Integrable systems and group
Groupoids and Algebroids
· and Differential
Geometry/Mathematical Physics in the large....
My research deals with geometrical and dynamical aspects of singularities.
In particular, I am interested in Hamiltonian systems and their singularities.
I study normal forms and equivariant geometric
problems arising in Symplectic, Contact, and
Poisson manifolds. I am also interested in rigidity problems for group actions
on these manifolds. I also work in geometric quantization of real polarizations.
Some years ago, I started to consider geometrical
problems on b-manifolds (inspired by Melrose
b-calculus on manifolds with boundary). This is a fascinating new subject that
I am working on which lies between the Symplectic and
Poisson worlds. I am lately
trying to understand
possible generalizations of b-manifolds
such as almost regular foliations and E-symplectic manifolds and finding
(unexpected!) applications of b-theory to problems in celestial mechanics.
My research is financed by
the Catalan Institution for Research and Advanced Studies via an ICREA Academia
2016 Prize by the MTM research project
MTM2015-69135-P/FEDER, Geometría y Topología de variedades, álgebra y aplicaciones
(IP: Marta Casanellas and Eva Miranda) based at UPC and by the project EXPLORA
ciencia MTM2015-72876-EXP based at ICMAT-CSIC (Members: Alberto Ibort, Eva
Miranda and Francisco Presas(IP)).
I am in the head of the
Laboratory of Geometry and Dynamical Systems.
My academical trajectory in a glimpse:
1. Ph.D thesis
"On symplectic linearization of singular Lagrangian foliations" at the University of Barcelona
in September 2003.
2. October 2004-May 31, 2007, Marie Curie EIF postdoc at Laboratoire Émile Picard, Université Paul Sabatier.
3. June 1st, 2007 – August 31, 2009, Juan de la Cierva Fellow at the Departament
de Matemàtiques at Universitat
Autònoma de Barcelona.
4. September 2009-August 2013- Professor Lector (Lecturer) at the
Department of Applied Mathematics I, UPC.
5. September 2013-September 2015- Professor Agregat
Interí/Interim Associate Professor at Universitat Politècnica de Catalunya.
6. Currently (since October 2015), Associate Professor (Professor Agregat) at UPC.
Since January 2016, I am principal investigator of the MTM Research project
MTM2015-69135-P, Geometría y Topología de variedades, álgebra y aplicaciones
with 24 members.
8. Since December 2016, I am in
charge of the
Laboratory of Geometry and Dynamical Systems at EPSEB.
9. Since January 2017 and for 5
years I am an ICREA Academia Professor.
Affiliations and memberships:
1. Associate Professor at UPC, member at ICMAT (via Ginzburg
lab) and member of Barcelona Graduate School of Mathematics BGSMath.
2. I am a member of the European Mathematical Society and a member of Societat Catalana de Matemàtiques.
3. Since 2011 I am the corresponding member for the SCM and EMS.
am qualified as Full Professor in the area of Geometry and Topology by AQU
since October 2016.
Since February 2010,
I am qualified as Professeur des
Universités en Section 25 (Mathématiques) by the French CNU (Conseil
des Universités). I was qualified as MCF in February
I am qualified as
Professor agregat by
AQU since 2010.
I am qualified as
Profesor Titular de Universidad since April 2015
Eva Miranda, "On symplectic linearization of
singular Lagrangian foliations" , June, 2003, edicions de la UB, http://www.tdx.cbuc.es/
My research papers
(the versions posted here might differ slightly from the final published
Publications (as author):
On geometric quantization of
b-symplectic manifolds (with V. Guillemin and J. Weitsman),
arXiv:1608.08667, accepted at
Advances in Mathematics, 2018.
The geometry of E-manifolds, (with G. Scott),
quantization of $b^m$-symplectic manifolds,
Guillemin and J. Weitsman),
preprint, 2018, submitted.
Convexity of the moment map image for torus actions on b^m-symplectic
(with V. Guillemin and J. Weitsman),
b^m-Nambu structures of top degree
(with A. Planas), C. R. Math. Acad. Sci. Paris , 2017.
Integrable systems and
closed one forms (with R. Cardona), arXiv:1712.08156, submitted.
Zeroth Poisson homology, foliated cohomology and perfect Poisson manifolds
(with D. Martínez-Torres), to appear at Regular and Chaotic
An invitation to Singular Symplectic Geometry (with R. Braddell,
A. Delshams, C. Oms and A. Planas), arXiv:1705.03846, accepted at
International Journal of Geometric Methods in Modern Physics, 2017.
(with V. Guillemin
and J. Weitsman),
arXiv:1512.05303, accepted at IMRN, International
Mathematics Research Notices.
Rigidity of infinitesimal momentum maps (with
C. Esposito), arXiv:1410.5202, Israel Journal of Mathematics,
Israel J. Math.
219 (2017), no. 2, 757–781.
Cotangent models for integrable
Communications in Mathematical Physics,10.1007/s00220-016-2720-x
Comm. Math. Phys.
350 (2017), no. 3, 1123–1145.
Weakly Hamiltonian actions (with D. Martínez-Torres),http://arxiv.org/abs/1602.03542,
Journal of Geometry and Physics,
J. Geom. Phys.
115 (2017), 131–138.
Examples of integrable and
non-integrable systems on singular symplectic manifolds (with A. Delshams and A. Kiesenhofer),
Journal of Geometry and Physics,
J. Geom. Phys.
115 (2017), 89–97.
Geometric Quantization of
Semitoric Systems and almost toric manifolds (with F. Presas and R. Solha),
preprint 2017, submitted.
surfaces and Nambu structures (with
systems on b-symplectic manifolds (with A. Kiesenhofer),
Regul. Chaotic Dyn.
21 (2016), no. 6, 643–659.
Convexity for Hamiltonian
torus actions on b-symplectic
(with V. Guillemin,
A.Pires, G. Scott) arXiv:1412.2488,
letters, to appear.
A note on
symplectic topology of b-symplectic manifolds (with
P. Frejlich and D. Martinez Torres), preprint
2013, arXiv:1312.7329, accepted at the Journal of Symplectic Geometry.
Action-angle variables and a
KAM theorem for b-Poisson manifolds (with A.
Kiesenhofer and G. Scott) ,
Journal des Mathématiques
Pures et Appliquées,
J. Math. Pures Appl. (9) 105 (2016), no. 1, 66-85.
Geometric Quantization of real
polarizations via sheaves (with F. Presas)
The Journal of Symplectic Geometry (2015) volume 13, number 2, 421-462.
A note on symplectic and
Poisson linearization of semisimple Lie algebra actions,
and Poisson geometry on b-manifolds
Guillemin and A.Pires), Adv. Math. 264 (2014), 864–896.
Toric actions on b-manifolds
(with V. Guillemin, A.Pires and G. Scott),
Int Math Res Notices
(2015) 2015 (14): 5818-5848
Poincaré lemma in Geometric Quantisation (with R. Solha), Journal of Geometric Mechanics,
473 - 491, Volume 5, Issue 4, 2013.
On a Poincaré lemma for
foliations (with R. Solha),
Foliations 2012: pp. 115-137 .
Integrable systems and group
actions, Cent. Eur. J. Math. 12 (2014), no. 2, 240–270.
Coupling symmetries with
Acta Math. Vietnam. 38 (2013), no. 1, 21–32.,
for Hamiltonian actions on Poisson manifolds( with P. Monnier
and N. T. Zung) ,
Adv. Math. 229 (2012), no. 2, 1136–1179.
one symplectic foliations and regular Poisson manifolds (with V. Guillemin and A. Pires),
Braz Math Soc, New Series
From action-angle coordinates to geometric
quantization: a round trip,
Geometric quantization in the non-compact
Action-angle coordinates for integrable systems on Poisson manifolds,
with C. Laurent-Gengoux and P.Vanhaecke,
(for previous version see math.SG arxiv.0805.1679)
(31 pages), Int. Math. Res. Not. IMRN 2011, no. 8,
Geometric quantization of integrable systems with
with M. Hamilton,
Annales de l'Institut Fourier,
vol. 60 (1) p. 51-85, 2010. (36 pages)
and singularities of Hamiltonian systems,
175 012011, 2009.
linearization of semisimple actions, preprint 2008.
for Poisson group actions, Oberwolfach report for the meeting on
Poisson Geometry and its applications, Oberwolfach Report,
Report number, 25, 2007, pages 33—36 (ISSN: 1660-8933), April 2007.
rigidity results for Symplectic and Poisson group actions,
International Workshop on Geometry and Physics,,
Publ. R. Soc. Mat.
R. Soc. Mat. Esp., Madrid, 2007.
note on Equivariant normal forms of Poisson structures,
(with N. T. Zung)
Mathematical Research Letters, vol 13-6, pages 1001-1012, 2006.
normal form theorem for integrable systems on contact manifolds,
Proceedings of the XIII Fall Workshop on Geometry and Physics,
Publ. R. Soc. Mat. Esp., 9, R. Soc. Mat. Esp.,
singular Poincaré Lemma
IMRN International Mathematics Research Notices ,
normal form for nondegenerate singular orbits of integrable Hamiltonian
(with Nguyen Tien Zung)
Sci. Ecole Norm. Sup.,37
(2004), no. 6, 819--839 2004.
linearization of singular Lagrangian foliations
(with C. Curras-Bosch), Differential Geometry and its
(2), 195-205, 2003.
symplectic linearization of singular Lagrangian foliations"
D. thesis, Universitat de Barcelona, June, 2003.
the symplectic classification of singular Lagrangian foliations,
Proceedings of the IX Fall Workshop
on Geometry and Physics (Vilanova i
2000), 239--244, Publ. R. Soc. Mat. Esp.,
3, R. Soc. Mat. Esp.,2001.
- The Hirsch Conjecture has been disproved: an interview with Francisco
Santos, Newsletter of the EMS, "Newsletter
of the European Mathematical Society", 2012, vol. 86, p. 31-37.
de la EMS al Notícies de la SCM, Març 2012, 9-11, 32, (2012).
de la EMS al Noticies de la SCM, Febrer 2013, (2013).
Clay Public Lecture and Conference on the Poincaré Conjecture, Paris, 7-9
June 2010, Eur. Math. Soc. Newsl, issue 77,
pages 21-23, 2010.
Newsletter of the European Mathematical Society. (editor since
Editor of a theme issue for the
of the Royal Society A (editor in 2017).
Editor of a Special Issue for the Journal of Geometry and Physics (deadline
to submit: December 2017).
Guest editor of Special
Issue at Journal
of Geometry and
Physics (deadline to
submit: December 2015).
Guest editor of a Topical Issue on Integrable Systems
at Journal of Geometry and Physics.
Journal of Geometry and Physics Volume 87, Pages 1-496
Finite dimensional integrable systems: on the crossroad of algebra, geometry and physics
Edited by Vladimir Matveev, Eva Miranda, Vladimir Roubtsov,
Sergei Tabashnikov and San Vu Ngoc
Editor of new Special Issue at Journal of Geometry and Physics. More
information available at:
Editor (together with Vladimir Matveev) of a
book in the collection CRM-Advanced Courses (Springer) entitled Geometry
and Dynamics of Integrable systems
Guest editor of a Special issue of Geometriae Dedicata for the conference GESTA 2011. This issue was published in 2013 (volume 1,
issue 265, August).
Guest editor of a Special issue of Acta Mathematica Vietnamica for the conference GEDYTO. This issue has been published in January 2013 (issue
Curras-Bosch i Eva Miranda, Report sobre el llibre
“Symplectic geometry of integrable Hamiltonian systems” ,Notícies de la Societat
Catalana de Matemàtiques, 19, 43-44, 2003.
"La sombra de mi alma
huye por un ocaso de alfabetos,
niebla de libros
Federico García Lorca, excerpt from La Sombra de mi Alma, Libro