This project aims to prove rigorous results on the generation of unstable dynamics in the dispersive Hamiltonian water waves and geophysical fluid equations: I refer to the outstanding open problems of the formation of energy cascades from low to high frequencies, orbital instabilities and extreme rare phenomena such as rogue waves. All these behaviors are well documented in experiments, real world data and numerical simulations, but still lack a rigorous mathematical proof. Accordingly the project has three lines of research: 1) Energy cascades from low to high frequency modes: I plan to construct solutions of water waves and geophysical fluids equations in which energy shifts from low to high Fourier frequencies, induced by resonant interactions, provoking the growth of Sobolev norms. This will be attacked via a novel mechanism based on dispersive estimates in the frequency space, that I have pioneered in the linear setting; 2) Orbital instabilities of Stokes and Rossby waves: I plan to study the linear and nonlinear modulational instabilities of traveling solutions like the Stokes and Rossby waves in the higher dimensional setting, proving long-time conjectures in fluid dynamics and geophysics. This will be attacked by extending a program I have initiated in the one dimensional setting; 3) Extreme phenomena formation: I plan to construct rogue wave solutions of the water wave equations, confirming (or disproving) two of the most renowned physical conjectures regarding their formation. This will be achieved combining deterministic normal forms and probabilistic methods, like large deviation principles applied to PDEs. These goals aim to open new paradigms to understand the long time dynamics of dispersive Hamiltonian partial differential equations originating from fluids.

This action supports physical and blended mobility of higher education students and staff from EU Member States and third countries associated to Erasmus+ to any country in the world. Students in all study fields and cycles can take part in a study period or traineeship abroad. Higher education teaching and administrative staff can take part in professional development activities abroad, as well as staff from the field of work in order to teach and train students or staff at higher education institutions.

The aim of AROMA-CFD is to create a team of scientists at SISSA for the development of Advanced Reduced Order Modelling techniques with a focus in Computational Fluid Dynamics (CFD), in order to face and overcome many current limitations of the state of the art and improve the capabilities of reduced order methodologies for more demanding applications in industrial, medical and applied sciences contexts. AROMA-CFD deals with strong methodological developments in numerical analysis, with a special emphasis on mathematical modelling and extensive exploitation of computational science and engineering. Several tasks have been identified to tackle important problems and open questions in reduced order modelling: study of bifurcations and instabilities in flows, increasing Reynolds number and guaranteeing stability, moving towards turbulent flows, considering complex geometrical parametrizations of shapes as computational domains into extended networks. A reduced computational and geometrical framework will be developed for nonlinear inverse problems, focusing on optimal flow control, shape optimization and uncertainty quantification. Further, all the advanced developments in reduced order modelling for CFD will be delivered for applications in multiphysics, such as fluid-structure interaction problems and general coupled phenomena involving inviscid, viscous and thermal flows, solids and porous media. The advanced developed framework within AROMA-CFD will provide attractive capabilities for several industrial and medical applications (e.g. aeronautical, mechanical, naval, off-shore, wind, sport, biomedical engineering, and cardiovascular surgery as well), combining high performance computing (in dedicated supercomputing centers) and advanced reduced order modelling (in common devices) to guarantee real time computing and visualization. A new open source software library for AROMA-CFD will be created: ITHACA, In real Time Highly Advanced Computational Applications.

The project is a cutting-edge exploration of the dynamics of black hole collisions in general relativity and in modified gravity theories in an innovative way that makes the merging of black holes amenable to analytic treatment in the extreme-mass-ratio limit. By developing an approach based on ray tracing, the project assumes a pioneering stance, leveraging strong field tests of gravity to impart stringent constraints on modified gravity theories and learning more about black hole merging and matter collapse. The approach is complementary to other techniques currently employed, but in a regime that is not accessible to them. Central to its timeliness is the burgeoning of gravitational wave astronomy, hastening the need for empirical validation. The forthcoming Laser Interferometer Space Antenna (LISA) adds further urgency, promising novel insights into strong gravity within a decade.

Despite written language is not part of our genetic endowment, literate adults process an impressive amount of information as they read, and do that extremely flawlessly and nearly error-free. How this happens is largely unknown, and represents a fundamental issue for theories of human learning. Building on data from nonhuman primates, human infants and psycholinguistic experiments on word internal structure, STATLEARN tests the hypothesis that one fundamental cognitive mechanism underlies visual word identification, i.e., statistical learning. Human infants learn to chunk smaller perceptual units (e.g., oriented lines) into larger, meaningful objects (e.g., tools, faces), taking advantage of recurrent patterns in their distribution. As developing readers, they would apply this very same mechanisms to a newly–encountered type of visual objects, i.e., letters. On this basis, they would build progressively higher–order orthographic units, which eventually make their visual word identification as adult readers astonishingly efficient. The project is composed of four work packages. One aims at identifying which principle(s) drive(s) statistical learning, and contrasts overall frequency, contextual diversity, and letter transitional probabilities. Because these factors co-vary in real languages, a second work package will involve adult readers in learning artificial languages, where we will build in any statistical properties we might need to test. A third package will seek signs of statistical learning directly into the performance of developing readers. A fourth package will assess positional constraints in the identification of morphemes (e.g., kind and ness in kindness). These work packages include behavioural, eye tracking, ERP, MEG and fMRI work. Bringing together evidence from such a wide array of approaches will allow to understand how statistical learning unfolds, and what kind of representations it brings into the human reading system.