantum systems, particularly focusing on the key measure known as Entanglement Asymmetry. The core of the work introduces and applies Entanglement Asymmetry. This quantity is defined based on the difference in information content between a quantum state and a version of that state where the symmetry has been enforced (or "symmetrized"). It represents an alternative approach to traditional, often problematic, local order parameters for measuring symmetry breaking: asymmetry is zero only if the state perfectly preserves the symmetry. The major contributions of the thesis are structured as follows: Symmetry Breaking in Bulk Critical Systems: The research analyzes Entanglement Asymmetry in two-dimensional Conformal Field Theories (CFTs) where the symmetry is explicitly broken. This work derives the asymptotic behavior of the asymmetry as a function of the subsystem size, extending earlier finite-size results to the critical continuum limit. Boundary Effects and Quenches: The analysis is extended to cases where the symmetry holds in the bulk of a CFT but is broken at the edge by a boundary condition. The thesis provides formulas describing this boundary-induced asymmetry, including power-law corrections whose exponents are linked to the properties of boundary-changing operators. It also explores the time evolution of asymmetry in quantum quench protocols. Generalization of Asymmetry to Modern Symmetries: The concept of Entanglement Asymmetry is generalized to include finite generalized symmetries, such as higher-form and non-invertible symmetries, which are a major topic in modern QFT. This involves establishing a generalized procedure for "symmetrizing" a state without relying on traditional group mathematics. Entanglement in Non-Hermitian Systems: The final chapter shifts focus to explore other entanglement properties, specifically symmetry-resolved entanglement and the entanglement Hamiltonian, within non-Hermitian models and their corresponding non-unitary CFTs.