Páginas personales

  1. Portada
  2. Publications

Publications

Preprints

  1. Stratification of SU(r)-character varieties of twisted Hopf Links, (with A. González-Prieto, J. Martínez, V. Muñoz), arXiv:2303.06218.

Peer-reviewed journals

  1. On character varieties of singular manifolds, (with A. González-Prieto), accepted in Research in the Mathematical Sciences (2023)

  2. Symplectic geometry of a moduli space of framed Higgs bundles, (with I. Biswas and A. Peón-Nieto), IMRN Volume 2021, Issue 8, (2021), 5623–5650.

  3. A lax monoidal Topological Quantum Field Theory for representation varieties, (with A. González- Prieto and V. Muñoz), Bull. Sci. math. 161 (2020) 102871.

  4. Moduli spaces of framed G–Higgs bundles and symplectic geometry, (with I. Biswas and A. Peón- Nieto),  Comm. Math. Phys. 376 (2020), no. 3, 1875–1908.

  5. On Higgs bundles on nodal curves, SIGMA Symmetry Integrability Geom. Methods Appl.15 (2019), 024, 16 pages.

  6. Integrable systems and Torelli theorems for the moduli spaces of parabolic bundles and parabolic Higgs bundles, (with I. Biswas and T. Gómez), Canad. J. Math. 68 (2016), no.3, 504–520.

  7. Bohr–Sommerfeld Lagrangians of moduli spaces of Higgs bundles, (with I. Biswas and N.L. Gammelgaard), J. Geom. Phys. 94, (2015), 179–184.

  8. Hodge polynomials of the SL(2,C)-character variety of an elliptic curve with two marked points (with V. Muñoz), Internat. J. Math. 25 (2014), no. 14, 1450–125.

  9. The topology of parabolic character varieties of free groups, (with I. Biswas, C. Florentino and S. Lawton), Geom. Dedicata 168 (2014), 143–159.

  10. Hodge polynomials of SL(2,C)-character varieties of surfaces of low genus, (with V. Muñoz and P. Newstead), Rev. Mat. Complut., 26 (2013), no.2, 635–703.

  11. Brauer group of moduli spaces of pairs, (with I. Biswas and V. Muñoz), Comm. Algebra 40 (2012), no. 5, 1605–1617.

  12. On the moduli space of Hitchin pairs, (with I. Biswas and P.B. Gothen), Math. Proc. Cambridge Philos. Soc. 151 (2011), no.3, 441–457.

  13. Connection on parabolic vector bundles over curves, (with I. Biswas), Internat. J. Math. 22 (2011), no. 4, 593–602.

  14. Torelli theorem for the moduli space of parabolic Higgs bundles, (with T. Gómez), Adv. Geom. 11 (2011), no. 3, 429-444.

  15. Moduli of parabolic Higgs bundles and Atiyah algebroids, (with J. Martens), J. Reine Angew. Math. 649, (2010), 89–116.

  16. Torelli theorem for the Deligne-Hitchin moduli space, (with I. Biswas, T. Gómez and N. Hoffmann), Comm. Math. Phys. 290 (2009), no. 1, 357–369.

  17. Moduli spaces of parabolic U(p, q)-Higgs bundles, (with O. García-Prada, V. Muñoz), Q. J. Math. 60 (2009), no. 2, 183–233.

  18. Betti numbers of parabolic U(2, 1)-Higgs bundles moduli spaces, Geom. Dedicata 123 (2006), 187— 200.

Peer-reviewed Conference Proceedings/Book chapters

  1. Motive of the representation varieties of torus knots for low rank affine groups, (with A. González-Prieto and V. Muñoz), Analysis, Geometry, Nonlinear Optimization and Applications (E. Pardalos and Th.M. Rassias, eds.), World Scientific Publ. Co., pp. 435-452 (2023).

  2. Representation variety for the rank one affine group, (with A. González-Prieto and V. Muñoz), "Mathematical Analysis in Interdisciplinary Research" (I.N. Parasidis, E. Providas and Th.M. Rassias, eds.), Springer, vol 179, 2021. The accompanying counting script can be obtained here.

  3. Rationality of the moduli space of pairs over a curve, (with I. Biswas and V. Muñoz),Non-linear analysis: Stability, Approximation and Inequalities In honor of Th.M.Rassias in his 60th birthday, Springer Optimization and Its Applications, Vol. 68, (Eds.) Pardalos, Panos M.; Georgiev, Pando G.; Srivastava, Hari M. (2012) ISBN 978-1-4614-3497-9.

Book

  1. ¿Qué sabemos de las geometrías y otras revoluciones? (What do we know about the many geometries and other related revolutionary ideas?) Editorial Catarata: Colección qué sabemos de...? Madrid, 2018.

Scientific Dissemination

  1. Reaparece la tesis de María Wonenburger, la pionera matemática española, que permaneció décadas en el olvido, (with Otto Rutwig Campoamor-Stursberg and Ágata Timón García-Longoria). Ciencia/Materia, El País 14 Junio 2022.
  2. Podem escoltar la forma d’un tambor?, Compàs d'amalgama, Edicions de la Universitat de Barcelona, ISSN 2696-0982, No. 5 (2022), 70-73.
  3. Katherine Johnson, una mente entre las estrellas, Gaceta de la Real Sociedad Matemática Española,  ISSN 1138-8927, Vol. 23, Nº2, 2020,  235-241.
  4. Book Review for the EMS Newsletter “Donaldson Type Invariants for Algebraic Surfaces, Transitions on Moduli Stacks, by Takuro Mochizuki. LNM1972 Springer”, no. 91 March 2014, European Mathematical Society, 57–58.

Education 

  1. Students and teachers using Mentimeter: technological innovation to face the challenges of COVID-19 pandemic and post-pandemic in higher education, (with J. Ignacio Pichardo, Esteban López-Medina, Olga Mancha, Isabel González-Enríquez, Alejandro Hernández-Melián, Maribel Blázquez-Rodríguez, Virginia Jiménez, David Carabantes-Alarcon, Mónica Ramos-Toro, Esther Isorna, Mónica Cornejo-Valle, Oriol Borrás Gené), Educ. Sci. 2021, 11 (11), 667
  2. El uso de Mentimeter para promover la generación colectiva de conocimiento y la participación del alumnado en el aula y en el campus virtual (with J. I. Pichardo Galán, M. I. Blázquez Rodríguez, O. Borras Gené, D. Carabantes Alarcón, M. Cornejo Valle, I. González Enríquez, A. D. Hernández Melián, E. Isorna Alonso, V. Jiménez Rodríguez), to appear in AprendETIC-21
  3. Usando Mentímeter en educación superior: herramienta digital en línea para incentivar y potenciar la adquisición de conomiento de manera lúdica, (with V. Jiménez Rodríguez, M. Blázquez-Rodríguez, J. I. Pichardo Galán, D. Carabantes-Alarcón, O. I. Mancha-Cáceres, O. Borras-Gené, E. F. López-Medina, M. Cornejo-Valle, I. González-Enríquez, E. Isorna Alonso, A. Hernández-Melián, M. Ramos-Toro) Aceptado para publicarse en Ethic@net.

Diversity in Science

  1. Stop discriminación. Evaluación de la aplicación de la Ley 14/2011 de la ciencia en lo referente a la perspectiva de género. Propuestas de mejora. (As member of the Comisión de Mujeres y Matemáticas de la Real Sociedad Matemática Española). DOI: 10.13140/RG.2.2.23521.33124, 2020.
  2. La bandera arcoíris ondea en la puerta de Oxford Ciencia/Materia, El País, 14 Junio 2016.

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