One of the major challenges in theoretical physics is the development of systematic methods for describing and simulating quantum many body systems with strong interactions. Given the huge experimental progress and technological potential in manipulating strongly correlated atoms and electrons, there is a pressing need for such a better theory. The study of quantum entanglement holds the promise of being a game changer for this question. By mapping out the entanglement structure of the low-energy wavefunctions of quantum spin systems on the lattice, the prototypical example of strongly correlated systems, we have found that the associated wavefunctions can be very well modeled by a novel class of variational wavefunctions, called tensor network states. Tensor networks are changing the ways in which strongly correlated systems can be simulated, classified and understood: as opposed to the usual many body methods, these tensor networks are generic and describe non-perturbative effects in a very natural way. The goal of this proposal is to advance the scope and use of tensor networks in several directions, both from the numerical and theoretical point of view. We plan to study the differential geometric character of the manifold of tensor network states and the associated nonlinear differential equations of motion on it, develop post tensor network methods in the form of effective theories on top of the tensor network vacuum, study tensor networks in the context of lattice gauge theories and topologically ordered systems, and investigate the novel insights that tensor networks are providing to the renormalization group and the holographic principle. Colloquially, we believe that tensor networks and the theory of entanglement provide a basic new vocabulary for describing strongly correlated quantum systems, and the main goal of this proposal is to develop the syntax and semantics of that new language.

Soil resources in semi-arid regions are rapidly degrading, posing an imminent threat to food, water and livelihood security. Caveats in our understanding of geomorphological responses to extreme events are a major hindrance for attributing soil erosion and sediment flux dynamics to environmental drivers. Using the Burdekin and Makuyuni catchments as natural laboratories for semi-arid regions, the AsFoRESEEN project will assess feedback dynamics in soil erosion through the lens of variable sediment connectivity to test the hypothesis that extreme events can trigger regime shifts towards highly connected ephemeral gully networks. The proposed knowledge transfer strategies will bring the researcher’s scientific and analytical skills to the international standard, underpinning his ambition to combine academic and consultancy work within a leading European research institution. The researcher's unique skillset will be applied to develop novel approaches and integrate them with established techniques in an open-access diagnostic toolkit to support targeted soil- and water management interventions. Temporal dynamics in fine sediment and Phosphorous transport will be quantified using high-frequency sensors and sediment dating techniques. We will be the first to evaluate the use of secondary weathered metal species as tracers, providing a new pathway for attributing the contribution of gully erosion in deeply weathered or alluvials soils. Stream monitoring and sediment source tracing outputs will be integrated in a dynamic sediment budget to elucidate non-linear geomorphological responses to extreme events and land use changes. As a source of innovation, we will couple a machine-learning gully quantification tool with a dynamic catchment model, wherein gullies are both a direct source of sediment and a driver of changing sediment connectivity. The hybrid model will be used to test the efficacy of gully remediation strategies under current and future climatic conditions.

COSMOPOET aims to rethink the relationship between poetry and astronomy and ultimately, it investigates medieval Greek solutions to the question as to how to explain the cosmos through literary means. This is a project about the interaction of science and literature and about interpreting scientific literature as literature in the context of the intellectual space of the Byzantine schools and the multiple curricula coexisting at the higher educational level. COSMOPOET studies the medieval Greek and early modern manuscript tradition of the didactic poem "Phaenomena" by Aratus of Soli (d. before 239 BCE) and compares it to transmission of the introductory astronomical treatise "The Heavens" by Cleomedes (first century CE). Both texts introduce the reader-student to elementary cosmology and astronomy and prompted the production of commentaries of textual and of diagrammatic nature, as their popularity in Byzantium increased from the late thirteenth century onwards. COSMOPOET studies 1) the textual dimension of both discourses (especially the didactic use of formal literary features such as verse and rhythm); 2) their respective graphic features (e.g., layout and diagrams); 3) the associated paratexts (e.g., epigrams, scholia, marginal and interlinear annotations) and 4) standalone commentaries, and 5) how they change as evidenced in manuscripts copied from the tenth to the sixteenth century. Thus, COSMOPOET formulates and tests the hypothesis that the examination of both paratexts and graphic features of scientific discourse, and of their respective variations through time can answer questions concerning the practices of teaching and learning cosmology and elementary astronomy in Byzantine advanced education.