Research

Research

See my publications

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
  • Mathematical Physics in the large

Summary

I am particularly interested in understanding connections between different areas such as Geometry, Dynamical Systems, Mathematical Physics and, more recently, Fluid Dynamics.

Singularities

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 Melrose b-calculus). Their symplectic reincarnations are called b-symplectic manifolds which appear to model several problems in Celestial Mechanics. 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. I also like localization theorems, equivariant cohomology and I am a recent fan of Floer homology and the study of periodic orbits which I am trying to understand in connection to problems in Celestial Mechanics such as the three-body problem. 3 body problem

Periodic orbits

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 the Weinstein Conjecture if we allow singularities in the contact form. In particular under compactness assumptions on the critical set we have been able to prove the existence of infinite periodic orbits on the critical set for 3-dimensional b^m-contact structure. This has led us to formulate the singular Weinstein conjecture about existence of singular periodic orbits on b^m-contact manifolds. Those singularities on contact structures model some problems of Beltrami flows on manifolds with boundary. This variant of the Weinstein conjecture is very revealing: The singular orbits are indeed periodic orbits which are no longer smooth but have points as marked singularities. This opens a door to a new world. In the direction of the singular Weinstein conjecture we are now trying to prove that the set of b^m-contact structures admitting singular Reeb orbits is generic in the set of b^m-contact forms. So far we could prove the existence of escape orbits and generalized singular periodic orbits in a number of cases where genericity occurs in the class of Melrose contact forms. Solar system

Fluid Dynamics: Universality of Euler flows, h-principle for contact geometry and Turing completeness in dimension 3

I have been recently interested in Fluid Dynamics where I entered driven by singularity theory. With Daniel Peralta Salas and Robert Cardona, we had been working on b-contact forms appearing in Fluid Dynamics using the correspondence between contact forms and Beltrami vector fields (see our paper on Phylosophical Transactions of the Royal Society below). In Febrary 17, 2019 I came across this entry (thank you Twitter!) in the blog of Terry Tao. This was a source of inspiration to work on h-principles for Reeb embeddings and proving universality properties of Euler flows and Turing completeness of Euler flows. This is the content of our paper arXiv:1911.01963. Just for the New Year's Eve of 2020 we finished our article on constructing Turing complete Euler flows in dimension 3, closing up an open problem since the 90's by Moore and also Tao recently. You can read it here: arXiv:2012.12828. More is to come! Stay tuned! Flow around a wing

Published papers

  1. Integrable systems on singular symplectic manifolds: From local to Global
    R. Cardona and E. Miranda
    IMRN
    [arXiv: 2007.10314]

  2. Looking at Euler flows through a contact mirror: Universality and undecidability
    R. Cardona, E. Miranda and D. Peralta-Salas
    Submitted.
    [arXiv: 2107.09471]

  3. The singular Weinstein Conjecture
    E. Miranda and C. Oms
    Advances in Mathematics,, Volume 389,2021,107925, ISSN 0001-8708, https://doi.org/10.1016/j.aim.2021.107925. (https://www.sciencedirect.com/science/article/pii/S0001870821003649) (want to know more? Check here: https://youtu.be/qwEuYuIPUJo )
    [arXiv: 2005.09568]

  4. Turing universality of the incompressible Euler equations and a conjecture of Moore
    R. Cardona, E. Miranda and D. Peralta-Salas
    To appear in IMRN
    [arXiv: 210404356]

  5. Constructing Turing complete Euler flows in dimension 3
    R. Cardona, E.Miranda, D. Peralta-Salas, F. Presas
    Proceedings of the National Academy of Sciences May 2021, 118 (19) e2026818118
    [arXiv: 2012.12828]

  6. The geometry of E-manifolds
    E. Miranda and G. Scott
    Rev. Mat. Iberoam. 37 (2021), no 3, 1207--1224
    [arXiv: 1802.02959]

  7. Geometric Quantization via cotangent models
    P. Mir and E. Miranda
    Anal.Math.Phys. 11, 118 (2021).
    [arXiv: 2102.02699]

  8. On the singular Weinstein conjecture and the existence of escape orbits for b-Beltrami vector fields
    E.Miranda, C. Oms and D. Peralta-Salas
    To appear in Contemporary Mathematics
    [arXiv: 2010.00564]

  9. b-Structures on Lie groups and Poisson reduction
    R. Bradel, A. Kiesenhofer and E. Miranda
    Submitted.
    [arXiv: 2010.04770]

  10. Rigidity of cotangent lifts and integrable systems
    E. Miranda and P. Mir
    The Journal of Geometry and Physics https://www.sciencedirect.com/science/article/pii/S0393044020301698
    [arXiv: 2006.12477]

  11. The geometry and topology if contact structures with singularities
    E. Miranda and C. Oms
    Submitted.
    [arXiv: 1806.05638]

  12. Reeb embeddings and Universality of Euler flows
    R. Cardona, E. Miranda, D. Peralta-Salas and F. Presas
    Submitted.
    [arXiv: 1911.01963]

  13. Euler flows and singular geometric structures
    R. Cardona, E. Miranda and D. Peralta-Salas
    Philos. Trans. Roy. Soc. A 377 (2019), no. 2158, 20190034, 15 pp.
    [arXiv: 1902.00039]

  14. On the volume elements of a manifold with transverse zeroes
    R. Cardona and E. Miranda
    Regul. Chaotic Dyn. 24 (2019), no. 2, 187–197.
    [arXiv: 1812.03800]

  15. A b-symplectic slice theorem
    R. Braddell, A. Kiesenhofer and E. Miranda
    Submitted.
    [arXiv: 1811.11894]

  16. Contact structures with singularities
    E. Miranda and C. Oms
    Submitted.
    [arXiv: 1806.05638]

  17. Open Problems, Questions, and Challenges in Finite-Dimensional integrable systems
    A. Bolsinov, V. Matveev, E. Miranda and S. Tabachnikov
    Philos. Trans. Roy. Soc. A 376 (2018), no. 2131, 20170430, 40 pp.
    [arXiv: 1804.03737]

  18. On geometric quantization of b-symplectic manifolds
    V. Guillemin, E. Miranda and J. Weitsman
    Adv. Math. 331 (2018), 941–951
    [arXiv: 1608.08667]

  19. Equivariant classification of b^m-symplectic surfaces
    E. Miranda and A. Planas
    Regular and Chaotic Dynamics.23, 355–371(2018)
    [arXiv: 1607.01748 ]

  20. Convexity of the moment map image for torus actions on b^m-symplectic manifolds
    V. Guillemin, E. Miranda and J. Weitsman
    Philos. Trans. Roy. Soc. A 376 (2018), no. 2131, 20170420, 6 pp.
    [arXiv: 1801.01097]

  21. Integrable systems and closed one forms
    R. Cardona and E. Miranda
    J. Geom. Phys. 131 (2018), 204–209
    [arXiv: 1712.08156]

  22. Singular fibers of the Gelfand--Cetlin system on $u(n)^*$
    D. Bouloc, E. Miranda and N.T Zung
    Philos. Trans. Roy. Soc. A 376 (2018), no. 2131, 20170423, 28 pp.
    [arXiv: 1803.08332]

  23. On geometric quantization of b^m-symplectic manifolds
    V. Guillemin, E.Miranda and J. Weitsman
    Submitted.
    [arXiv: 1801.03762]

  24. Classification of b^m-Nambu structures of top degree
    E. Miranda and A. Planas
    C. R. Math. Acad. Sci. Paris. 356 (2018), no. 1, 92–96
    [arXiv: 160701748]

  25. Zeroth Poisson homology, foliated cohomology and perfect Poisson manifolds
    D. Martínez-Torres and E. Miranda
    Regul. Chaotic Dyn. 23 (2018), no. 1, 47–53
    [arXiv: 170901176]

  26. An invitation to Singular Symplectic Geometry
    R. Braddell, A. Delshams, E. Miranda, C. Oms and A. Planas
    Int. J. Geom. Methods Mod. Phys. 16 (2019), suppl. 1, 1940008, 16 pp
    [arXiv: 1705.03846]

  27. Desingularizing b^m-symplectic structures
    V. Guillemin, E. Miranda and J. Weitsman
    Int. Math. Res. Not. IMRN 2019, no. 10, 2981–2998.
    [arXiv: 1512.05303]

  28. Rigidity of infinitesimal momentum maps
    C. Esposito and E. Miranda
    Israel J. Math. 219 (2017), no. 2, 757–781.
    [arXiv: 1410.5202]

  29. Cotangent models for integrable systems
    A. Kiesenhofer and E. Miranda
    Communications in Mathematical Physics. 350 (2017), no. 3, 1123–1145
    [arXiv: 1601.05041]

  30. Weakly Hamiltonian actions
    D. Martínez-Torres and E. Miranda
    J. Geom. Phys. 115 (2017), 131–138
    [arXiv: 1602.03542]

  31. Examples of integrable and non-integrable systems on singular symplectic manifolds
    A. Delshams, A. Kiesenhofer and E. Miranda
    Journal of Geometry and Physics. 115 (2017), 89–97
    [arXiv: 1512.08293 ]

  32. Geometric Quantization of Semitoric Systems and almost toric manifolds
    E. Miranda, F. Presas and R. Solha
    To appear in Journal of Symplectic Geometry
    [arXiv: 1705.06572]

  33. Non-commutative integrable systems on b-symplectic manifolds
    A. Kiesenhofer and E. Miranda
    Regul. Chaotic Dyn. 21 (2016), no. 6, 643–659
    [arXiv: 1606.02605]

  34. Convexity for Hamiltonian torus actions on b-symplectic manifolds
    V. Guillemin, E, Miranda, A.Pires and G. Scott
    Math. Res. Lett. 24 (2017), no. 2, 363–377
    [arXiv: 1412.2488]

  35. A note on symplectic topology of b-symplectic manifolds
    P. Frejlich, D. Martinez Torres and E. Miranda
    J. Symplectic Geom. 15 (2017), no. 3, 719–739
    [arXiv: 1312.7329]

  36. Action-angle variables and a KAM theorem for b-Poisson manifolds
    A. Kiesenhofer, E. Miranda and G. Scott
    J. Math. Pures Appl. 105 (2016), no. 1, 66-85
    [arXiv: 1502.03489]

  37. Geometric Quantization of real polarizations via sheaves
    E. Miranda and F. Presas
    J. Symplectic Geom. 13 (2015), no. 2, 421–462
    [arXiv: 1301.2551 ]

  38. A note on symplectic and Poisson linearization of semisimple Lie algebra actions
    E. Miranda
    undefined
    [arXiv: 1503.03840 ]

  39. Symplectic and Poisson geometry on b-manifolds
    V. Guillemin, E. Miranda and A. R. Pires
    Adv. Math. 264 (2014), 864–896
    [arXiv: 1206.2020]

  40. Toric actions on b-symplectic manifolds
    V. Guillemin, E. Miranda, A. R. Pires and G. Scott
    Int. Math. Res. Not. IMRN. 2015, no. 14, 5818–5848
    [arXiv: 1309.1897]

  41. A Poincaré lemma in Geometric Quantisation
    E. Miranda and R. Solha
    J. Geom. Mech. 5 (2013), no. 4, 473–491
    [arXiv: 1307.3275]

  42. On a Poincaré lemma for foliations
    E. Miranda and R. Solha
    Foliations 2012, pp. 115-137 (2013)
    [arXiv: 1301.5819]

  43. Integrable systems and group actions
    E. Miranda
    Central European Journal of Mathematics. 12 (2014), no 2, 240-270

  44. Coupling symmetries with Poisson structures
    C. Laurent-Gengoux, E. Miranda
    Acta Mathematica Vietnamica. 38 (2013), no 1, 21–32
    [arXiv: 1301.1329]

  45. Rigidity for Hamiltonian actions on Poisson manifolds
    E. Miranda, P. Monnier, N. T. Zung
    Advances in Mathematics. 229 (2012), no. 2, 1136–1179
    [arXiv: 1102.0175]

  46. Codimension one symplectic foliations and regular Poisson manifolds
    V. Guillemin, E. Miranda, A. R. Pires
    Bulletin of the Brazilian Mathematical Society, New Series. 42(4), 603-623, 2011
    [arXiv: 1009.1175]

  47. From action-angle coordinates to geometric quantization: a round trip
    E. Miranda
    Oberwolfach Report, Geometric Quantization in the non-compact setting. 1107 (2011)

  48. Action-angle coordinates for integrable systems on Poisson manifolds
    C. Laurent-Gengoux, E. Miranda, P. Vanhaecke
    IMRN International Mathematics Research Notices. 2011, no. 8, 1839–1869
    [arXiv: 0805.1679]

  49. Geometric quantization of integrable systems with hyperbolic singularities
    M. Hamilton, E. Miranda
    Annales de l'Institut de Fourier. vol 60 (1) p. 51-85, 2010
    [arXiv: 0808.0338]

  50. Symmetries and singularities of Hamiltonian systems
    E. Miranda
    Journal of Physics: Conference Series. vol 175 (2009), 1

  51. Symplectic linearization of semisimple actions
    E. Miranda
    Preprint

  52. Rigidity for Poisson group actions
    E. Miranda
    Oberwolfach Report. Report number, 25, 2007, pages 33—36 (ISSN: 1660-8933), April 2007

  53. Some rigidity results for Symplectic and Poisson group actions
    E. Miranda
    XV International Workshop on Geometry and Physics, 177-183, Publ. R. Soc. Mat. Esp., 11, R. Soc. Mat. Esp., Madrid, 2007.

  54. A note on Equivariant normal forms of Poisson structures
    E. Miranda, N. T. Zung
    Math. Res. Lett. 13 (2006), no. 5-6, 1001–1012.
    [arXiv: math/0510523]

  55. A normal form theorem for integrable systems on contact manifolds
    E. Miranda
    Publicaciones RSME

  56. A singular Poincaré Lemma
    E. Miranda, S. Vu Ngoc
    IMRN International Mathematics Research Notices. 10.1155/IMRN.2005.27
    [arXiv: math/0405430]

  57. Equivariant normal form for nondegenerate singular orbits of integrable Hamiltonian systems
    E. Miranda, N. T. Zung
    Ann. Sci. Ecole Norm. Sup.,37 (2004), no. 6, 819--839 2004.
    [arXiv: math/0302287]

  58. Symplectic linearization of singular Lagrangian foliations
    C. Curras-Bosch, E. Miranda
    Differential Geometry and its applications, 18, (2), 195-205, 2003.

  59. On symplectic linearization of singular Lagrangian foliations
    E. Miranda
    Ph. D. thesis, Universitat de Barcelona, June, 2003. published as a book under ISBN: 9788469412374 (all rights protected)

  60. On the symplectic classification of singular Lagrangian foliations
    E. Miranda
    Proceedings of the IX Fall Workshop on Geometry and Physics (Vilanova i la Geltrú, 2000), 239--244, Publ. R. Soc. Mat. Esp., 3, R. Soc. Mat. Esp., 2001.


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ResearchTeam

My Research Team

I am the group leader of the research group in Geometry at UPC, GEOMVAP. I am also the director of the Laboratory of Geometry and Dynamical Systems.

My research team

GEOMVAP

The Geometry, Topology, Algebra, and Applications Group (GEOMVAP) is a group of researchers with interests in a wide range of fields, which include algebraic, differential and symplectic geometries, algebraic topology, commutative algebra and their applications. The group is composed of researchers rooted or formed at the Universitat Politècnica de Catalunya.

Our group works on topological and differentiable manifolds, algebraic varieties, and their applications, viewing problems from a variety of different perspectives. The group has a long tradition working on various different interfaces of algebra, geometry and topology. In the last decade we have become active contributors in interdisciplinary science and we are now focused on both a theoretical point of view and the transversal applications to several disciplines including Robotics, Machine Learning, Physics and Celestial Mechanics. Our research can be grouped in 8 different research lines which are closely related and interact in a dynamic manner. The 4 first lines are theoretical and the 4 last ones are interdisciplinary.

  • AGE: Algebraic Geometry.
  • CAN: Commutative Algebra and Number theory.
  • TOP: New Challenges in Algebraic Topology.
  • SYM: New trends in Differential Geometry, Symplectic Geometry and Geometric Mechanics.
  • BIO: Applications to Biology
  • ROB: Applications to Control Theory, Machine Learning and Robotics
  • CEL: Applications to Dynamical Systems and Celestial Mechanics
  • PHY: Applications to Physics
GEOMVAP in action
The Lab of Geometry and Dynamical systems

The Laboratory of Geometry and Dynamical Systems at UPC-EPSEB promotes the collaboration between Geometers and Dynamicists interested in common problems from different perspectives and with complementary techniques. The lab focuses on questions which are on the crossroads of Symplectic Geometry and Dynamical Systems.

The lab consists currently of 2 Full Professors, 1 Associate Professor, 2 postdocs, 7 Ph.D. students, 1 visiting PhD students, 1 master student.

Supervision

Current Ph.D. students
  • Alessandro Tamai (Msc. Trieste)
    Symmetries and singularities in the Beltrami-contact mirror.
    Funding: applying (to start in September 2021)
    • Pau Mir (Msc. UPC)
      Singularities and symmetries on the crossroads of Symplectic geometry and Physics.
      Funding: La Caixa Retaining Grants
    • Joaquim Brugués (Msc. UPC)
      On Floer Homology of Poisson manifolds. Co-supervision with Sonja Hohloch (University of Antwerp).
      Funding: FI-AGAUR
    • Anastasia Matveeva (Msc. Higher School of Economics, Moscow)
      Poisson structures on moduli spaces and group actions.
      Funding: InPHinit La Caixa
Former Ph.D. students
  • Robert Cardona (Msc. UPC)
    Contact topology and Reeb dynamics with applications to ideal fluids.
    Funding: FPI - MdM - BGSMath Next position: Postdoc in Strasbourg
  • Cédric Oms (Msc. ULB)
    Global Hamiltonian Dynamics of singular symplectic manifolds, October 2, 2020.
    Currently, postdoc under my supervision funded with my ICREA Academia project. Next position: Postdoc at ENS-Lyon
  • R. D. Braddell (Msc. Padova-Bordeaux)
    New geometrical and dynamical techniques for problems in Celestial Mechanics. Co-supervision with Amadeu Delshams.
    Funded with my ICREA research project. Defended on Feb 17, 2021. Currently postdoc at BCAM.
  • Arnau Planas (Msc. UPC)
    Symmetries and singularities of Poisson manifolds, September 2020. Currently, Senior Data Scientist at Caixabank Business Intelligence.
  • Anna Kiesenhofer
    Integrable systems on b-Poisson structures (2016)
    Currently postdoc at EPFL (also known for her Gold medal in Cyclism in Tolyo 2021).
  • Romero Solha
    Geometric Quantization of Integrable systems with singularities (2013)
    Currently postdoc at UPV
Postdoc supervision

Collaborators

Collaborators (other than former or current PhD students)
  • Alexey Bolsinov
  • Carlos Curras
  • Chiara Esposito
  • Pedro Frejlich
  • Victor Guillemin
  • Mark Hamilton
  • Camille Laurent-Gengoux
  • David Martínez Torres
  • Vladimir Matveev
  • Philippe Monnier
  • Ryszard Nest
  • Daniel Peralta-Salas
  • Sergei Tabachnikov
  • Nguyen Tien Zung
  • Ana Rita Pires
  • Fran Presas
  • Nicolai Reshetikhin
  • Geoffrey Scott
  • Pol Vanhaecke
  • Vu Ngoc San
  • Jonathan Weitsman

My research networks

Along my academical trajectory I have been proactive in the creation of laboratories and research networks such as the Viktor Ginzburg Lab, the European Network CAST or the forthcoming Institute of Mathematics at the UPC-IMTECH. I am currently actively implied with the following research institutes, organizations and nodes:
Schedule

Schedule

Organized conferences (this list is not updated)

  • Workshop on Geometric methods in Symplectic Topology ICMAT.
  • Workshop on Women in Geometry and Topology ICMAT.
  • FDIS2017 CRM.
  • FDIS2017 CRM.
  • FDIS2017 CRM.
  • JISD2017 CRM.
  • GESTA2016.
  • JuniorGESTA.
  • Geometry and Dynamics of Foliations ICMAT.
  • GESTA 2014 ICMAT.
  • Symplectic Techniques of Dynamical Systems ICMAT.
  • Qdays in Barcelona CRM.
  • Conference on Integrability, Topological obstructions to Integrability and interplay with Geometry CRM.
  • GESTA 2013 Toulouse.
  • Advanced Course on Geometry and Dynamics of Integrable Systems CRM.
  • Research Programme on Geometry and Dynamics of Integrable Systems CRM.
  • CAST conference ICMAT.
  • GESTA 2011 UPC.
  • GEDYTO Hanoi.
  • Conference in honour of Paulette Libermannn IHP.
  • Geometric flows and equivariant problems in Symplectic Geometry CRM.
  • GESTA 2008 UAB.
  • GAP VI, Geometry and Physics VI CIM-CRM.
  • Conference on Moment Maps .
  • Weeken(oïd) Géométrie de Poisson Toulouse.
  • GESTA 2006 Toulouse.
  • Geometry of Integrable Hamiltonian Systems at CRM, Barcelona 2001. CRM.

Organized seminars

  • Organizer of 23 workshops and 2 Research programmes at CRM-Barcelona.
  • Former organizer, with Jaume Amorós, of the Teen Seminar on geometry.
  • Organizer of the regular one day intensive seminar HIS (Hamiltonian Intensive Seminar).
  • Former organizer of the special Seminar on Symplectic and Poisson Geometry in Barcelona.
boards

Boards

Governing Boards

  • Personnalité extérieure of the Conseil d'administration (Board of Directors) of the IHP-Institut Henri Poincaré (2020-).
  • Member at the Governing Board of the BGSMath (2018-).

Scientific Boards

  • Member of the Scientific advisory board of the Centre de Recerca Matemàtica (2017-).
  • Member of the Scientific advisory board of the RSME (2021-).
  • Member of the Scientific committee of the Poisson 2018 events.
  • Member of the Scientific Committee of the FDIS conferences (2015-).

Editorial Boards

CV

CV

Distinctions

  • Chaire d'Excellence 2017 de la Fondation des Sciences Mathématiques de Paris.
  • ICREA Academia 2016 Professor.
  • Giovanni Prodi Chair at Würzburg 2017-2018 (declined).
  • Invited address at 8ECM.

Active grants

  • Co-Principal investigator of the Maria de Maeztu program CEX2020-001084-M (Principal Investigator: Marcel Guardia, Center of Award: Centre de Recerca Matemàtica): Total amount: 2M euros for 5 years (date of award July 2021).
  • Principal investigator of an ICREA Academia Project: Total amount: 200000 euros (Start date January 2017, duration of the grant 5 years).
  • Principal investigator of an AEI project Geometría, Álgebra, Topología y Aplicaciones Multidisciplinares code PID2019-103849GB-I00: Total amount:160.809,00 € .
  • Principal investigator of an SGR Research project 2017SGR932: 65898 euros 2017-2019 (total number of members 21).
  • Principal investigator of the project Geometría, Álgebra, Topología y Aplicaciones Multidisciplinares GATA-Tech with code PID2019-103849GB-I00 , total number of participants: 30. Total funding: 160.809,00 €. Start date June 2020 end date May 2024.
  • Principal investigator of the project MTM2015-69135-P, total number of participants: 24. Total funding: 182.226,00 €. Start date January 2016 end date December 2020.
  • Principal investigator for an AFR-Ph.D. project 2016-2019, Total amount: 160.901,19 euros.

Affiliations and memberships

Additional services for the mathematical community

  • Referee for a list of journals including among others: Acta Mathematica, Archive for Rational Mechanics and Analysis, Nonlinearity, Annales de l’Institut Fourier, Journal of the London Mathematical Society, Ergodic Theory and Dynamical Systems, Discrete & Continuous Dynamical Systems, Journal of Geometry and Physics, Journal of Mathematical Physics, Journal of Symplectic Geometry, Quaterly Journal of Mathematics, Journal of Regular and Chaotic Dynamics, Revista Matemática Complutense, Differential Geometry and its applications, Acta Mathematica Applicandae, AIP Publications, Birkhauser Advanced CRM courses.
  • Research expert for several (inter)national research agencies including DFG, ANEP, AEI, ANR, NWO.
Teaching

Teaching

Supervision

Current Ph.D. students
  • Alessandro Tamai (Msc. Trieste)
    Equivariant singular contact geometry and applications to Fluid dynamics and celestial mechanics.
    Funding: applying (to start in September)
    • Pau Mir (Msc. UPC)
      Singularities and symmetries on the crossroads of Symplectic geometry and Physics.
      Funding: La Caixa Retaining Inphinit grants
    • Joaquim Brugués (Msc. UPC)
      On Floer Homology of Poisson manifolds. Co-supervision with Sonja Hohloch (University of Antwerp).
      Funding: FI-AGAUR
    • Anastasia Matveeva (Msc. Higher School of Economics, Moscow)
      Poisson structures on moduli spaces and group actions.
      Funding: InPHinit La Caixa
Former Ph.D. students
  • Robert Cardona (Msc. UPC)
    Contact topology and Reeb dynamics with applications to ideal fluids.
    Funding: FPI - MdM - BGSMath, next, moving to Strasbourg as postdoc.
  • Roisin Braddell (Msc. Padova-Bordeaux)
    New geometrical and dynamical techniques for problems in Celestial Mechanics. Co-supervision with Amadeu Delshams.
    Funded with my ICREA research project, Current situation: BCAM postdoc.
  • Cédric Oms
    Global Hamiltonian Dynamics of singular symplectic manifolds, October 2, 2020.
    Currently, postdoc under my supervision funded with my ICREA Academia project. Next, postdoc at ENS Lyon.
  • Arnau Planas
    Symmetries and singularities of Poisson manifolds, September 2020. Currently, Senior Data Scientist at Caixabank Business Intelligence.
  • Anna Kiesenhofer
  • Anna Kiesenhofer
    Integrable systems on b-Poisson structures (2016)
    Currently postdoc at EPFL also known for her gold medal in cyclism in Tokyo.
  • Romero Solha
    Geometric Quantization of Integrable systems with singularities (2013)
    Currently postdoc at Universidad del Pais Vasco.
Postdoc supervision
Master and undergraduate supervision
  • Pablo Nicolás
    Undergraduate thesis (joint with Kolya Reshetikhin) On the spin Calogero-Moser systems and b-Symplectic Geometry (2021)
  • Pau Mir
    Master thesis: Rigidity of group actions, cotangent lifts and integrable systems (2020)
  • Joaquim Brugués
    Master thesis: Morse and Floer Homology (2019)
  • Robert Cardona
    Master thesis: Integrable Systems on Folded Symplectic manifolds (2018)
  • Robert Cardona
    Undergraduate thesis: Symplectic Toric manifolds, Delzant theorem and applications (2017)
  • Arnau Planas
    Master thesis: Symplectic surfaces with singularities (2015)
  • Alexander Thiele
    Master thesis: Transversality, old and new (2014)

New proposals for supervision

For more details about each work and some additional proposals, please, visit the intranet.
Master thesis proposals
  • Classical and Quantum integrable systems: Can we hear the shape of a drum?
  • Geometry and Physics of semitoric and almost toric manifolds
  • Quantization, symmetries and singularities in interaction
  • The mathematics of Maryam Mirzakhani
  • Vortex equations and celestial mechanics
  • The quest of periodic orbits: From Seifert to Conley and Weinstein
  • Locally conformally symplectic manifolds and Celestial Mechanics
Undergraduate thesis proposals
  • Els grups de Lie i les seves accions
  • Del teorema del punt fix de Lefschetz al teorema de Poincaré-Hopf
  • Formes diferencials i foliacions de codimensió 1
  • Les equacions de Hamilton, els grups de Lie i la geometria simplèctica
  • Teoria de Morse
  • Projecte Hévea: Construint tors plans a R^3
  • Projecte Hévea: Contruint esferes reduïdes

Teaching

2020-2021
  • Smooth manifolds (UPC), Master Course. The videos of this course are on ATENEA.
2019-2020
  • Smooth manifolds (UPC), Master Course With the total fun of teaching during confinement I opened a youtube channel. Check it out here: https://www.youtube.com/channel/UC8Fzyf58s0EiZ-gdYgz2ghw?view_as=subscriber
2018-2019
  • Smooth manifolds (UPC), Master Course
2017-2018
  • Geometry and Dynamics of Singular Symplectic manifolds (IHP)
  • Smooth manifolds (UPC), Master Course
2016-2017
  • Fonaments Matemàtics d’Enginyeria de l’Edificació a Arquitectura Tècnica (UPC)
  • Master Course on Differentiable manifolds (UPC)
  • Fonaments Matemàtics d’Enginyeria de l’Edificació a Arquitectura Tècnica (UPC)
  • Geometria Diferencial al Grau de Matemàtiques (UPC)
2015-2016
  • Fonaments Matemàtics d’Enginyeria de l’Edificació a Arquitectura Tècnica (UPC)
  • Fonaments Matemàtics d’Enginyeria de l’Edificació a Arquitectura Tècnica (UPC)
  • Geometria Diferencial al Grau de Matemàtiques (UPC)
  • Symplectic Techniques in Dynamical Systems and Mathematical Physics (BGSMath)
2012-2013
  • Fonaments Matemàtics d'Enginyeria de l'Edificació (UPC)
  • Topologia al Grau de Matemàtiques (UPC)
  • Geometria Diferencial al Grau de Matemàtiques (UPC)
2011-2012
  • Fonaments Matemàtics d'Enginyeria de l'Edificació (UPC)
  • Topologia al grau en Matemàtiques (UPC)
  • Geometria Diferencial al grau en Matemàtiques (UPC)
2010-2011
  • Fonaments Matemàtics d'Enginyeria de l'Edificació (UPC)
  • Estadística Aplicada d'Enginyeria de l'Edificació (UPC)
  • Topologia al grau en Matemàtiques (UPC)
2009-2010
  • Fonaments Matemàtics d'Enginyeria de l'Edificació (UPC)
  • Estadística Aplicada d'Enginyeria de l'Edificació (UPC)
  • Topologia al grau en Matemàtiques (UPC)
2008-2009
  • Geometria Diferencial (UAB)
2007-2008
  • Geometria Riemanniana (UAB)
  • Algebra Lineal (UAB)
2005-2006
  • Geometria Diferencial (UB)
  • Introducció a l `algebra i la Geometria (UB)
2003-2004
  • Curs de doctorat: Geometria Simplèctica (UB)
  • Geometria Diferencial (UB)
  • Geometria Proyectiva (UB)
  • Grups i Algebres de Lie (UB)
2002-2003
  • Geometria Proyectiva (UB)
  • Geometria Diferencial (UB)
  • Grups i Algebres de Lie (UB)
2001-2002
  • Geometria Proyectiva (UB)
  • Geometria Diferencial (UB)
  • Geometria Diferencial (UB)
  • Grups i Algebres de Lie (UB)
  • Algebra Lineal (UB)
  • Càlcul Infinitesimal (UPC)
2000-2001
  • Grups i Algebres de Lie (UB)
  • Introducció a l´Algebra i la geometria (UB)
  • Geometria Diferencial (UB)
  • Fonaments Matemàtics I (UPC)
1999-2000
  • Grups i Algebres de Lie (UB)
  • Algebra Lineal (UB)
  • Geometria Diferencial (UB)
  • Geometria Diferencial de Corbes i Superficies (UB)
  • Fonaments Matemàtics I (UPC)
  • Algebra Lineal (UPC)
  • Càlcul (UPC)
1998-1999
  • Grups i Algebres de Lie (UB)
  • Geometria Diferencial (UB)
  • Geometria Diferencial de Corbes i Superficies (UB)
  • Algebra Lineal (UdL)
  • Matemàtiques I (UdL)
1997-1998
  • Geometria Lineal (UB)
  • Geometria Diferencial de Corbes i Superficies (UB)
  • Algebra Lineal (UB)
  • Càlcul i Algebra II (UB)
  • Algebra Lineal (UdL)
  • Ampliació d´Anàlisi Matemàtic (UdL)
1996-1997
  • Algebra Lineal (UB)
  • Algebra Lineal (UB)
  • Càlcul i Algebra II (UB)
Outreach

Outreach

Media

  1. Où vas-tu, petit canard ? Une question indécidable ! Pour la Science, Juillet 2021.
  2. . Four mathematicians demonstrate it is impossible to predict where 29,000 rubber ducks in the sea will wash up El País, June 2021.
  3. Cuatro matemáticos demuestran que era imposible predecir el destino de 29.000 patitos de goma en el mar. El País, May 2021.
  4. Matemáticos demuestran la indecibilidad de ciertos fenómenos de hidrodinámica La Vanguardia, May 2021..
  5. Més enllà de la teoria del caos: mai es podrà saber on va l'ampolla amb el missatgeNotícies de TV3.
  6. Científicos españoles diseñan la primera máquina de Turing de agua El mundo, Mayo 2021.
  7. Soluciones para un fluido capaz de simular cualquier máquina de Turing Clarín, Mayo 2021.
  8. Soluciones para un fluido capaz de simular cualquier máquina de Turing Europa Press, Mayo 2021.
  9. Interview at El ABCdario de las matemáticas. April, 2017. ABC.
  10. Interview at La Mirada. April 22, 2019. Canal Sur.

    11. Interviews and talks

    1. Interview by the CNRS. May 12, 2020. The webpage of CNRS (9 pages of interview).
    2. Interview at the Newsletter of the European Mathematical Society. ABC.
    3. Interview by the FSMP to promote the bid for ICMA2022 for Paris. ABC.
    4. Viajando en el tiempo con las matemáticas. Pint of science.

    Dissemination articles at El País

    1. Anna Kiesenhofer: del infinito al oro olímpico. Agosto 2021 El País.
    2. La matemática de los fenómenos que se repiten. 9 de Noviembre de 2018. El País.
    3. La matemática ucraniana que podría haber ganado la medalla fields. 14 de Agosto de 2018. El País.
    4. En recuerdo a Maryam Mirzakhani, la exploradora de Superfícies. July 14, 2018. El Pais.

    Other outreach writings

    1. Dones en Xarxa, Efecto Matilda, Dones en Xarxa.
    2. Entrevista a Sílvia Casacuberta. Boletin de la RSME 576, 2018.
    3. El efecto Matilda. Boletin de la RSME.
    4. Faces of Women in mathematics. Boletin de la RSME, 573, 2018.
    5. Congresos y charlas plenarias. Boletin de la RSME.
    6. Maryam Mirzakhani, una luz que nunca se apagará. Boletín de la RSME. 544, 2017.
    7. The Clay Public Lecture and Conference on the Poincaré Conjecture. News EMS Eur. Math. Soc. Newsl, issue 77, pages 21-23, 2010.
    8. Columna de la EMS al Noticies de la SCM, Febrer 2013, (2013).
    9. Columna de la EMS al Notícies de la SCM, Març 2012, 9-11, 32, (2012).
    10. Columnes de la EMS al Noticies de la SCM 2011-2017.
    11. Maryam Mirzakhani, una llum que mai no s’apagará. SCM notícies.
    12. The Hirsch Conjecture has been disproved: an interview with Francisco Santos. Newsletter of the EMS 2012, vol. 86, p. 31-37.

    Gender Equality and Human Rights

    1. Participation in the Round Table "Mesa redonda con investigadoras" at BCNSpiracy, October 2018, CaixaForum, Barcelona.
    2. Organization of Dia internacional de la Dona i la Nena en la Ciencia, February 14 2019, iec.
    3. Participation at the round table Matemàtica i Dones: les barreres socials i les acadèmiques, organized by BGSMath and SCM, February 14th 2019.
    4. Participation at the round table STEAM-MAT-mat-es-ella Barcelona, Universidad de Barcelona, April 2019.
    5. Participation in the Panel "Human Rights" at International Conference of Mathematical Physics, ICMP, 2021, Geneva, August 6..