Antonio is a mathematician working on symplectic geometry and higher structures. His postdoctoral project focuses on the notion of observable quantities in multisymplectic geometry, investigating applications to the study of symmetries of Lagrangian field theories and their numerical integration.
Host University: Sapienza Università di Roma, Italy
Host research group or department: Department of Mathematics Guido Castelnuovo - MAT
Co-host University: National and Kapodistrian University of Athens, Greece
Secondment institution: Institut Camille Jordan, France (ICJ)
Advisor: Dr. Domenico Fiorenza
Co-advisor: Dr. Iakovos Androulidakis
Secondment mentor: Dr. Alessandra Frabetti
My research
MultiSymORI - Multisymplectic geometry: observables, reduction, and numerical Integrators
The notion of multisymplectic manifold is a common generalisation of symplectic and orientable smooth manifold with a fixed volume form. Originally, it has been introduced as a tool for encoding continuum mechanical systems,which in principle would involve infinite dimensional spaces, in a finite dimensional setting.The present project proposes some mutually intermingled research paths, mostly focussed towards multisymplectic geometry together with applications to mathematical physics. It aims at clarifying the role and algebraic structure of observables in multisymplectic geometry, introducing in the same context suitable notions of pre quantization and reduction in terms of higher homotopy algebras, and proposing applications of this abstract framework to the concrete settings of multisymplectic integrators. The latter, in cascade, have significant application potential in computer simulations in fluid dynamics and magneto dynamics, which, in turn, are crucial in the field of environmental and energy technologies.
The approach suggested for this study is essentially based on algebraic methods. Lie infinity algebras, in particular,play a central role, since higher homotopy structures provide a precise language to encode the notion of observables and conserved quantities along symmetries in this generalized setting.
Date started – Date End
01.02.2024 - 31.01.2026
