Research
Current
Research Interests:
·
Symplectic Geometry
·
Poisson Geometry
· Integrable systems and group actions
·
Foliation theory
· Geometric quantization
· Groupoids and Algebroids
· Hamiltonian Dynamics
· Fluid Dynamics and Contact Geometry
· and Differential
Geometry/Mathematical Physics in the large....
I am particularly interested in understanding connections between different areas such as Geometry, Dynamical Systems, Mathematical Physics and, more recently, Fluid Dynamics.
My research deals with geometrical and dynamical aspects of singularities. In particular, I am interested in Hamiltonian systems, their singularities and the so-called realm of Hamiltonian Dynamics. 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
Many of the problems that I study are connected to Celestial mechanics in one way or another
The Weinstein conjecture on periodic orbits asserts that the Reeb vector field of a compact contact manifold always have periodic orbits. With my student Cédric Oms we have understood how to construct a counterexample to the Weinstein Conjecture if we allow singularities in the contact form. Those singularities on contact structures model some problems of Beltrami flows on manifolds with boundary (see my recent preprint with my student Robert Cardona and Daniel Peralta Salas).
This counterexample to the Weinstein conjecture is achieved via plugs and is very revealing: The orbits that give the counterexample are indeed periodic orbits which are no longer smooth but have points as marked singularities. This opens a door to a new world.
What's next? ....maybe this.
My research is financed by the Catalan Institution for Research and Advanced Studies via an ICREA Academia 2016 Prize and partially supported by several research projects. I am the principal investigator of the AGAUR SGR research project GEOMVAP with code 2017SGR932 (26 members) and the MTM research project MTM2015-69135-P/FEDER, Geometría y Topología de variedades, álgebra y aplicaciones (together with Marta Casanellas).
From September 2017 until February 2018, I have been a Chaire d'Excellence de la Fondation Sciences Mathématiques de Paris and my work has been supported by a public grant overseen by the French National Research Agency (ANR) as part of the "Investissements d'Avenir" program (reference: ANR-10-LABX-0098). I am also a member of the research project EXPLORA ciencia MTM2015-72876-EXP based at ICMAT-CSIC (Members: Alberto Ibort, Eva Miranda and Francisco Presas(IP)). I am a collaborator of the National Science Foundation project New Avenues in Symplectic Geometry DMS 12/11819 (PI: Jonathan Weitsman).
Since December 2016 I am in the head of the Laboratory of Geometry and Dynamical Systems which I created together with Amadeu Delshams.
Since May 2018 I am the group leader of the UPC research group GEOMVAP (Geometry of varieties and applications).
My academical trajectory in a glimpse:
Ph.D thesis "On symplectic linearization of singular Lagrangian foliations" at the University of Barcelona in September 2003.
October 2004-May 31, 2007, Marie Curie EIF postdoc at Laboratoire Émile Picard, Université Paul Sabatier.
June 1st, 2007 – August 31, 2009, Juan de la Cierva Fellow at the Departament de Matemàtiques at Universitat Autònoma de Barcelona.
September 2009-August 2013- Professor Lector (Lecturer) at the Department of Applied Mathematics I, UPC.
September 2013-September 2015- Professor Agregat Interí/Interim Associate Professor at Universitat Politècnica de Catalunya.
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.
Since December 2016, I am in charge of the Laboratory of Geometry and Dynamical Systems at EPSEB.
Since January 2017 and for 5 years I am an ICREA Academia Professor.
From September 2017 until February 2018, I have been a Chaire d'Excellence de la Fondation Sciences Mathématiques de Paris and my work has been supported by a public grant overseen by the French National Research Agency (ANR) as part of the "Investissements d'Avenir" program (reference: ANR-10-LABX-0098).
I have been selected under the Programa Càtedres-UPC 2017 for promotion to Full Professor.
I am the principal investigator of the AGAUR SGR research project 2017SGR932 (21 members).
Since May 2018 I am the group leader of the UPC research group GEOMVAP (Geometry of varieties and applications).
Since November 2018, Full Professor (Professor Catedrático) at UPC.
Affiliations and memberships:
1. Full Professor at UPC, Chercheur Affilié at Observatoire de Paris, Honorary Doctor Vinculado at ICMAT 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. During the period 2011-2018 I was the corresponding member for the SCM and EMS.
Accreditations:
I 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 2008.
I am qualified as Professor agregat by AQU since 2010.
I am qualified as Profesor Titular de Universidad since April 2015
Distinctions:
Chaire d'Excellence 2017 de la Fondation Sciences Mathématiques de Paris.
Giovanni Prodi Chair at Würzburg 2017-2018 (declined).
Curriculum Vitae
Complete cv in English (last update May 2018)
Publications:
·
My thesis:
Eva Miranda, "On symplectic linearization of
singular Lagrangian foliations" , June, 2003, edicions de
·
My research papers
(the versions posted here might differ slightly from the final published
versions):
Publications (as author):
Universality of Euler flows and flexibility of Reeb embeddings (with R. Cardona, D. Peralta-Salas and F. Presas), preprint, 2019, https://arxiv.org/abs/1911.01963.
Geometric Quantization of almost toric manifolds (with F. Presas and R. Solha), arXiv:1705.06572, Journal of Symplectic Geometry, to appear, J. Symplectic Geom (2019).
Euler flows and singular geometric structures (with R. Cardona and D. Peralta-Salas), https://arxiv.org/abs/1902.00039, Philosophical Transactions of the Royal Society A 2019, DOI 10.1098/rsta.2019.0034.
On the volume elements of a manifold with transverse zeroes (with R. Cardona), https://arxiv.org/abs/1812.03800 accepted for publication in Regular and Chaotic Dynamics, scheduled for Volume 24, Issue 2 of 2019.
Cotangent
models for group actions on
Contact structures with singularities (with C. Oms), https://arxiv.org/abs/1806.05638 (new version available on arxiv containing a study of the singular Reeb dynamics and realization of $b^m$-contact structures. For a talk announcing some of the results this november Look here.).
Open Problems, Questions, and Challenges in Finite-Dimensional integrable systems, (with A. Bolsinov, V. Matveev and S. Tabachnikov), arXiv:1804.03737, Philosophical Transactions of the Royal Society A, 2018.
On geometric quantization of b-symplectic manifolds (with V. Guillemin and J. Weitsman), arXiv:1608.08667, Adv. Math. 331 (2018), 941–951.
Equivariant classification of $b^m$-symplectic surfaces(with A. Planas), https://arxiv.org/abs/1607.01748, to appear at Regular and Chaotic Dynamics, Volume 23, Issue 4 of 2018.
Convexity of the moment map image for torus actions on b^m-symplectic manifolds (with V. Guillemin and J. Weitsman), https://arxiv.org/abs/1801.01097, Philosophical Transactions of the Royal Society A, 2018.
Integrable systems and closed one forms (with R. Cardona), arXiv:1712.08156, J. Geom. Phys. 131 (2018), 204–209.
Singular fibers of the Gelfand--Cetlin system on u(n)* (with D. Bouloc and N.T Zung), arXiv:1803.08332, Philosophical Transactions of the Royal Society A, 2018.
The geometry of E-manifolds, (with G. Scott), arXiv:1802.02959, preprint 2018, submitted.
On geometric quantization of $b^m$-symplectic manifolds, (with V. Guillemin and J. Weitsman), arXiv:1801.03762 preprint, 2018, submitted.
Classification of b^m-Nambu structures of top degree (with A. Planas), C. R. Math. Acad. Sci. Paris 356 (2018), no. 1, 92–96.
Zeroth Poisson homology, foliated cohomology and perfect Poisson manifolds (with D. Martínez-Torres), Regul. Chaotic Dyn. 23 (2018), no. 1, 47–53.
An invitation to Singular Symplectic Geometry (with R. Braddell, A. Delshams, C. Oms and A. Planas), arXiv:1705.03846, Int. J. Geom. Methods Mod. Phys. 16 (2019), suppl. 1, 1940008, 16 pp.
Desingularizing b^m-symplectic structures (with V. Guillemin and J. Weitsman), arXiv:1512.05303, IMRN, International Mathematics Research Notices
Rigidity of infinitesimal momentum maps (with C. Esposito), arXiv:1410.5202, Israel J. Math. 219 (2017), no. 2, 757–781.
Cotangent models for integrable systems (with A. Kiesenhofer), http://arxiv.org/abs/1601.05041 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, J. Geom. Phys. 115 (2017), 131–138.
Non-commutative integrable systems on b-symplectic manifolds (with A. Kiesenhofer), https://arxiv.org/abs/1606.02605, Regul. Chaotic Dyn. 21 (2016), no. 6, 643–659.
Convexity for Hamiltonian torus actions on b-symplectic manifolds (with V. Guillemin, A.Pires, G. Scott) arXiv:1412.2488, Math. Res. Lett. 24 (2017), no. 2, 363–377.
Book (New!):
I am currently working on a book project entitled "Geometry and Dynamics of singular symplectic manifolds" (by invitation of the Societé Mathématique de France jointly with Fondation Sciences Mathématiques de Paris) for the collection Cours Spécialisées of the SMF. By special agreement with FSMP the publication will be made available in open access.
This book aims to be an enhanced and (hopefully) comprehensive version of the course I delivered in October-November-December 2017 at Institut Henri Poincaré during my Chaire d'Excellence de la Fondation Sciences Mathématiques de Paris. The webpages of the course are available here: https://www.sciencesmaths-paris.fr/fr/le-cours-deva-miranda-933.htm https://mat-web.upc.edu/people/eva.miranda/coursIHP.htm
Stay tuned!
Divulgatio:
Media:
Interview at the Newsletter of the EMS, September 2019.
A video promoting the bid ICM2022 for Paris
Publications (as editor):
Book reports:
"La sombra de mi alma
huye por un ocaso de alfabetos,
niebla de libros
y palabras."
Federico García Lorca, excerpt from La Sombra de mi Alma, Libro de Poemas.