Topology is the study of shapes, focusing on persistent features unchanged by deformations. Our research is inspired by its fundamental role in mathematics and physics, and adopts an innovative approach facilitated by rapid advances in theories and computing. We explore the intricate topology of three-manifolds and knots, leveraging insights from number theory and algebra. Employing artificial intelligence (AI), we decode topological invariants, revealing hidden correlations. We create AI-driven computational tools for systems with non-trivial topology, set to impact fields from mathematics to fundamental physics and engineering. This interdisciplinary approach elevates our understanding with concrete applications, promising transformative insights.

Determining neutrino mass ordering is crucial for understanding neutrino properties, and advancing beyond the Standard Model physics. The ability of KM3NeT/ORCA to determine the neutrino mass ordering critically depends on accurately distinguishing between low-energy muon (anti)neutrinos and electron (anti)neutrinos. However, this precision can be greatly improved by implementing novel reconstruction techniques that analyse detailed features of neutrino interactions in seawater, rather than solely focusing on the outgoing lepton. Achieving this will provide critical insights into models that explore neutrino masses and enhance sensitivity in beyond the Standard Model processes that depend on the ordering.

The materials from which life is built are typically soft, adaptable and active. In order to study them, we need model materials with similar properties. Based on new insights into a complex material class called elasto-viscoplastics, which includes toothpaste, I propose to develop a new class of active elasto-viscoplastics (A-EVP). These materials could mimic natural life processes like cell migration and embryo development. I will integrate advanced experiments and simulations to develop a mechanical framework, enhancing our understanding of biological mechanics and advancing the creation of innovative, bio-inspired materials like smart 3D-printed and autonomous active matter.

Modern transmission electron microscopes now can routinely visualize materials all the way down to the atomic level. At the same time, recent developments in nanophotonics and plasmonics make it possible to concentrate light nearly to the atomic scale within picoseconds, opening up unprecedented control over where, when and how energy is injected into a material. SHINE will bring light directly into the transmission electron microscope to enable us to watch solar harvesting materials transform at the atomic level under relevant operating conditions.

The perennial appeal of condensed matter science lies in its apparently limitless set of possibilities. Combining different sorts of constituent particles in different ways leads to myriads of remarkable phenomena; one cannot help but wonder that of these countless possibilities, only a few are known, and the simplest understood. Our problem is that the predictive power of our standard approaches is quickly rendered inapplicable by the potent mixture of quantum mechanics, interparticle interactions and reduced dimensionality. The ubiquitous strategy of focusing on low-energy, universal features only often lacks the depth to explain or predict important, observable and potentially useful features of key strongly-correlated systems. This proposal aims to establish a new framework for tackling strong correlations, in which universal scaling results at low energies are superseded by detailed, quantitative results valid at arbitrary energies, but in more specific circumstances. This will be achieved by capitalizing on recent breakthroughs on `pioneer systems: these `Bethe liquids find experimental realizations in forms ranging from magnetic materials and cold atomic gases to quantum dots and nanostructures. Their theoretical description will be unified into a consistent framework, bridging diverse fields from the mathematics of representation theory all the way to concrete physical applications, and offering urgently-needed, detailed quantitative calculations of many experimental observables beyond the reach of traditional methods. The theoretical foundations of Bethe liquids will in fact be robust enough to support the treatment not only of equilibrium but also of out-of-equilibrium situations, allowing detailed studies of fundamental questions relating to dynamics, decoherence, relaxation and thermalization in many-body interacting quantum systems, providing stringent new benchmarks for alternative methods, setting new challenges for experiments, and providing an altogether new way of thinking about strong correlations.