Silvia Vilariño Fernández

 

Profesora del Centro Universitario de la Defensa

Academia General Militar

Carretera de Huesca, s/n

E-50090 Zaragoza, Spain

Email: silviavf@unizar.es

Phone: +34 976 739 850

 

Docencia/ Teaching

Curso 2015 - 2016. Investigación Operativa

Curso 2014 - 2015. Investigación Operativa.

Curso 2013 - 2014. Estadística.

Curso 2012 - 2013. Estadística.

Curso 2011 - 2012. Estadística.

 

Investigación/ Research

 

Research lines:


Clasical Field Theories

K-symplectic and k-cosymplectic geometry

Symmetries and reduction

Nonholonomic field theories

Lie algebroids

Lie systems

 

Ph.D. Thesis


S. Vilariño. Nuevas aportaciones al estudio de los formalismos k-simpléctico y k-cosympléctico.  Ph.D. dissertation. University of Santiago de Compostela. January 2009. Advisor: Modesto R. Salgado Seco.

 

Biographical overview


Professor at Centro Universitario de la Defensa Zaragoza. AGM. Spain, (september 2011- today)

Professor at University of A Coruña. Department of Mathematics, Spain, (october 2009-august 2011).

Ph.D. Thesis in Mathematics. Department of Geometry and Topology. University of Santiago de Compostela, Spain ( Januay 2009). Advisor: Modesto R. Salgado Seco.

Degree in Mathematics. University of Santiago de Compostela, Spain (2004).

 

List of Publications:


 

Papers in journals:

  1. J. de Lucas, M. Tobolski, S. Vilariño. Geometry of Riccati Equations over normed division algebras. J. Math. Anal. Appl. 2016. In press

  2. L. Búa, I. Bucataru, M. de León, M. Salgado and S. Vilariño. Symmetries in lagrangian field theoryReports on Mathematical Physics, vol. 75, no. 3 (2015), 333-357

  3. J. de Lucas, M. Tobolski and S. Vilariño. A new application of k-symplectic Lie systems International Journal of Geometric Methods in Modern Physics.  Vol 12  (2015) 1550071 (6 pages) doi:10.1142/S0219887815500711.
  4. J.C. Marrero, N. Román-Roy, M. Salgado, S. vilariño. Reduction of polysymplectic manifolds. J. Phys. A.: Math. Theor 48 (2015), 055206 (43pp).  doi:10.1088/1751-8113/48/5/055206 .
  5. J. de Lucas, S. Vilariño. K-symplectic Lie systems: theory and applications. J. Diff. Eq. 258 (6), (2015), pp 2221-2255. doi:10.1016/j.jde.2014.12.005
  6.  M. de León, S. Vilariño. Hamilton-Jacobi theory in k-cosymplectic field theories.   International Journal of Geometric Methods in Modern Physics.  Vol 11, No 1 (2014) 1450007 (18 pages). DOI: 10.1142/S0219887814500078.
  7. N. Román-Roy, M. Salgado, S. Vilariño. Higher order Noether symmetries in k-symplectic Hamiltonian field theory.  International Fall Workship on Geometry and Physics.  International Journal of Geometric Methods in Modern Physics.  Vol 10, No 8 (2013).  1360013 (9 pages)
  8. M. de León, S. Vilariño. Lagrangian submanifolds in k-symplectic settingsMonatsh. Math. 170 (2013), no. 3-4, 381–404.
  9. A. M. Rey, N. Román-Roy, M. Salgado, S. Vilariño. k-cosymplectic classical field theories: Tulckzyjew and Skinner-Rusk formulations. Mathematical Physics, Analysis and Geometry , vol 15, nº 2, (2012), 85-119. DOI 10.1007/s11040-012-9104-z
  10. A. M. Rey, N. Román-Roy, M. Salgado, S. Vilariño. On the k-symplectic, k-cosymplectic and multisymplectic formalisms of classical field theories. JGM, vol 3, no 1, (2011), 112-137.
  11. J.C. Marrero, N. Román-Roy, M. Salgado , S. Vilariño. On a kind of Noether symmetries and conservation laws in k-cosymplectic field theory. J. Math. Phys. 52, no 1, (2011), 20pp.
  12. N. Román-Roy, M. Salgado , S. Vilariño. SOPDES and nonlinear connections. Publ. Math. Debrecen, vol 78, no 2, (2011), 297-316.
  13. M. de León, J.C. Marrero, D. Martín de Diego, M. Salgado,  S. Vilariño.  Hamilton-Jacobi theory in k-symplectic field theories. I.J. Geom. Methods Mod. Phys. Vol 7, no 8, (2010), 1491-1507.
  14. D. Martín de Diego, S. Vilariño. Reduced Classical Field Theories:  K-cosymplectic formalism on Lie algeobroids.  J.Phys. A: Math and Theor. 43 (2010), 32 pp.
  15. M. Muñoz-Lecanda, M.Salgado, S. Vilariño. K-sympectic and k-cosymplectic Lagrangian field theories: some interesting examples and applications. I.J. Geom. Methods Mod. Phys. Vol 7, no 4, (2010), 669-692.
  16. M. de León, D. Martín de Diego, M. Salgado, S. Vilariño.  K-symplectic formalism on Lie algebroids. J. Phys. A: Math and Theor. 42, no 38, (2009), 31 pp.  DOI:10.1088/1751-8113/42/38/385209
  17. M. de León, D. Martín de Diego, M. Salgado, S. Vilariño. Nonholonomic constraints in k-symplectic classical field theories.  I.J. Geom. Methods Mod. Phys. Vol 5, no 5, (2008), 799-830. DOI: 10.1142/S0219887808003077
  18. N. Román-Roy, M. Salgado, S. Vilariño. Symmetries and conservation laws in the Günther k-symplectic formalism of field theory. Rev. Math. Phys. 19, no 10, (2007), 1117-1147. DOI: 10.1142/S0129055X07003188
  19. M. Muñoz-Lecanda, M. Salgado, S. Vilariño. Nonstandard connections in k-cosymplectic field theory. J. Math. Phys. 46, no 12, (2005), 122901, 25 pp. DOI: 10.1063/1.2146191

Conference Proceedings

  1. J. C. Marrero,  N. Román-Roy, M. Salgado, S. Vilariño. Symmetries, Noether’s theorem and reduction in k-cosymplectic field theories. Geometry and Physics: XVIII International Fall Workshop, M. Asorey, J.F. Cariñena, J. Clemente-Gallardo, e. Martínez (eds). AIP Conference Proceedings, Vol 1260 (2010), 173-179 pp.
  2. N. Román-Roy, M. Salgado, S. Vilariño. Lie algebroid formulation of k-cosymplectic field theories. Geometry and Physics: XVII International Fall Workshop, F. Etayo, M. Fioravanti, R. Santamaría (eds), AIP Conference Proceedings, vol 1130 (2009), pp 176-181.
  3. N. Román-Roy, M. Salgado, S. Vilariño. Symmetries in k-symplectic field theories. Geometry and Physics: XVI International Fall Workshop, R.L. Fernandes, R. Picken (eds), AIP Conference Proceedings, vol 1023, (2008), pp 197-201.

Books

  1. M. de León, M. Salgado, S. Vilariño (2015): Methods of Differential Geometry in Classical Field Theories: k-symplectic and k-cosymplectic Approaches. World Scientific. ISBN: 978-981-4699-75-4.
  2. J. Martínez, J. Olmo, M. Rodriguez, S. Vilariño (2012): Introducción a la Estadística: ejercicios y prácticas.  Edita Centro Universitario de la Defensa. ISBN: 978-84-938411-5-7.
  3. Nuevas aportaciones al estudio de los formalismos k-simpléctico y k-cosympléctico. Publ. Dto. Geom. Top. Vol 114, (2009).  ISBN 978-84-89390-31-7. Servizo de Publicacións e Intercambio Científico (electronic), ISBN:  978-84-9887-183-8

Other publications

  1. A. Martínez Calvo, M. Pérez Fernández de Córdoba, S. Vilariño (editors): As matemáticas do veciño. Seminario de Iniciación á Investigación Vol IV,  Instituto de Matemáticas, University of Santiago de Compostela, 2009.
  2. R. M. Crujeiras Casais, P. Fernández Ascariz, M.T. Sánchez Rúa, S. Vilariño (editors): As matemáticas do veciño. Seminario de Iniciación á Investigación Vol III,  Instituto de Matemáticas, University of Santiago de Compostela, 2008.

 

Talks and posters.


Talks at congresses

  1. k-symplectic Lie systems. Lie systems: theory, generalizations, applications. September 22-27, 2014. Warsaw. Poland.
  2. K-symplectic Lie systems: theory and applications. 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications. Special Session Geometric Mechanics. July 7-11, 2014. Madrid. Spain.
  3. Discrete Mechanics and Discrete Field theories. Thematic day on discrete mechanics and geometric integrators. January 30, 2014. Zaragoza Spain.
  4. Hamilton-Jacobi equation in field theory.  III Work days on Geometric Mechanics. La Laguna (Tenerife, Spain). October 2-3, 2013. 
  5. Estructuras k-simplécticas y k-cosimplécticas: teoría y aplicaciones. Encuentro Geometría Diferencial y sus Aplicaciones. Homenaje al prof. Eugenio Merino Gayoso. Ferrol (Spain). June 27-28, 2013.
  6. Reduction of polysymplectic manifolds.  I Meeting Lie systems: theory, generalizations, applications. Warsaw (Poland). May 20-24, 2013.
  7. On the geometry of k-symplectic manifolds and their lagrangian submanifolds. XIV Encuentro de Invierno. Zaragoza. February 6-7, 2012.
  8. k-symplectic manifolds and their Lagrangian submanifolds. VI International Young Researcher Workshop on Geometry, Mechanics and Control. Coimbra, Portugal. January 10-13, 2012.
  9. Polysymplectic structures and Marsden-Weinstein reduction for field theories. ESF Exploratory Workshop on current problems in differential calculus over conmutative algebras, secondary calculus and solution singularities of nonlinear PDEs. Vietri sul Mare, Italy, June, 13-16, 2011.
  10. Geometric Structures in Classical Field Theory. Thematic Day on Classical Field Theory. Zaragoza, Spain, January 28, 2011.
  11. From Classical Field Theory to Mechanics. II Iberoamerican Meeting on Geometry, Mechanics and Control. Bariloche, Argentina, January 10-14, 2011.
  12. Tulczyjew and Skinner-Rusk formulations. V International Young Researcher Workshop on Geometry, Mechanics and Control. La Laguna, Spain, December 7-11, 2010.
  13. Sobre la reducción polisimpléctica a lo Marsden-Weinstein. Encontro de Xeometría 2010. Ferrol, Spain, October 7, 2010.
  14. Polysymplectic manifolds and Marsden-Weinstein reduction. IV International Summer School on Geometry, Mechanics and Control. Santiago de Compostela, Spain, July 5-9, 2010.
  15. Marsden-Weinstein reduction for polysymplectic manifolds. Thematic Day on Geometry structures in Mechanics. Zaragoza, Spain, February 3, 2010.
  16. Field theory on Lie algebroids: k-cosymplectic approach. IV International Young Researchers Workshop on Geometry, Mechanics and Control. Ghent, Belgium, January 11-13, 2010.
  17. k-symplectic formalism on Lie algebroids. III International Young Researchers Workshop on Geometry, Mechanics and Control (Continuous and Discrete Geometric Mechanics). Barcelona, Spain, December 16-18, 2008.
  18. k-symplectic formalism on Lie algebroids. Geometry Meeting 2008. Ferrol, Spain, December 2, 2008.
  19. Formalismo k-symplectico en algebroides de Lie. X Encuentro de Invierno de Geometría, Mecánica y Control. Zaragoza, January 30-31, 2008.
  20. Formalismo k-simpléctico y k-cosimpléctico en teorías clásicas de campos. II Encuentro de Jóvenes Investigadores en Geometría, Mecánica y Control, CSIC. Madrid, Spain, December 18-20, 2007.
  21. Simetrías y leyes de conserva ción en teoría de campos. Encuentro de nuevos métodos geométricos en mecánica y  teoría de campos. Ferrol, Spain, October 1-5, 2007.

Posters at congresses

  1. A new setting of applications of k-symplectic geometry: Lie systems. XXIII International Fall Workshop on Geometry and Physics. Granada, Spain, September 1-6, 2014.
  2. Symmetries, Noether's theorem and reduction in k-cosymplectic field theories. XVIII International Fall Workshop on Geometry and Physics, Centro de Ciencias de Benasque Pedro Pascual, Benasque, Spain, September 6-11, 2009.
  3. Lie-algebroid formulation of k-cosymplectic field theories (poster). XVII International Fall Workshop on Geometry and Physics, CIEM, Castro Urdiales, Spain, September 3-6, 2008.
  4. k-symplectic field thoeries:symmetries and conservation laws (poster). I Iberoamerican Meeting on Geometry, Mechanics and Control. Santiago de Compostela, Spain, June 23-27, 2008.
  5. Symmetries in k-symplectic field theories (poster). XVI International Fall Workshop on Geometry and Physics. Lisbon, Portugal, September 5-8, 2007.

Talks at seminars

  1. Geometric structures and Lie systems: some examples. Seminary Teen on Geometry of the Universitat Politécnica de Catalunya (UPC). Barcelona 10/12/2015.
  2. Differential geometry and Lie systems: what is a k-symplectic Lie system?. Universidad de La Laguna. Spain. June 18, 2015.
  3. Lie systems and geometric structures. Seminar on Geometry of the Universitat Politécnica de Catalunya (UPC). Barcelona, July 18, 2014.
  4. Marsden-Weinstein reduction for polysymplectic manifolds. Seminar on Geometry of the Universitat Politècnica de Catalunya (UPC). Barcelona. April 5, 2013.
  5. Ondas, partículas de jabón, electromagnetismo,... ¿qué tienen en común?. Seminario de investigación del Centro Universitario de la Defensa. Zaragoza, April 26, 2012.
  6. Reducción de Marsden-Weinstein en Teoría Clásica de Campos. Seminario de Física Matemática de la Universidad de Zaragoza. Zaragoza. October 21, 2011.
  7. Teoría de campos k-cosimpléctica: formulaciones de Skinner-Rusk y Tulckzyjew.  Seminario de Geometría de la Universidad de La Laguna.  La Laguna, Tenerife, Spain, October 29, 2010.
  8. Formas y tensores: aplicaciones al electromagnetismo. Seminario de Iniciación a la investigación de la USC. Santiago de Compostela, April 27, 2009.
  9. Métodos geométricos de las teorías clásicas de campos. Seminario de iniciación a la investigación de la USC. Santiago de Compostela. April 2, 2008.
  10. Simetrías y leyes de conservación. Seminario Vidal Abascal. Departamento de Xeometría e Topoloxía de la USC. Santiago de Compostela. March 22, 2007.
  11. Introducción a la geometría k-simpléctica. Seminario de Iniciación a la Investigación de la USC. Santiago de Compostela. November 29, 2005.

 

Links:



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Geometry, Mechanics and Control Network

RSME

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ArXiv.org e-Print Archive

MathSciNet

Zentralblatt Math

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