Objective "A large number of partial differential equations of Physics have the structure of an infinite-dimensional Hamiltonian dynamical system. In this class of equations appear, among others, the Schrödinger equation (NLS), the wave equation (NLW), the Euler equations of hydrodynamics and the numerous models that derive from it. The study of these equations poses some fundamental questions that have inspired an entire research field in the last twenty years: the investigation of the main invariant structures of the phase space of a Hamiltonian system, starting from its stationary, periodic and quasi-periodic orbits. As in the case of finite-dimensional dynamical systems, one of the main problems in this field is linked to the well-known ""small divisors problem''. A further difficulty is due to the fact that ''physically'' interesting equations, without outer parameters, are typically resonant and/or contain derivatives in the non-linearity. There are many fundamental open questions in this field. Our main goals are 1) the study of quasi-periodic solutions, in particular for semi-linear and quasi-linear equations. 2)Study of normal forms, both in integrable and non-integrable cases. 3) Applications to hydrodynamics and search of quasi-periodic solutions in water wave problems.4) Study of almost periodic solutions for nonlinear PDEs. 5) quasi-periodic solutions for resonant systems with minimal restrictions on the non-linearity. Together with my group in Naples we already have developed several techniques to approach these problems and we have several ideas of possible innovative approaches, combining Nash-Moser and KAM methods, Normal Form Theory, Para-differential calculus, combinatorial methods." Fields of science natural sciencesmathematicsapplied mathematicsdynamical systemsnatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equations Programme(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Topic(s) ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations Call for proposal ERC-2012-StG_20111012 See other projects for this call Funding Scheme ERC-SG - ERC Starting Grant Host institution UNIVERSITA DEGLI STUDI ROMA TRE EU contribution € 297 772,46 Address VIA OSTIENSE 133 00154 Roma Italy See on map Region Centro (IT) Lazio Roma Activity type Higher or Secondary Education Establishments Administrative Contact Virgilio Lo Presti (Mr.) Principal investigator Michela Procesi (Prof.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data Beneficiaries (3) Sort alphabetically Sort by EU Contribution Expand all Collapse all UNIVERSITA DEGLI STUDI ROMA TRE Italy EU contribution € 297 772,46 Address VIA OSTIENSE 133 00154 Roma See on map Region Centro (IT) Lazio Roma Activity type Higher or Secondary Education Establishments Administrative Contact Virgilio Lo Presti (Mr.) Principal investigator Michela Procesi (Prof.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data UNIVERSITA DEGLI STUDI DI NAPOLI FEDERICO II Italy EU contribution € 215 272,56 Address CORSO UMBERTO I, 40 80138 Napoli See on map Region Sud Campania Napoli Activity type Higher or Secondary Education Establishments Administrative Contact Carmela Ippolito (Ms.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data UNIVERSITA DEGLI STUDI DI ROMA LA SAPIENZA Italy EU contribution € 164 954,98 Address Piazzale Aldo Moro 5 00185 Roma See on map Region Centro (IT) Lazio Roma Activity type Higher or Secondary Education Establishments Administrative Contact Maria Rita Ullucci (Ms.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data