Main Reaserch Interests
Hamiltonian Partial Differential Equations:
Periodic and Quasi-Periodic solutions for semi-linear PDEs
Normal forms, Periodic and Quasi-Periodic solutions for completely resonant PDE's
Lindstedt series and Small divisor problems in high dimensional PDE's
Nash-Moser Implicit Function Theorems
Dynamical Systems: Arnold Diffusion
Integrable PDEs
finanziamenti
PRIN:
2002- Problemi Nonlineari: Equazioni ellittiche e Sistemi Hamiltoniani (Ambrosetti)
2009- Sistemi Hamiltoniani infinito dimensionali ed Equazioni alle Derivate Parziali (Terracini)
2012- Aspetti variazionali e perturbativi nei problemi differenziali nonlineari (Terracini)
2015- Variational methods, with applications to problems in mathematical physics and geometry. (Malchiodi)
2020- Local coordinator of: Hamiltonian and dispersive PDEs (Berti)
2022- Stability in Hamiltonian dynamics and beyond (Sorrentino)
Publications:
[0] A. Degasperis e M. Procesi A test in Asymptotic Integrability of 1 + 1 wave equations in Proceedings of the international conference in Tiruchirapalli India, Feb 1998 pp.17-23
[1] A. Degasperis, M. Procesi: Asymptotic Integrability, in Proceedings of the International Workshop on Symmetry and Perturbation Theory SPT98, A. Degasperis, G. Gaeta ed. World Scientic Press pp. 23-37. This paper has more than 600 citations on Scopus
[2] M. Procesi: Exponentially small splitting and Arnold diffusion for multiple time scale systems Rev. Math. Phys. 15, 4 (2003), pp. 339-386
[3] G. Gentile, V. Mastropietro, M. Procesi: Periodic solutions of completely resonant nonlinear wave equations Comm. Math. Phys. 256, 2 (2005), pp. 437-490
[4] M. Procesi: Quasi-periodic solutions for completely resonant nonlinear wave equations in 1D and 2D Discr. Cont. Dyn. Syst. A 13, 3 (2005) pp. 541-552
[5] G. Gentile, M. Procesi: Conservation of resonant periodic solutions for the one dimensional nonlinear Schrodinger equation, Comm. Math. Phys. 262, 3 (2006), pp. 533-553.
[6] M. Berti, M. Procesi: Quasi-periodic oscillations for wave equations under periodic forcing Rendiconti Mat. Acc. Naz. Lincei. s.9 16 (2005) pp. 109-116.
[7] M. Berti, M. Procesi: Quasi-periodic solutions of completely resonant forced wave Comm. in PDEs 31 , 6 (2006), pp.959-985.
[8] V. Mastropietro, M. Procesi: Lindstedt series for periodic solutions of beam equations under quadratic and velocity dependent nonlinearities Comm. Pure Appl. Anal. 5, 1, (2006) pp. 1-28
[9] G. Gentile, M. Procesi: Periodic solutions for the Schrodinger equation with non-local smoothing nonlinearities in higher dimension. J. Diff. Eq. Vol. 245, (2008) pp. 3253-3326
[10] G. Gentile, M. Procesi: Periodic solutions for a class of nonlinear partial differential equations in higher dimension. Comm. Math. Phys. vol. 289; pp. 863-906 (2009)
[11] M. Berti, P. Bolle, M. Procesi: An abstract Nash Moser theorem with applications to non linear PDEs Annales Inst. Poincare vol. 27; (2010) pp. 377-399.
[12] M. Berti, M. Procesi: Nonlinear wave equations on Compact Lie groups and homogeneous manifolds. Duke Math. J. Vol. 159, n. 3 (2011), p. 479-538.
[13] L. Corsi, G. Gentile, M. Procesi: KAM theory in conï¬guration space and cancellations in the Lindstedt series Communications in Mathematical Physics 302 (2011), no. 2, 359-402.
[14] M. Procesi: A normal form for beam and non-local nonlinear Schrodinger equations J. Phys. A: Math. Theor. Vol: 43 (2010) n. 434028
[15] Procesi C.and Procesi M.: A normal form of the nonlinear Schrodinger equation with analytic non--linearities Comm. Math. Phys 312 (2012), 501-557
[16] Berti M. , Biasco L. Procesi M.: KAM theory for the Hamiltonian derivative wave equation Annales Scientifiques de l' ENS 46 (2) 2013
[17] Procesi M. and Xu X.: Quasi-Toplitz Functions in KAM Theorem. SIAM J. of Math. Anal. vol. 45, p. 2148-2181
[18] Bich V. Procesi C. and Procesi M.: The energy graph of the nonlinear Schrodinger equation. Rend. Lincei Mat. Appl., 24, 2013.
[19] Berti M. , Biasco L. Procesi M. Existence and stability of quasi-periodic solutions for derivative wave Rend. Lincei Mat. Appl. p. 199-214 vol 24, 2013
[20] Berti M. , Biasco L. Procesi M. KAM for Reversible Derivative Wave Equations, Archive for Rational Mechanics and Analysis: Volume 212, Issue 3 (2014), Page 905-955
[21] Berti M., Corsi L., Procesi M. An abstract Nash-Moser theorem and quasi-periodic solutions for NLW and NLS on compact Lie groups and homogeneous manifolds Comm. Math. Phys. 334 (2015) n.3 pp. 1413-1454
[22] M. Procesi, C. Procesi: A KAM algorithm for the resonant non-linear Schroedinger equation Advances in math. (2015), pp. 399-470
[23] L.Corsi, E. Haus, M. Procesi: A KAM result on Compact Lie Groups, Acta Appl. Math, 137 (2015) 41–59.
[24] E. Haus, M. Procesi: Growth of Sobolev norms for the quintic NLS on T^2, Analysis and PDEs 8 (2015), 883-922.
[25] R. Feola, M. Procesi: Quasi-periodic solutions for fully nonlinear forced reversible Schroedinger equations, J. D.E. 259 (2015) 7.
[26] M. Procesi, C. Procesi: Reducible quasi-periodic solutions for the non linear Schrödinger equation. Boll. Unione Mat. Ital. 9 (2016) 189–236.
[27] M. Guardia, E. Haus, M. Procesi: Growth of Sobolev norms for the defocusing analytic NLS on T^2. Advances in Math. 301 (2016), 615–692.
[28] Procesi, C.; Procesi, M. The NLS on a torus. Theory and applications in mathematical physics, 107–118, World Sci. Publ., Hackensack, NJ, 2016. 35Q55
[29] E. Haus, M. Procesi: KAM for beating solutions of the quintic NLS , Comm. Math. Phys. 354 (2017) 3. pp 1101–1132
[30] L.Corsi, R. Feola, M. Procesi:Finite dimensional invariant KAM tori for tame vector fields, , 2019, 372(3), pp. 1913–1983
[31] Maspero, A., Procesi, M. Long time stability of small finite gap solutions of the cubic nonlinear Schrödinger equation on T2 (2018) Journal of Differential Equations, 265 (7), pp. 3212-3309.
[32] Feola, R., Giuliani, F., Montalto, R., Procesi, M. Reducibility of first order linear operators on tori via Moser's theorem (2019) Journal of Functional Analysis, 276 (3), pp. 932-970.
[33] Biasco, L., Massetti, J.E., Procesi, A note on the construction of Sobolev almost periodic invariant tori for the 1d NLS Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni, 31 (4), pp. 981-993
[34] Biasco, L., Massetti, J.E., Procesi, M. An Abstract Birkhoff Normal Form Theorem and Exponential Type Stability of the 1d NLS (2020) Communications in Mathematical Physics, 375 (3), pp. 2089-2153
[35] Feola, R., Giuliani, F., Procesi, M. Reducible KAM Tori for the Degasperis–Procesi Equation
(2020) Communications in Mathematical Physics, 377 (3), pp. 1681-1759.
[36] Montalto, R., Procesi, M. Linear Schrödinger equation with an almost periodic potential (2021) SIAM Journal on Mathematical Analysis, 53 (1), pp. 386-434.
[37] Biasco, L., Massetti, J.E., Procesi, M.Almost periodic invariant tori for the NLS on the circle (2021) Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, 38 (3), pp. 711-758.
[38] Corsi, L., Montalto, R., Procesi, M. Almost-Periodic Response Solutions for a Forced Quasi-Linear Airy Equation (2021) Journal of Dynamics and Differential Equations, 33 (3), pp. 1231-1267.
[39] Procesi, M., Stolovitch, L. About Linearization of Infinite-Dimensional Hamiltonian Systems (2022) Communications in Mathematical Physics, 394 (1), pp. 39-72.
[40] Guardia, M., Hani, Z., Haus, E., Maspero, A., Procesi, M. Strong nonlinear instability and growth of sobolev norms near quasiperiodic finite-gap tori for the 2d cubic NLS equation,J. Eur. Math. Soc. 25 (2023), no. 4, pp. 1497–1551
[41] Biasco, L., Massetti, J.E., Procesi, Weak Sobolev almost periodic solutions for the 1D NLS, Duke Math. J. 172 (2023), pp. 2643–2714
[42] Haus, E., Langella, B., Maspero, A., Procesi, M., Reducibility and nonlinear stability for a quasi-periodically forced NLS to appear on Pure and Applied Mathematics Quarterly
Invited speaker in international conferences:
-Trimester on Dynamical systems, Sissa Trieste sept.-dec ’03.
-Dynamical Systems: Classical, Quantum and Stochastic, Acireale sept. ’04.
-Integrable Systems, Cuernavaca (Mx) 9-16 nov. ’04
-AIMS’ Sixth International Conference on Dyn. Systems, Diff. Equations and Applications 25-28 june 2006.
-SPT2007 (Otranto 2-9 june 2007).
-Dynamics Days Europe, Loughborough (UK) 9-13 luglio 2007.
-Renormalization in dynamical systems Inst. Erwin Schrodinger Vienna october 2007.
-Summer School Hamiltonian PDE’s and Variational Methods, CAPRI, Villa Orlandi 8-12 sept. 2008.
-Indam-ERC intensive period: New connections between dynamical systems and Hamiltonian PDEs NAPOLI, April 1- June 6, 2009.
-Workshop on ”New connections between dynamical systems and Hamiltonian PDEs”, Capri October 15-16 2010.
-Workshop KAM theory and Cauchy problems for PDEs, 23-27 may 2011.
-Integrability and Physics, Conference in honour of Antonio Degasperis 70's birthday, La Sapienza, Rome, 25/03/2011.
-XIX Congresso UMI, Bologna, 12 settembre 2011.
-Mechanics: classical, statistical and quantum (in honor of the 70th birthday of Giovanni Gallavotti), La Sapienza, Rome, 2-5/07/2012.
-Nonlinear Hamiltonian PDEs, Ascona, July 1 - 6, 2012.
- Hamiltonian and Dispersive Equations CIRM Luminy 24-28 july 2013.
- Multiscale methods in Small Divisor problems. Maiori 16-20 Sept. 2013.
- "16th General Meeting of the European Women in Mathematics", Bonn (Germany), Sept. 2013- Plenary speaker.
-SPT 2014, Cala Gonone (Italy), May 2014.
-Geometric and Analytic Aspects of Integrable and nearly-Integrable Hamiltonian Systems ,
University of Milano-Bicocca (Italy), 18-20 June 2014
- Dynamics and PDEs, Cargese (Corsica, France) 11-14 November 2014.
- KAM and Dispersive Methods in PDEs, Milano (Italy) 1-5 December 2014.
- Two-day meeting in honor of Antonio Ambrosetti, Venezia (Italy) 14-15 December 2014.
- The Conference on Hamiltonian Dynamical Systems, Fudan University in Shanghai (China), 4-10 January 2015.
- "Sixth Itinerant Meeting in PDEs" Trieste, 14-16 January 2015.
- Summer school "Normal forms and large time behavior for nonlinear PDE", Nantes (France), 22 June-3 July 2015.
-SIAM Conference Analysis and PDEs, Scottsdale (USA), 7-10 Dec 2015
- Dynamics of Evolution Equations, CIRM -Luminy (France) March 21-25, 2016
- Dynamical Systems, Differential Equations and Applications Orlando July 1-5, 2016.
-Summer School Nonlinear Waves, IHES Paris (France) 18-29 July 2016,
-Dynamics and PDEs, Saint Etienne de Tinée (France), Feb. 2017.
Invited speaker for Mini-courses
- Dynamics and PDEs , S. Etienne de Tinée, 3-8 Fevrier 2013.
-Summer School Nonlinear Waves, IHES Paris (France) 18-29 July 2016.
Workshop "dynamics of hamiltonian PDEs" La Thuile, Feb 2018
- Workshop “Variational Methods in analysis, geometry and physics” Pisa, Feb 2018
-Workshop on Quasi-periodic Dynamics and Schrödinger operators Nanjing 3-7 Set. 2018.
-Leaning tori (Scuola Normale Superiore, Pisa, 20-23 May 2019
-Invited speaker to the international Congress of Mathematical Physics (section Dynamical systems) Geneva, 2-7 Aug 2021
-INdAM Workshop "Qualitative properties of dispersive PDEs", Roma 2-7 Sept. 2021
-Dynamics Days (Journées de Dynamique) at the University of Paris, Oct. 2021
-Invited speaker to Iternational Congress of Mathematics (section Dynamical systems) July 2022
-H2020 in Hamiltonian Dynamics, Venezia, July 2022
- UZH,CH, “Analysis and Hamiltonian PDEs, a conference in memoriam of Thomas Kappeler”, June 2023
-Wave dynamics- ICTP Trieste, Aug 2023
Invited speaker per Mini-corsi in conferenze:
- Dynamics and PDEs , S. Etienne de Tinée, 3-8 Fevrier 2013.
-Summer School Nonlinear Waves, IHES Paris (France) 18-29 July 2016.
- Interactions between Dynamical Systems and Partial Differential Equations, Barcellona June 2018
-Normal forms and splitting methods Pornichet June 2022
-School of Mathematical Physics Ravello, Sept. 2022
-Dynamics Days -Paris June 2024
Attività organizzative di convegni/scuole:
Congresso UMI- Siena 2015 ho organizzato la sessione S1 Analisi non lineare e sistemi Hamiltoniani
Membro del Comitato organizzativo:
• Summer School Hamiltonian PDE’s and Variational Methods, CAPRI, Villa Orlandi
8-12 september 2008.
• Indam-ERC intensive period: New connections between dynamical systems and
Hamiltonian PDEs NAPOLI, April 1- June 6, 2009.
• Workshop on ”New connections between dynamical systems and Hamiltonian
PDEs”, October 15-16 2010.
• International Workshop on “KAM and Cauchy Theory for PDEs”, June 4-7 2012.
• School and Workshop “New perspectives in nonlinear PDEs”, September 17-29 2012.
Membro del comitato scientifico e organizzativo:
• Symmetry and perturbation theory SPT(2007) 2-9 june 2007.
• KAM theory and Cauchy problems for PDEs, school and workshop 17-27 may
2011.
• Workshop on Multiscale methods in Small Divisor problems. Maiori 16-20 Sept.
2013
• Roman Summer School and Workshop: KAM Theory and Dispersive PDEs. Rome 1-11 Sept. 2014
• Hamiltonian Dynamics PDEs and Waves on the Amalfi coast, Maiori 5-11 Sept. 2016
• “Analysis and Dynamics, in occasion of Luigi Chierchia's 60th birthday” Patù, 12-15
ottobre 2017.
• Hamiltonian and Dispersive PDEs, 2 school and workshop Roma 15-19 Maggio 2023
Nell'ambito del progetto ERC di M. Berti a Napoli ho organizzato i cicli di seminari settimanali e minicorsi per il dottorato e post.doc.
Nell'ambito del progetto ERC di cui sono stata responsabile ho organizzato seminari e minicorsi per il dottorato e post.doc.
Referee per vari giornali internazionali fra cui:
Inventiones, Annals of Math, Comm. Math. Phys., Discr. Cont. Dyn. Syst., Ann. Inst. H. Poincare, Comm. Pure and Applied Math., Nonlinearity.
Referee per l’Agencie Nationale de la Recherche
CoEditor di Zeithschirft fur Angevante Math. Phys.