Piccione received his Laureate Degree in Mathematics in 1987 from the University of Rome La Sapienza and received his PhD in 1995 from the University of Pennsylvania with Adrian Ocneanu ( Discrete Regular Subalgebras of Semifinite Von Neumann Algebras ). In 1998 he completed his habilitation in Brazil and became a professor at the University of São Paulo .
He deals with the calculus of variations (Morse theory, bifurcation theory), global analysis and differential geometry, in particular semi-Riemannian geometry with applications in general relativity. Among other things, he investigated spherical-symmetrical gravitational collapse in 2003 with barotropic equations of state of matter, whereby, according to Piccione, naked singularities are formed (the case had previously been treated for the case of dust balls , i.e. vanishing pressure).
In 2012 he became a member of the Brazilian Academy of Sciences (ABC). As of 2018, he is President of the Brazilian Mathematical Society (SBM) and on the Council of the International Mathematical Union .
- with F. Giannoni, A. Masiello: A variational theory for light rays in stably causal Lorentzian manifolds: Regularity and multiplicity results, Comm. Math. Phys., Volume 187, 1997, pp. 375-415
- with F Giannoni, A Masiello: A Morse theory for light rays on stably causal Lorentzian manifolds, Annales de l'Institut Henri Poincare A, Volume 69, 1998, pp. 359-412
- with Fabio Giannoni: An intrinsic approach to the geodesical connectedness of stationary Lorentzian manifolds, Communications in Analysis and Geometry, Volume 7, 1999, pp. 157-197
- with Daniel V. Tausk: A note on the Morse index theorem for geodesics between submanifolds in semi-Riemannian geometry, J. of Math. Phys., Volume 40, 1999, pp. 6682-6688
- with DV Tausk: The Maslov index and a generalized Morse index theorem for non-positive definite metrics, Compte Rendu Acad. Sci. Paris, Volume 331, 2000, pp. 385-389
- with DV Tausk: An index theorem for non-periodic solutions of Hamiltonian systems, Proc. London Math. Soc., Vol. 83, 2001, pp. 351-389
- with Daniel V. Tausk: The Morse index theorem in semi-Riemannian geometry, Topology, Volume 41, 2002, pp. 1123-1159
- with R. Giambo, F. Giannoni, G. Magli: New solutions of Einstein equations in spherical symmetry: the cosmic censor to the court, Communications in Mathematical Physics, Volume 235, 2003, pp. 545-563, Arxiv
- with Giambo, Giannoni, Magli: New mathematical framework for spherical gravitational collapse, Classical and Quantum Gravity, Volume 20, 2003, L 75, Arxiv
- with Robert Giambo, Fabio Giannoni, Giulio Magli: Naked singularities formation in the gravitational collapse of barotropic spherical fluids, General Relativity and Gravitation, Volume 36, 2004, pp. 1279-1298,
- with A. Portulari, DV Tausk: Spectral flow, Maslov index and bifurcation of semi-Riemannian geodesics, Annals of Global Analysis and Geometry, Volume 25, 2004, pp. 121-149
- Paolo Piccione in the Mathematics Genealogy Project (English)
- Arxiv Preprint on this. The work was done by H. Iguchi et al. a. criticized, Class. Quant Gravity, Volume 22, 2005, p. 841, Arxiv . Answer from Piccione u. a .: Arxiv 2004 .
|BRIEF DESCRIPTION||Italian mathematician|
|DATE OF BIRTH||April 24, 1964|
|PLACE OF BIRTH||Rome|