Research

Degrees:

• Graduate in Physics: Faculty of Physics, University of Barcelona (UB), 1979.
• Ph D in Physics: UB, 1986

My research begun in 1981 in the field of mathematical physics, under the supervision of Prof. Joaquim Gomis Torné,
at the then-called Department of Theoretical Physics,
now the Quantum Physics and Astrophysics, of the UB.

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My research interest is differential geometry and its applications to mathematical physics. In particular:

• Geometry of Classical Field Theories and applications.
• Geometric Mechanics (regular and singular systems, and dissipative systems).
• Symplectic, multisymplectic, and contact geometry and applications.
• Geometric Quantization.
• Geometric structures of ordinary and partial differential equations.
• Geometric Control Theory.

In 1992, with other colleagues, we became the research group on
Differential Geometry, Dynamical Systems, and Applications.
which is integrated in the UPC research group
Geometry of Manifolds and Applications (GEOMVAP) (Geometría de Variedades y Aplicaciones)
and in the
Geometry Mechanics and Control Network.
 

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Research Projects

1. Title: Geometría, Física, Control y Aplicaciones (GeFiCoA).
   Code: PGC2018-098265-B-C33 (Coordinated Project: PGC2018-098265-B).
   Supported by: Ministerio de Ciencia, Innovación y Universidades (Spain).
   Duration: 2019-2021.
   Main reseacher: Narciso Román-Roy. (Coordinated Project: Eduardo Martínez Fernández (UZ)).


2. Title: Aspectos Geométricos en Mecánica, Control, Teoría de Campos y Gravitación (MeCoTeG).
   Code: MTM2014-54855-P.
   Supported by: Ministerio de Economía y Competitividad (Spain).
   Duration: 2015-2019.
   Main reseacher: Narciso Román-Roy.


3. Title: Geometría de Sistemas Físicos y de Control y Aplicaciones (GeSFiCoA).
   Code: MTM2011-22585.
   Supported by: Ministerio de Ciencia e Innovación.
   Duration: 2012-2014.
   Main reseacher: Narciso Román-Roy.


4. Title: Algoritmos de Ligaduras y Reducción en Sistemas Dinámicos, Física y Control (AgeRSiFiC).
   Code: MTM2008-00689.
   Supported by: Ministerio de Ciencia e Innovación (Spain).
   Duration: 2009-2012.
   Main reseacher: Narciso Román-Roy.


5. Title: Geometría y Control: Aplicaciones a la Física y la Tecnología (GeCoAFT).
   Code: MTM2005-04947.
   Supported by: Ministerio de Educación y Ciencia (Spain).
   Duration: 2006-2008.
   Main reseacher: Narciso Román-Roy.


6. Title: Principios Variacionales, Control Óptimo y Aplicaciones (PVCoA).
   Code: BFM2002-03493.
   Supported by: Ministerio de Ciencia y Tecnología (Spain).
   Duration: 2002-2005.
   Main reseacher: Narciso Román-Roy.


7. Title: Seminario Conjunto sobre Técnicas Geométricas en Teoría de Control.
   Code: AFC 2001-0431-CO.
   Supported by: Ministerio de Educación, Cultura y Deporte (Spain).
   Duration: 2002.
   Main reseacher: Miguel C. Muñoz Lecanda (UPC).


8. Title: Sistemas no Holónomos y Control.
   Code: CICYT PB98-0920.
   Supported by: Ministerio de Ciencia y Tecnología (Spain).
   Duration: 1999-2001.
   Main reseacher: Miguel C. Muñoz Lecanda (UPC).


9. Title: Control no Lineal de un Bus Energético.
   Code: CICYT TAP97-0969-C03-01.
   Supported by: Ministerio de Ciencia y Tecnología (Spain).
   Duration: 1997-1999.
   Main reseacher: Enric Fossas Colet (UPC).


10. Title: Técnicas Geométricas en Control no Lineal.
    Code: CICYT TAP94-0552-C03-02.
    Supported by: Ministerio de Ciencia y Tecnología (Spain).
    Duration: 1994-1996.
    Main reseacher: Jordi Riera Colomer (UPC).


11. Title: Temas de la Teoría de las Partículas y los Campos.
    Code: CAICYT AE 86-0016.
    Supported by: Ministerio de Universidades e Investigación (Spain).
    Duration: 1985-1986.
    Main reseacher: Rolf Tarrach (UB).


12. Title: Temas de Física Teórica.
    Code: CAICYT AE 86-0016.
    Supported by: Ministerio de Universidades e Investigación (Spain).
    Duration: 1983-1984.
    Main reseacher: Pedro Pascual de Sans (UB).


13. Title: Geometria de Varietats i Aplicacions (GEOMVAP) (Geometry of Manifolds and Applications).
    Code: 2017 SGR 932.
    Supported by: Dep. d'Innovació, Universitats i Empresa (Generalitat de Catalunya).
    Duration: 2018-2021.
    Reseach Coordinator: Eva Miranda Galcerán (UPC).


14. Title: Geometria de Varietats i Aplicacions (GEOMVAP) (Geometry of Manifolds and Applications).
    Code: 2014 SGR 634.
    Supported by: Dep. d'Innovació, Universitats i Empresa (Generalitat de Catalunya).
    Duration: 2014-2018.
    Reseach Coordinator: María Alberich Carramiñana (UPC).


15. Title: Geometria Diferencial, Sistemes Dinamics i Aplicacions.
    Code: 2009 SGR 1338.
    Supported by: Dep. d'Innovació, Universitats i Empresa (Generalitat de Catalunya).
    Duration: 2009-2014.
    Reseach Coordinator: Miguel C. Muñoz Lecanda (UPC).


16. Title:Red Temática Geometry, Mechanics and Control.
    Codes: MTM2005-24556-E / MTM2006-27467-E / MTM2007-30168-E / MTM2008-03606- E / MTM2009-08166-E / MTM2010-12116-E / MTM2011-15725-E.
    Supported by: Ministerio de Educación y Ciencia (Spain).
    Duration: 2006-2013.
    Main reseachers: Juan Carlos Marrero González, Edith Padrón Fernández (U. La Laguna).


17. Title: Grups Precompetitius.
    Code: PRE 89/18.
    Supported by: Universitat Politécnica de Catalunya.
    Duration: 1990-1992.
    Main reseacher: Miguel C. Muñoz Lecanda (UPC).

 

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Direction of Ph. D. Thesis and Master Thesis

Ph. D. THESIS:

1. Xavier Rivas Guijarro.
   Geometrical aspects of k-presymplectic and k-precosymplectic classical field theories.
   Ph. D. in Applied Mathematics; FME (2021).
   (Co-directed with Xavier Gràcia Sabaté).
   
   
2. Jordi Gaset Rifa.
   A Multisymplectic Approach to Gravitational Theories.
   Ph. D. in Applied Mathematics; FME (2018).
   
   
3. Pedro Daniel Prieto Martínez.
   Geometrical Structures of Higher-order Dynamical Systems and Field Theories.
   Ph. D. in Applied Mathematics; FME (2011, under way).
   

MASTER THESIS:

1. Arnoldo Guerra IV.
   The Covariant Constraint Analysis of Field Theories in the Multisymplectic Formalism.
   Master of Astrophysics, Particle Physics and Cosmology;; Fac. Física, UB (2021).
   (Co-directed with Joaquim Gomis Torné).
   
   
2. David Adame Carrillo.
   The second-order problem for singular Lagrangian field theories in the k- presymplectic formulation.
   Master of Science in Advanced Mathematics and Mathematical Engineering (MAMME); FME (2020).
   
   
3. Xavier Rivas Guijarro.
   Constraint algorithm for singular k-cosymplectic field theories.
   Master of Science in Advanced Mathematics and Mathematical Engineering (MAMME); FME (2015).
   (Co-directed with Xavier Gràcia Sabaté).
   
   
4. Pedro Daniel Prieto Martínez.
   Estudi de les estructures geomètriques dels sistemes dinàmics d'ordre superior.
   Master of Science in Advanced Mathematics and Mathematical Engineering (MAMME); FME (2011).
   
   
5. Mónica Aymerich Valls.
   Lagrangian Lie algebroids of the canonical symplectic Lie algebroid.
   Master of Science in Advanced Mathematics and Mathematical Engineering (MAMME); FME (2011).
   (Co-directed with Juan Carlos Marrero González).

 

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Organization of scientific meetings and workshops

1. Geometry of Mechanics, Field Theory and Control: A workshop celebrating the 65th birthday of M.C. Muñoz Lecanda
   Department of Applied Mathematics IV, FME, Universitat Politècnica de Catalunya. Barcelona (Spain). December 2011.


2. III International Summer School on Geometry, Mechanics, and Control.
   Department of Applied Mathematics IV. Ametlla de Mar (Spain). June 2009.


3. La mujer: elemento innovador en la ciencia.
   Department of Applied Mathematics IV. Barcelona (Spain). Barcelona (Spain). December 2007.


4. I Encuentro Mujeres y Matemáticas.
   University of Santiago de Compostela. Santiago de Compostela (Spain). October 2005.


5. XIX International Workshop on Differential Geometric Methods in Theoretical Mechanics.
   (Organization of the session on Reduction).
   S. Banach International Mathematical Center. Bedlewo (Poland). August 2004.


6. IV Winter Meeting: Seminar on geometric techniques in Control theory.
   Department of Applied Mathematics IV. Barcelona (Spain). February 2002.


7. XVI International Workshop on Differential Geometric Methods in Theoretical Mechanics.
   (Organization of the session on Geometry of the Quantum-Classical transition).
   S. Banach International Mathematical Center. Bedlewo (Poland). August 2001.


8. IX Fall Workshop on Geometry and Physics.
   Department of Applied Mathematics IV. Vilanova i la Geltrú (Spain). July 2000.
   


9. II Fall Workshop on Differential Geometry and its Applications.
   Department of Applied Mathematics and Telematics. Barcelona (Spain). June 1993.

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(Unpublished) Communications and Seminars

1. "Higher-order contact mechanics: Lagrangian, Hamiltonian and unified formalism".
   Geometry, Mechanics and Control Seminar 2021.
   ICMAT. Online Seminar. (2021).


2. "The k-contact formalism in field theories with disipation".
   Geometry, Mechanics and Control Theory.
   Dept. Física Teórica (U. Zaragoza). (2019).


3. "Some aspects of the multisymplectic approach to gravitational theories".
   Congreso Bienal de la Real Sociedad Matemática Española 2017 (Special session on Recent Advances on Geometry, Mechanics and Control).
   Fac. Física (U. Zaragoza). (2017).


4. "Sobre Simetrías y Constantes del Movimiento en Sistemas Hamiltonianos".
   Encuentro Geometría Diferencial y sus Aplicaciones (Homenaje al Prof. Eugenio Merino Gayoso).
   (U. La Coruña). (2013).


5. "Hamilton-Jacobi Theory: Geometric approach and Classical approach".
   III Work Days in Geometric Mechanics.
   (U. La Laguna). (2013).


6. "Simetrías y leyes de conservación en sistemas hamiltonianos".
   Seminario Vidal Abascal.
   Department of Geometry and Topology (USC). (2010).


7. "Simetrías de sistemas hamiltonianos en teoría de campos".
   Department of Fundamental Mathematics (ULL). (2009).


8. "Constraint algorithm for k-presymplectic singular field theories".
   Geometry Meeting 2008.
   Escola Politècnica Superior (UAC). (2008).


9. "Algunas reflexiones sobre el formalismo k-simpléctico en teoría de campos".
   Jornadas de Geometía y Mecánica.
   Department of Fundamental Mathematics (ULL). (2008).


10. "k-symplectic field theories: Symmetries and conservation laws".i>
    (II Iberoamerican Meeting on Geometry, Mechanics and Control).
    Department of Geometry and Topology (USC). (2008).


11. "Formalismos lagrangiano y hamiltoniano multisimpléctico de las teorías de campos".
    (Primer Congreso Conjunto de Matemáticas RSME-SCM-SEIO-SEMA).
    Faculty of Mathematics (UV). (2005).


12. "Formulación multisimpléctica de las teorías de campos lagrangianas y hamiltonianas".
    VII Reunión de Invierno: Mecánica Geométrica y Teoría de Campos.
    Department of Theoretical Physics (UZ). (2005).


13. "Sistemas hamiltonianos en teoría de campos multisimpléctica".
    Jornadas de Geometía y Mecánica.
    Department of Fundamental Mathematics (ULL). (2004).


14. "Sistemas dinámicos singulares".
    FME (UPC). (2002).


15. "Una formulación del operador K en teoría clásica de campos".
    III Encuentro de Invierno: Mecánica Geométrica y Teoría de Control.
    Department of Theoretical Physics (UZ). (2001).


16. "Fibrados de multimomentos y transformación de Legendre en teoría de campos".
    Seminario de Geométria Simpléctica y Física Matemática.
    Department of Theoretical Physics (UZ). (1999).


17. "Ecuaciones lagrangianas de la teoría de campos en términos de campos multivectoriales".
    Seminario sobre Geometría Diferencial, Sistemas Dinámicos y Aplicaciones.
    Department of Applied Mathematics and Telematics (UPC). (1999).


18. "Construcción de sistemas hamiltonianos en teoría de campos".
    Seminario sobre Geometría Diferencial, Sistemas Dinámicos y Aplicaciones.
    Department of Applied Mathematics and Telematics (UPC). (1999).


19. "Sistemas dinámicos descritos por lagrangianas".
    Department of Theoretical Physics (UZ). (1992).


20. "El operador de evolución temporal".
    I Workshop de Otoño: Geometría Diferencial y sus Aplicaciones.
    CSIC - UCM. (1991).


21. "Formulación presimpléctica de sistemas con ligaduras".
    "Transformaciones canónicas para sistemas presimplécticos".
    II Jornadas de Mecánica y Física Matemática.
    Universidad Internacional Menéndez y Pelayo. (1984).

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Other activities

• Member of the Editorial board of the journal:
  International Journal of Geometric Methods in Modern Physics (IJGMMP) (Until 2018).


• Referee for the journals:
  Advances in Mathematical Physics,
  Classical and Quantum Gravity,
  General Relativity and Gravitation,
  Georgian Mathematical Journal,
  International Electronic Journal of Geometry,
  International Journal of Geometric Methods in Modern Physics,
  Journal of Geometric Mechanics,
  Journal of Physics A: Mathematics and Theoretical,
  Mediterranean Journal of Mathematics,
  Physics Letters A,
  Physica Scripta,
  SIAM Journal of Control and Optimization,
  Symmetry, Integrability and Geometry: Methods and Applicationa (SIGMA),
  
  
• Referee for the agencies:
  Agencia Nacional de Evaluación y Prospectiva. (ANEP).
  Agéncia de Gestió d'Ajuts Universitaris i de Recerca. (AGAUR).
  Axencia para a Calidade do Sistema Universitario de Galicia. (ACSUG).
  programa ACADEMIA de la Agencia Nacional de la Evaluación de la Calidad y Acreditación. (ANECA).
  
  
• Reviewer of:
  Mathematical Reviews (American Mathematical Society) (see reviews),
  Zentralblatt MATH Database (European Mathematical Society) (see reviews).
  

 

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