Out-of-equilibrium quantum many-body systems stand at the forefront of modern theoretical physics, addressing fundamental questions on thermalization, transport, and universal phenomena. These fields, already well established in condensed matter, statistical physics, quantum optics, and quantum information theory, are progressively gaining even greater relevance with the rapid development of quantum technologies and simulation, which inherently operate in dynamical regimes. In recent years, t...
Xia-Gibbs syndrome (XGS) is a rare neurodevelopmental disorder caused by pathogenic variants in AHDC1. However, the cellular and molecular functions of AHDC1 remain poorly defined. In this thesis, I investigated AHDC1 function by combining RNA silencing in a controlled steady-state neuronal-like model with reanalysis of AHDC1-mutant differentiation datasets. In SH-SY5Y cells, AHDC1 silencing activated ribosome-related transcriptional programs, increased MYCN expression, and was associated wit...
In this thesis, we study the deformation theory and the enumerative geometry of the Quot scheme of points Quot_Y(F, n) parametrizing zero-dimensional quotients of length n of a locally free sheaf F on a smooth (quasi)-projective 3-fold Y.
We construct on Quot_Y(F, n) an almost perfect obstruction theory of virtual dimension zero. The notion of an almost perfect obstruction theory recently introduced by Kiem--Savvas is a weaker notion of a perfect obstruction theory in the sense of Beh...
In addition to orchestrate telencephalic development, the transcription factor Foxg1 is involved in mutual positive feedback with neuronal activity. Based on that, we hypothesized an involvement of it in learning and engram dynamics. We observed that its sparse and mild neuronal upregulation improved learning abilities as evaluated by a CFC assay. This effect was specifically pronounced upon early memory retrieval and disappeared when Foxg1-GOF neurons were silenced by a Gi DREADD effector. A...
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...