Gabriella pinzari vitae & studiorum
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gabriella pinzari B gabriella.pinzari@unina.it
Í https://www.docenti.unina.it/gabriella.pinzari
vitae & studiorum Assistant Professor, Federico II University, Naples
education
1986–1990 master in physics, sapienza, university of rome, roma.
supervisor: professor g. gallavotti
1992–1996 master in mathematics, sapienza, university of rome, roma.
supervisor: professor c. marchioro
2004–2009 PhD, roma tre university, roma.
supervisor: professor l. chierchia
PhD dissertation
title on the kolmogorov set for many–body problems
university roma tre, rome
year 2009
supervisor professor luigi chierchia (roma tre, rome)
report1 professor massimiliano berti (sissa, trieste)
report2 professor jacques féjoz (ceremade, paris)
judging professor massimiliano berti (sissa, trieste), professor alessandra celletti (tor vergata, rome),
committee professor jacques féjoz (ceremade, paris), professor corrado falcolini (roma tre, rome)
abstract In my dissertation I obtained a constructive proof of a famous statement by V. I. Arnold about the
stability of planetary motions, 1963. The reason of such delay with respect to the initial statement
was due to understanding certain degeneracies in the problem, not yet clear at Arnold’s times. A
complete, general proof of Arnold’s statement had been obtained in 2004, by M. Herman and
J. Féjoz. After their paper, some important questions had remained open yet, concerning the
structure of the phase space of the problem, the existence of a non–degenerate normal form for the
problem, the measure of the invariant set. Arnold’s initial ideas were based on the application of a
sophisticated perturbation theory that Arnold himself had developed in the same paper. My personal
contribution started with the rediscovery, that I made during the year 2008, of a symplectic set of
canonical coordinates (that I describe in §4 of my thesis), which had been already considered in the
80s by F. Boigey and A. Deprit, but remained substantially unnoticed since then. These coordinates
perform explicitly the reduction of rotation invariance of the system. I adapted Boigey–Deprit
coordinates to the planetay problem by producing a set of rectangular variables sharing many
good properties (regularity, symmetries) with the classical Poincaré coordinates (extensively used in
Celestial Mechanics). These new coordinates allowed me to recover Arnold’s design, since they let
the system free of its degeneracy. As a consequence, I obtained an explicit measure of the density
of stable motions in the planetary problem. The results of my thesis were published in Invent.Math.
2011 and motivated my invitation to give a lecture at the 2014’s ICM, seoul.arXiv source 1309.7028
research field and interests
my current research fields are: hamiltonian systems, perturbative techniques, celestial
mechanics.
honors
2014 Invited Speaker to the International Congress of Mathematicians, Seoul (Session no
9 Dynamical Systems)
2015 Awarded of ERC Starting Grant 2015
Project no 677793, “StableChaoticPlanetM, Stable and Chaotic Motions in the
Planetary Problem”. 900,000 euros
2015 Editor of Springer Monographs in Mathematics
academic positions
2009–2010 post-doc, university of napoli federico II, since march, 1st, 2009 to february, 28,
2010, position supported by ERC grant 204979 (p.i. massimiliano berti).
2010–2011 post-doc, university of napoli federico II, since april, 1st, 2010 to march, 31, 2011,
position supported by ERC grant 204979 (p.i. massimiliano berti).
2011–2012 post-doc, university of roma roma tre, since june, 1, 2011 to may, 31, 2012.
2012–2013 post-doc, university of roma roma tre, since october, 1st, 2012 to september, 30,
2013.
call 2012, italian national scientific qualification, (“abilitazione scientifica nazionale”), as
2013 Associate Professor in Mathematical Physic, valid until 2020.
2013–2015 assistant professor (RTDA), university of napoli federico II, position supported
by ERC grant 306414 (p.i. michela procesi).
2015–present assistant professor (RTDB), University of Naples “Federico II”.
2017 Associate Professor, University of Padova (“Chiamata diretta”), expected to begin
March 2017.
teaching
2015–2016 university of napoli federico II, calculus, module II (“analisi II”), for students of
chemical engineering, 72 hours.
2014–2015 university of napoli federico II, calculus, module II (“analisi II”), for students of
chemical engineering, 72 hours.
2013–2014 university of napoli federico II, calculus, module II (“analisi II”), for students of
chemical engineering, 72 hours.
2007–2008 university of roma roma tre, calculus, module I (“analisi I”), for students of
physics, 12 hours.2010–2011 to university of roma tor vergata, master for spacial science and technology for
2013–2014 graduated students (“master di II livello in scienza e tecnologia spaziale”), Class:
“classical orbit determination”, 5–10 hours each class.
some international conferences
2017 { DinAmicI IV: Modern trends in the ergodic theory of dynamical system. Rome,
June 5–9 (Organized by C. Bonanno). invited speaker.
{ celmec. international conference on celestial mechanics. san martino al cimino,
viterbo, roma. invited speaker.
{ winter school in conservative dynamics. Engelberg, Switzerland, February 5–11.
Organized by the ETH Institute for Theoretical Studies (Organizers: Marcel
Giardia, Vadim Kaloshin, Alfonso Sorrentino). Invited lecture.
2016 { The 11th AIMS Conference on Dynamical Systems, Differential Equations and
Applications. orlando (florida), july 1–5. organizer of special session no 16
“hamiltonian systems and the planetary problem”
2015 { minisymposium on "Celestial Mechanics". Equadiff conference. lyon, july 6-10,
2015.org: v. kaloshin and m. guardia.
{ Conference on Dynamical Systems at ICTP, Trieste, which will take place on July
27 - August 07, 2015.org: s. luzzatto, c. yoccoz, m. viana.
{ European Women in Mathematics. cortona. august, 31- sept., 4
{ Convegno Umi. Siena, 1-6 Sett.
{ hamiltonian systems and celestial mechanics, Oaxaca, Mexico September 6-11,
BIRS, workshops. org: e. pereze–chavela, f. diacu, j. libre.
2014 { Symposium on Mathematical Physics. University of Züric. nov. 10–11.
{ Symplectic Techniques in Topology and Dynamics. colonia, germany. september,
22– 26
{ International Congress of Mathematicians. coex, seoul, south corea. august
13–21.
{ 10th AIMS conference on dynamical systems, differential equations and applica-
tions. madrid, spain. july, 7–11.
{ spt 2014. cala gonone, sardegna, italy. may 26 – june, 1
2013 { Planetary Motions, Satellite Dynamics and Spaceship Orbits. CRM, montreal.
canada. july, 22–26.
{ New Perspectives on the N–body Problem. BIRS, banff, canada. january, 13–18.
2012 { Variational Methods in N–body and Vortex Dynamics. june 4–8, 2012. lecce,
italy.2011 { Dynamical Systems and Classical Mechanics: a Conference in Celebration of
Vladimir Arnold 1937 -2010. edinburgh, great britain. october 3–7.
{ International Symposium on Orbit Propagation and Determination. lille, france.
september, 26–28.
{ KAM and Cauchy Theories, napoli, may 21–18.
2010 { Conference on Celestial Mechanics and Hamiltonian Dynamics. university of
maryland, college park (USA). april 15-18.
2009 { Observatoire de Paris. December 14–18.
visiting
invitations.
2016 { university of barcelona. june. 5–10. invited by m. guardia.
2014 { university of zurich. nov. 10–11. invited by v. schroeder.
2010 { university of maryland. april. invited by v. kaloshin. three days.
2009 { observatoire de paris. december. invited by j. féjoz. one week.
schools as a lecturer.
2013 { CIRM, luminy, marseille, france. lecturer. eight ours
schools as a participant.
2013 { st. etienne de tinée. winter school. one week. february, 3-9. (by l. stolovich)
2012 { school on Variational Methods in N–body and Vortex Dynamics. Università del
Salento, (by a. portaluri and s. terracini). may 28–june 1
2011 { school Ciclo di Lezioni at milano bicocca university (by v. barurello and v. felli) .
february 7–9. Milan, Italy;
2009 { school New Connections Between Dynamical Systems and Hamiltonian PDEs.
april–may (by m. berti et al.).
grants (as a participant)
2014–2017 PRIN 2012 (italian national relevance research project).
project variational and perturbative aspects of nonlinear differential problems
duration 8/3/2014–8/3/2017funding MIUR (italian ministry of university school and research)
p. i. susanna terracini (university of torino)
2012–2017 ERC ideas 2012.
project hamiltonian PDEs and small divisor problems: a dynamical system approach (306414)
participation 1/11/2012–31/10/2017
funding european research council
p. i. michela procesi (university of roma la sapienza)2009–2012 ERC starting grant.
project Hamiltonian PDEs new connections between dynamical systems and Hamiltonian
PDEs with small divisors phenomena (204979)
funding european research council
duration 2008–2012
p. i. massimiliano berti (sissa, trieste)
2009 prin 2009 (italian national relevance research project).
project Critical Point Theory and Perturbative Methods for Nonlinear Differential Equations
duration 2008–2012
funding MIUR (italian ministry of university school and research)
p. i. susanna terracini (university of torino)
others
spoken languages
italian reading, writing, conversation level: native
english reading, writing, conversation level: good
programming languages
fortran, c++
mathematica
publications and e-prints
{ Pinzari, Gabriella. Co–existence of maximal and whiskered tori for the planetary three–
body problem, with the outer planet in retrograde motion. preprint 2016 arXiv 1611:
00508.
{ Pinzari, Gabriella. A first integral to the partially averaged Newtonian potential of the
three-body problem. preprint 2016 arXiv 1611:03056
{ Pinzari, Gabriella. Perihelia Reduction and Global Kolmogorov Tori in the Planetary
Problem. 2016. To appear in Mem. Amer. Math. Soc. arXiv:1501.04470. 78 p.
{ Pinzari, Gabriella. Global Kolmogorov Tori in the Planetary N-Body problem. Announce-
ment of Result. Electron. Res. Announc. Math. Sci. 22 (2015), 55–75
{ Pinzari, Gabriella. Canonical Coordinates for the Planetary Problem. 2014. Acta Appl
Math (2015) 137:205–232
{ Chierchia, Luigi and Pinzari, Gabriella. Metric stability of the planetary N-body problem.
Proceedings of the International Congress of Mathematicians, Coex, Seoul, 2014. To
appear.{ Pinzari, Gabriella. Aspects of the planetary Birkhoff normal form. Regul. Chaotic Dyn.
18 (2013), no. 6, 860–906. Special Issue dedicated to Alain Chenciner’s 70th birthday.
{ Chierchia, Luigi and Pinzari, Gabriella . Planetary Birkhoff normal forms. J. Mod. Dyn.
5 (2011), no. 4, 623–664.
{ Chierchia, Luigi and Pinzari, Gabriella . The planetary N-body problem: symplectic
foliation, reductions and invariant tori. Invent. Math. 186 (2011), no. 1, 1–77.
{ Chierchia, Luigi and Pinzari, Gabriella . Deprit’s reduction of the nodes revisited. Celestial
Mech. Dynam. Astronom. 109 (2011), no. 3, 285–301.
{ Chierchia, Luigi and Pinzari, Gabriella . Properly-degenerate KAM theory (following V. I.
Arnold). Discrete Contin. Dyn. Syst. Ser. S 3 (2010), no. 4, 545–578.
{ Celletti, Alessandra and Pinzari, Gabriella . Dependence on the observational time
intervals and domain of convergence of orbital determination methods. Celestial Mech.
Dynam. Astronom. 95 (2006), no. 1-4, 327–344.
{ Celletti, Alessandra and Pinzari, Gabriella . Four classical methods for determining
planetary elliptic elements: a comparison. Celestial Mech. Dynam. Astronom. 93 (2005),
no. 1-4, 1–52.
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