Roma Tre University

The objective of this research proposal is to understand the evolution of plate margins when multiple tectonic processes (e.g. plate convergence, subduction, and backarc extension) interact within a small area (e.g. the Calabrian arc in the Central Mediterranean). These margins are prone to catastrophic earthquakes, tsunami and volcanic eruptions, and are all linked to long-term dynamic tectonic processes. Various models explain the evolution of these plate margins, however, lack detail on the extension and rifting that takes place along the arcs. The earthquakes in these areas have a strong dependence on their location along the arc, and hence in any effort aimed at mitigating seismic risk, it is crucial to have a complete understanding of how plate tectonics work when multiple tectonic processes act. We propose a multidisciplinary geophysical and geodynamic investigation of seismic data with additional physical constraints and analogue modelling to improve our understanding on this important aspect of plate tectonics. This will be accomplished by studying the Calabrian Arc, with a special attention on the Sicily Channel Rift Zone. We will incorporate the results into a regional analogue model to understand the nature and role of these processes, which can then be exported for studying other regions. This will allow us to characterise the evolution of plate margins along backarc systems in unprecedented detail, and to investigate the link between plate convergence, subduction, and backarc extension with the tectonics along and at the front of the arc, thus providing a new insight on the evolution of our planet. The study will ultimately contribute to the mitigation of seismic risk by improving the seismic hazard assessment of the countries affected. Some of these places are highly inhabited areas, home to millions of citizens, a destination to millions of tourists, and have strong commercial activity off shore.

Universality is a central concept in several branches of mathematics and physics. In the broad context of statistical mechanics and condensed matter, it refers to the independence of certain key observables from the microscopic details of the system. Remarkable examples of this phenomenon are: the universality of the scaling theory at a second order phase transition, at a quantum critical point, or in a phase with broken continuous symmetry; the quantization of the conductivity in interacting or disordered quantum many-body systems; the equivalence between bulk and edge transport coefficients. Notwithstanding the striking evidence for the validity of the universality hypothesis in these and many other settings, a fundamental understanding of these phenomena is still lacking, particularly in the case of interacting systems. This project will investigate several key problems, representative of different instances of universality. It will develop along three inter-connected research lines: scaling limits in Ising and dimer models, quantum transport in interacting Fermi systems, continuous symmetry breaking in spin systems and in models for pattern formation or nematic order. Progresses on these problems will come from an effective combination of the complementary techniques that are currently used in the mathematical theory of universality, such as: constructive renormalization group, reflection positivity, functional inequalities, discrete harmonic analysis, rigidity estimates. We will pay particular attention to the study of some poorly understood aspects of the theory, such as the role of boundary corrections, the loss of translational invariance in multiscale analysis, and the phenomenon of continuous non-abelian symmetry breaking. The final goal of the project is the development of new tools for the mathematical analysis of strongly interacting systems. Its impact will be an improved fundamental understanding of universality phenomena in condensed matter.