We study the geometry and topology of Quot schemes on smooth projective curves. First, we give an explicit presentation of the rational cohomology ring of the Quot scheme parametrising torsion quotients on $\PP^1$. Next, we construct a stratification of the corresponding relative Quot scheme, which recovers several known results by specialisation. We also use this stratification to prove that the integral cohomology of the Quot scheme parametrising torsion quotients is torsion-free, thereby s...
The olfactory system is crucial for the detection of chemical cues from the environment, allowing species survival. Olfactory sensory neurons (OSNs) within the olfactory epithelium (OE) are responsible for odorant detection and signal transmission to the brain. To investigate olfaction, rodents, along with other species such as amphibians and fishes, have been extensively used as laboratory models. In the first part of this thesis, we provided the first electrophysiological characterization o...
A prominent hypothesis in cognitive neuroscience is that the brain operates as an inference engine, relying on internal models to interpret sensory input and guide decision-making. While a great variety of behaviors and biases are explained through this approach, it is less clear how the brain builds and, most importantly, chooses among different models to interpret its environment. A general bias toward simpler interpretations is well-established, but critical gaps remain regarding the compu...
How does the brain recover a weak signal that is submerged in intense stochastic fluctuations to make fast yet accurate choices? We recast perceptual decision-making as the inference of a nonzero drift (v) in the presence of large diffusivity (D): the observer must determine the direction of motion when trajectories are dominated by diffusion. A concrete analogy is reading wind while hunting: turbulent gusts scramble moment-to-moment cues, yet a subtle, consistent drift in air motion carries ...
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...
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...
This thesis presents three studies elucidating aspects of entnaglement entropy in holography, harmonic lattices and non-realtivistic quantum field theory.
In the first part we review the geodesic bit thread forumlation for holographic entanglement entropy and show that in presence of an event horizon we can recover the holographic thermal entropy.
In the second part we study the entanglement hamiltonian for a two-interval system in a harmonic lattice, in both the massless and super massiv...
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 altern...
In this thesis we present several works dealing with multiscale phenomena. First, we treat a model of pattern formation: the Ising model with competing short-range and long-range interactions. We compute the energy asymptotic of excitations above the periodic ground states. In a second work we study a model of Quantum Hall Effect with a single edge-mode and subject to quasi-periodic disorder: through a combination of rigorous Renormalization Group techniques and \textsc{kam}-like estimates we...
Controlling the properties of quantum matter is a central goal of condensed matter physics. In recent years, cavity embedding—that is, shaping the electromagnetic environment surrounding a material by placing it inside a cavity—has emerged as a new potential tuning knob. While such concepts were first successfully explored with ultracold atomic clouds, more recent experiments have demonstrated their feasibility in solid-state systems. Despite the differences between these platforms, they shar...