"The applicant will study the existence of unstable nonlinear travelling wave solutions to the Navier-Stokes equations in isothermal ducts of square and rectangular cross-section where the basic flow is homogeneos in the streamwise direction. After this, more challenging situations will be considered with streamwise inhomogeneous base flows: boundary layer and backward facing step . Discovering such states is crucial for the understanding of turbulence and for its control. Relating the solutions found to experimental/DNS observations of vortices in square ducts is a clear step towards the development of ”Hopf theory of chaos”, which interprets turbulence as the wandering of the flow system’s trajectory in phase space among mutually repelling states. Further progress towards a dynamical-system-based theory of turbulence will be achieved by assessing the 3D global stability of the states found. The fellow will acquire complementary skills in parallel computing and collaborate to the development of novel numerical algorithms for global stability problems. The minimum direct outcome of the research will be three papers in leading archival journals; more importantly, the research will open a new path in the study of turbulence. The proposed project fits with ongoing research at Genova and matches perfectly the fellow’s ambitions and interests. The researcher will find the ideal environment to expand his scientific expertise in fluid mechanics, stability theory and parallel computing."