INITIUM: an Innovative Negative Ion TIme projection chamber for Underground dark Matter searches. INITIUM goal is to boost the advancement of gaseous Time Projection Chamber detectors in the Dark Matter (DM) searches field, one of the most compelling issues of todays fundamental physics. I believe this approach to be superior because of its active neutron/electron discrimination, directional and fiducialization capability down to low energies and versatility in terms of target material. Thanks to recent advances in Micro Pattern Gas Detectors amplification and improved readout techniques, TPCs are nowadays mature detectors to aim at developing a ton-scale experiment. INITIUM focuses on the development and operation of the first 1 m3 Negative Ion TPC with Gas Electron Multipliers amplification and optical readout with CMOS-based cameras and PMTs for directional DM searches at Laboratori Nazionali del Gran Sasso (LNGS). INITIUM will put new significant constraints in a DM WIMP-nucleon scattering parameter space still unexplored to these days, with a remarkable sensitivity down to 10-42-10-43 cm2 for Spin Independent coupling in the 1-10 GeV WIMP mass region. As a by-product, INITIUM will also precisely and simultaneously measure environmental fast and thermal neutron flux at LNGS, supplying crucial information for any present and future experiment in this location. Consequently, I will demonstrate the proof-of-principle and scalability of INITIUM approach towards the development of a ton-scale detector in the context of CYGNUS, an international collaboration (of which I am one of the Spokespersons and PIs) recently gathered together with the aim to establish a Galactic Directional Recoil Observatory, that can test the DM hypothesis beyond the Neutrino Floor and measure the coherent scatter of galactic neutrinos, generating a significant long-term impact on detection techniques for rare events searches.

Spontaneous pattern formation is an ubiquitous and fascinating phenomenon in nature, of enormous importance for the present and future of applications. A crucial aspect, both at zero and positive temperature, is that in dimension d>1 the physical states retain less symmetries than the interactions involved in the models. This phenomenon, known as symmetry breaking, coupled with nonlocality makes any attempt of giving a mathematical explanation of pattern formation extremely challenging and still largely not accessible with the current tools. ENDRISP aims at gaining deep insight into the mathematical mechanisms behind the phenomenon of energy-driven pattern formation, focusing on the following foremost questions in the field: Explain continuous symmetry breaking mechanisms for isotropic functionals; Show pattern formation and symmetry breaking in the positive temperature setting. The focus of ENDRISP will be on the formation of periodic one-dimensional structures in general dimension (i.e. striped/lamellar structures), as they are generally the first type of patterns to emerge from uniform phases when symmetry breaking occurs, in regimes in which the attractive and repulsive forces are of the same order. We will use precise nonlocal quantities of geometric character coming from the free energy to control the curvature of the physical states and derive rigidity and stability estimates. The techniques we developed to show pattern formation for continuous functionals retaining discrete symmetry together with our experience on representation theorems in the positive temperature setting and the new ideas in ENDRISP will be the ideal basement to the project. Major advances in Calculus of Variations, Geometric Measure Theory and Statistical Mechanics will be required, for which the transfer of knowledge with the supervisors, empowered by the unique training offered by Courant Institute in the outgoing phase and by GSSI in the return phase, will be extremely beneficial.

ACCESS aims to establish a new technique to perform precision measurements of forbidden beta-decays, whose spectral shape is a crucial benchmark for Nuclear Physics calculations and plays a pivotal role in Astroparticle Physics experiments. When fundamental conservation laws strongly suppress a beta decay, it features a high transferred momentum, as in the case of neutrinoless double-beta decay (NLDBD). Relying on this similarity, ACCESS will provide groundbreaking insights to evaluate Nuclear Matrix Elements for NLDBD. ACCESS will operate a pilot array of four tellurium dioxide crystals as cryogenic calorimeters. Three of them will be doped with different beta emitters, while the last natural one will be used for effective background subtraction. My experience with cryogenic calorimeters based on semiconductor sensors (i.e. NTD) will be a solid basement for the project, but an essential piece of the puzzle is still missing. ACCESS requires high statistical measurements in an ultra-clean underground cryostat, available for limited time slots. A fast detector is mandatory to collect the required number of signals, keeping the background low, and avoiding the pileup due to the high counting rate. To fulfill this requirement, I will complete my training during the first two years of the action at Queen’s University. Here I will learn to build and operate bolometers based on superconductive sensors (i.e. TES), among the faster sensors used in Astroparticle Physics. I will transfer my NTD-oriented expertise to the local group, and together we will integrate these two sensors for a novel application. In the last year, I will move to GSSI, a research center of excellence recently established in Italy. Here I will perform the final measurements at LNGS (Gran Sasso National Laboratory), a world-leading underground research infrastructure of INFN. My new skills and research network will enrich the local astroparticle group, extending its research field also to Nuclear Physics.

Clinical trials are a key tool for advancing medical knowledge, but they consist of a long and costly process entailing the recruitment of a representative cohort of participants to properly account for the population statistical variability. Computational engineering is a promising approach to gain more insight into patients' cardiac pathologies and to test innovative medical devices before running conclusive in-vivo experiments on animals or medical trials on humans. This technological breakthrough, however, is limited by some technical and epistemic challenges: (i) the reliability of cardiovascular computational models depends on the accurate solution of the hemodynamics coupled with the deforming biologic tissues; (ii) the resulting multi-physics solver requires an immense computational power and long time-to-results; (iii) a great variability among individuals exists, thus calling for a statistical approach. For the first time I will accomplish and employ a computational platform for determining the outcome of pathologies or devices implantation by combining my GPU-accelerated multi-physics solver for the accurate solution of cardiac dynamics with an uncertainty quantification analysis to account for the individuals variability. The input parameters of the computational model will be treated as aleatory variables, whose probability distribution function will be obtained using three-dimensional datasets of cardiac configurations available to the PI's group and acquired in-vivo by the clinical members involved in the project. Simulation campaigns (rather than a single simulation) will be then run in order to sweep the uncertain input distributions and obtain the synthetic population response in the case of selected pathologies like myocardial infarction and the optimal stimulation pattern for cardiac resynchronization therapy. My approach removes the main barrier that keeps up from a systematic use of computational engineering to run in-silico clinical trials.

Interacting bosons are unique quantum systems, whose low temperature phases exhibit fascinating quantum mechanics effects at a macroscopic scale. In the past two decades, the mathematical understanding of these systems improved tremendously. However, their behavior in the thermodynamic limit is still poorly understood, although this is the appropriate large scale limit to prove the emergence of scaling laws and universality, as well as to investigate the occurrence of phase transitions. MaTCh aims at investigating the low energy properties of interacting bosons in the thermodynamic limit, and at gaining a mathematical understanding of the emergence of correlated phases, in the form of Bose-Einstein condensation and quasi-long range order, as well as of their instabilities, due to thermal fluctuations or three-body recombination effects of Efimov type. Our plan is to exploit scaling limits as a framework to identify and overcome, one at a time, the mathematical obstructions that currently prevent us to control the system at finite density in the thermodynamic limit. In order to make progress on this program, MaTCh will introduce novel mathematical methods, inspired by renormalization group approaches and grounded in the second quantization techniques developed by the P.I. and collaborators, valid on an increasing sequence of scales. Ultimately, the research led by MaTCh will lay the foundation for the rigorous description of several phenomena which are at the frontiers of present theoretical and experimental research, where collective excitations of quantum systems are described in terms of emergent Bose gases, such as in the BCS theory for superconductivity, the molecular description of strongly interacting Fermi gases, and the spin-wave theory for quantum magnetism.