Home page di Michela Procesi




ERC- Grant

Hamiltonian Dynamics, PDEs and Waves on the Amalfi coast

Conference in occasion of Luigi Chierchia's 60' Birthday


DIDATTICA 2015/16
Corso di AM430: TOPICS IN ORDINARY DIFFERENTIAL EQUATIONS


DIDATTICA  2016/17

Corso di: Istituzioni di Matematica   per Biologia

Corso di AM550: Problemi di piccoli divisori

DIDATTICA  2017/18

Corso di: Istituzioni di Matematica   per Biologia

 Corso di AM120: Analisi Matematica

Curriculum:


  • Born in Rome 21-3-1973
  • Graduated in Physics at University of Rome ''La Sapienza'' , May 1997
  • PhD in Mathematics at University of Rome ''La Sapienza''  February 200
foto

Positions
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 150 citations on ISI  Web of Science

[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 configuration 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 to appear on Comm. Math. Phys.

[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

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.


 Member of the organizing comittee of:

• 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.

• “Analysis and Dynamics, in occasion of Luigi Chierchia's 60th birthday” Patù, 12-15 ottobre 2017.



Member of the scientific and organizing comittee: 

• 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