Research of R. Vitolo:
Geometric Methods in Mathematical Physics
Integrable Systems
Hamiltonian formalism for PDEs and Integrable Systems [22a,25a,26a,13c,29a,33a,34a,37a,38a,40a,41a,42a,44a,45a,46a,47a,48a, 49a,50a,53a,54a,55a,17c], differential equations which are uniquely characterized by their symmetry group [16a,17a,9c,10c,11c,15c,30a], generalized symmetries and applications [32a,35a,36a]. I contribute to the contents of the website http://gdeq.org/, which is a community of researchers who are interested in geometry and differential equations. I developed software for the research of integrability operators (Hamiltonian, symplectic and recursion operators) [1f,2f,42a]. Together with A.C. Norman I wrote a technical manual on REDUCE internals and programming [3f].
Applied Mathematics
Numerical methods for industrial engineering applications [43a,51a,52a,16c,56a,59a]. Scientific consultant of ESA for mathematical models in antenna design [56a,57a]. In this framework he is the inventor of a patent, see the list of publications.
Classical and quantum mechanics
Spherically symmetric solutions in Galilei relativity [2a], existence and classification of quantizations [4a,7a,3c], covariant symmetries in mechanics [2c,8a,15a,28a], classical and quantum mechanics of the rigid body [18a,19a,5c], covariant quantization and geometric quantization [6c,31a], geometry of polarizations [39a]. I recently published a paper of historical interest on an early contribution of Levi-Civita to the correspondence between symmetries and conserved quantities [27a].
Geometry of calculus of variations
I have studied variational sequences, on which I published a chapter of the Handbook of Global Analysis [2b]. These are exact sequences of spaces of differential forms on jets where one of the morphisms of the sequence is the Euler--Lagrange operator. In particular I devoted myself to variational sequences of finite order [3a,5a,6a,9a,10a,11a,12a,13a,14a,15a,20a,1c,4c,7c,12c,Tesi] and to variational multivectors, which are duals to forms in the variational sequence [8c,22a,13c,29a].
Classical field theory
Covariant Lagrangians for Einstein-Yang-Mills equations [1a,1b], inverse problem for Yang--Mills equations [21a].
Last updated: 07/04/2024