Jorge Caravantes' web page

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Research

Research.

Research interests:

  • Algebraic geometry: In particular, low-codimenson projective varieties, grassmannians, applications of formal geometry to projective geometry and syzygies.
  • Computer algebra and geometry: In particular, topology algorithms for algebraic curves and surfaces, fast matrix multiplication and GPS/LPS closed form solutions

Publication list:

  1. J. Caravantes, J.R. Sendra, D. Sevilla, C. Villarino. Sufficient conditions for the surjectivity of radical curve parametrizations, Journal of Algebra, Volume 640, 2024, Pages 129-146, ISSN 0021-8693, https://doi.org/10.1016/j.jalgebra.2023.11.004.
  2. J. Caravantes, G.M. Díaz-Toca, L. Gonzalez-Vega. Avoiding the General Position Condition When Computing the Topology of a Real Algebraic Plane Curve Defined Implicitly. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2023. Lecture Notes in Computer Science, vol 14071. Springer, Cham. https://doi.org/10.1007/978-3-031-38271-0_46
  3. J. Caravantes, J.R. Sendra, D. Sevilla, C. Villarino.  A note about rational surfaces as unions of affine planes. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 117, 69 (2023). https://doi.org/10.1007/s13398-023-01401-1
  4. J. Caravantes, G.M. Diaz–Toca, M. Fioravanti, L. Gonzalez-Vega. Solving the interference problem for ellipses and ellipsoids: New formulae. Journal of Computational and Applied Mathematics, Volume 407, 2022, 114072, DOI: 10.1016/j.cam.2021.114072.
  5. J. Caravantes, G.M. Diaz–Toca, M. Fioravanti, L. Gonzalez-Vega. On the Implicit Equation of Conics and Quadrics Offsets. Mathematics 2021, 9 (15), 1784. DOI: 10.3390/math9151784.
  6. J. Caravantes, S. Pérez-Díaz, J.R. Sendra. A Maple package to deal with the birationality of curves and surfaces parametrizations. Maple in Mathematics Education and Research. 4th Maple Conference, MC 2020, Waterloo, Ontario, Canada, November 2–6, 2020, Revised Selected Papers. Editors: Robert M. Corless, Jürgen Gerhard, Dr. Ilias S. Kotsireas. ISBN: 978-3-030-81697-1. Springer
  7. J. Caravantes, J.R. Sendra, D. Sevilla, C. Villarino . Covering Rational Surfaces with Rational Parametrization Images. Mathematics 2021, 9 (4), 338. DOI: 10.3390/math9040338.
  8. J. Caravantes, J.R. Sendra, D. Sevilla, C. Villarino. Transforming ODEs and PDEs from radical coefficients to rational coefficients. Mediterr. J. Math. 18, 96 (2021). DOI: 10.1007/s00009-021-01703-x
  9. Juan G. Alcázar; Jorge Caravantes; Gema M. Diaz-Toca; Elias Tsigaridas. Computing the topology of a plane or space hyperelliptic curve. Computer Aided Geometric Design 78 (2020) DOI: 10.1016/j.cagd.2020.101830
  10. Jorge Caravantes; Juan Rafael Sendra; Juana Sendra. A Maple Package for the Symbolic Computation of Drazin Inverse Matrices with Multivariate Transcendental Functions Entries. MC 2019: Maple in Mathematics Education and Research: 156-170 (2019) DOI: 10.1007/978-3-030-41258-6_12
  11. Jorge Caravantes; Gema M. Díaz-Toca; Mario Fioravanti; Laureano Gonzalez-Vega. Offsets to conics and quadrics: a new determinantal representation for their implicit equation. ACM Communications in Computer Algebra 52-3: 85-88 (2018) DOI: 10.1145/3313880.3313890
  12. Jorge Caravantes; Laureano Gonzalez-Vega. On the Interference Problem for Ellipsoids: Experiments and Applications. Mathematical Software – ICMS 2018 (LNCS 10931): 89-97 (2018) DOI: 10.1007/978-3-319-96418-8_11
  13. Juan G. Alcázar; Jorge Caravantes; Gema M. Diaz-Toca. The square-freeness of the offset equation to a rational planar curve, computed via resultants. International Journal of Algebra and Computation 28-03: 395-409 (2018) DOI: 10.1142/S0218196718500194
  14. Jorge Caravantes; Juan Rafael Sendra; David Sevilla; Carlos Villarino. On the existence of birational surjective parametrizations of affine surfaces. Journal of Algebra 501: 206-214 (2018) DOI: 10.1016/j.jalgebra.2017.12.028
  15. Jorge Caravantes; Mario Fioravanti; Laureano Gonzalez–Vega; Ioana Necula. An algebraic framework for computing the topology of offsets to rational curves. Computer Aided Geometric Design 52: 28-47 (2017) DOI: 10.1016/j.cagd.2017.03.007
  16. Jorge Caravantes; Laureano Gonzalez-Vega, Alejandro Piñera. Solving positioning problems with minimal data. GPS Solutions Vol.21, Issue 1 (January 2017), pp. 149-161. DOI: 10.1007/s10291-015-0507-8
  17. Jorge Caravantes, Paula Mediavilla, Antonio Tazón, Tomás Fernández, Juan Vassal'lo. New shield structure for retrodirective and invisible applications. Microwave and Optical Technology Letters. Vol. 58, Issue 11 (November 2016), pp. 2570–2577.
  18. Juan G. Alcázar; Jorge Caravantes; Gema M. Diaz-Toca. A new method to compute the singularities of offsets to rational plane curves. Journal of Computational and Applied Mathematics, Vol. 290 (December 2015), pp. 358-402.
  19. Jorge Caravantes; Laureano Gonzalez-Vega; Mariángeles Gomez-Molleda. A canonical form for the continuous piecewise polynomial functions. Journal of Computational and Applied Mathematics, Volume 283, (August 2015), Pages 17–27. Source code in Sage-Python is available here. DOI: 10.1016/j.cam.2014.11.033
  20. Jorge Caravantes; Mario Fioravanti; Laureano Gonzalez–Vega; Ioana Necula. Computing the Topology of an Arrangement of Implicit and Parametric Curves Given by Values. Computer Algebra in Scientific Computing (LNCS 8660), pp 59-73, (2014). DOI: 10.1007/978-3-319-10515-4_5
  21. Jorge Caravantes; Nicolas Perrin. Formal properties in small codimension. Collectanea Mathematica 65 - 2, pp 251-256, (2014). DOI: 10.1007/s13348-013-0095-2
  22. Jorge Caravantes. Bertini-type theorems for formal functions in Grassmannians. Revista Matemática Complutense 25 - 1, pp. 157 - 163,(2012). DOI: 10.1007/s13163-011-0063-x
  23. Jon González-Sánchez; Laureano González-Vega; Alejandro Piñera-Nicolas; Irene Polo-Blanco; Jorge Caravantes; Ignacio F. Rúa. Analyzing group based matrix multiplication algorithms. ISSAC 2009 proceedings, pp 159-166, (2009). DOI: 10.1145/1576702.1576726
  24. Enrique Arrondo; Jorge Caravantes. On The Picard Group of Low-codimension Subvarieties. Indiana University Mathematics Journal. 58-3, pp. 1023-1050, (2009). DOI: 10.1512/iumj.2009.58.3556
  25. Jorge Caravantes; Laureano Gonzalez-Vega. Improving the Topology Computation of an Arrangement of Cubics. Computational Geometry: Theory and Applications. 41-3, pp. 206-218, (2008). DOI: 10.1016/j.comgeo.2008.03.001
  26. Jorge Caravantes; Laureano Gonzalez-Vega. Computing the topology of an arrangement of implicitly defined real algebraic plane curves. Journal of Zhejiang University SCIENCE A. 9-12, pp. 1685-1693, (2008). DOI: 10.1631/jzus.A08GMP01
  27. Jorge Caravantes. Low codimension Fano–Enriques threefolds. Note di Matematica. 28-2, pp. 117-147, (2008). DOI: 10.1285/i15900932v28n2p117
  28. Jorge Caravantes; Laureano Gonzalez-Vega. Diseño Geométrico Asistido por Ordenador: Álgebra, Geometría y Computación. La Gaceta de la RSME. 11 - 1, pp. 109 - 150. Real Sociedad Matemática Española, 2008.
  29. Jorge Caravantes; Laureano Gonzalez-Vega. Computing the Topology of an Arrangement of Quartics. XII Mathematics of Surfaces (LNCS VOL. 4647), pp. 104-120, (2007). DOI: 10.1007/978-3-540-73843-5_7
  30. Jorge Caravantes. Extending divisors from complete intersection surfaces. Le Matematiche. 62-1, pp. 83-93, (2007). DOI:
  31. Jorge Caravantes. Fano threefolds with noncyclic torsion in the divisor class group.arXiv:0706.1958. 2007.

Patents

  • International patent PCT/ES2012/070123: DAISY ANTENNA FOR THE EMISSION AND RECEPTION OF LINEARLY AND CIRCULARLY POLARIZED ELECTROMAGNETIC WAVES, with Juan Llabrés Foyo, Juan Vassal'lo Sanz, Ángel Mediavilla Sánchez y Antonio Tazón Puente (2012).
  • Spanish utility model U201230226: MESA DIGITALIZADORA DE HERBARIO Y BIBLIOTECA, with Juan Vassal'lo Sanz, Andrés de Frutos Gómez y Gisela Oliván Martínez (2012).
  • Spanish patent P201130473: ANTENA MARGARITA PARA EMISION Y RECEPCION DE ONDAS ELECTROMAGNETICAS POLARIZADAS LINEAL Y CIRCULARMENTE, with Juan Llabrés Foyo, Juan Vassal'lo Sanz, Ángel Mediavilla Sánchez y Antonio Tazón Puente (2011).

Software