Luis Felipe Tabera Alonso

Docencia / Teaching

Preprints

• Geometry and algorithms for tropical geometry (in preparation)
  With: F. Santos and T. Theobald
• Tropical discriminants in positive characteristic (submitted)

Research Articles in Refereed Journals

1. Arithmetics and combinatorics of tropical Severi varieties of univariate polynomials
   With:A. Dickenstein, I. Herrero.
   Israel Journal of Mathematics. September 2017, Volume 221, Issue 2, Pages 741-777.
   https://doi.org/10.1007/s11856-017-1573-0
2. A parametric version of the Hilbert-Hurwitz theorem using hypercircles
   Mathematics of Computation. Volume 86, 2017, no. 38, Pages 3001-3018.
   https://doi.org/10.1090/mcom/3202
3. On Tubular vs. Swung surfaces
   With: T. Recio, J.R. Sendra, C. Villarino.
   Journal of Symbolic Computation. Volume 72, January-February 2016, Pages 55-64.
   https://dx.doi.org/10.1016/j.jsc.2014.12.003
4. On real tropical basis and real tropical discriminant
   Collectanea Mathematica. Volume 66, Issue 1, January 2015, Pages 77-92
   https://dx.doi.org/10.1007/s13348-014-0119-6
5. Factoring analytic multivariate polynomials and non-standard Cauchy-Riemann conditions
   With: T. Recio, J.R. Sendra, C. Villarino.
   Mathematics and Computers in Simulation. Volume 104, October 2014, Pages 43-57
   https://dx.doi.org/10.1016/j.matcom.2013.03.013
6. Ultraquadrics associated to affine and projective automorphisms
   With: T. Recio, J.R. Sendra, C. Villarino.
   Applicable Algebra in Engineering, Communication and Computing, Volume 25, Issue 6, December 2014, Pages 431-445
   https://dx.doi.org/10.1007/s00200-014-0236-1
7. Reparametrizing swung surfaces over the reals
   With: C. Andradas, T. Recio, J.R. Sendra, C. Villarino.
   Applicable Algebra in Engineering, Communication and Computing, April 2014, Volume 25, Issue 1-2, pp 39-65
   https://dx.doi.org/10.1007/s00200-014-0215-6
8. Computing Hypercircles by Moving Hyperplanes
   Journal of Symbolic Computation. Volume 50, March 2013, Pages 450-464
   https://dx.doi.org/10.1016/j.jsc.2012.09.001

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9. Singular Tropical Hypersurfaces
   With: A. Dickenstein.
   Discrete & Computational Geometry. Volume 47, Number 2 (2012), 430-453
   https://dx.doi.org/10.1007/s00454-011-9364-6
10. Optimal Affine Reparametrization of Rational Curves
    J. Symbolic Comput. 46(8) (2011), pp. 967-976
    https://dx.doi.org/10.1016/j.jsc.2011.04.001
11. Algorithmic Detection of Hypercircles
    With: J.R. Sendra, T. Recio, C. Villarino.
    Mathematics and Computers in Simulation, Volume 82(1) (2011), pp. 54-67
    https://dx.doi.org/10.1016/j.matcom.2010.07.017
12. Proper Real Reparametrization of Rational Ruled Surfaces
    With: C. Andradas, J.R. Sendra, T. Recio, C. Villarino.
    Computer Aided Geometric Design. Volume 28, Issue 2, February 2011, 102-113
    https://dx.doi.org/10.1016/j.cagd.2010.12.001
13. Tropical Plane Geometric Constructions: a Transfer Technique in Tropical Geometry
    Revista Matemática Iberoamericana, Volume 27, Number 1 (2011), 181-232.
    https://doi.org/10.4171/RMI/633
14. Generalizing Circles over Algebraic Extensions
    With: J.R. Sendra, T. Recio, C. Villarino.
    Mathematics of Computation 79 (2010), 1067-1089.
    https://doi.org/10.1090/S0025-5718-09-02284-4
15. Tropicalization and irreducibility of generalized Vandermonde determinants
    With: C. D'Andrea.
    Proceedings of the American Mathematical Society, 137(11), pp. 3647-3656. 2009
    https://doi.org/10.1090/S0002-9939-09-09951-1
16. On the Simplification of the coefficients of a parametrization
    With: C. Andradas, J.R. Sendra, T. Recio.
    J. Symbolic Comput. 44(2) (2009), pp. 192-210,
    https://dx.doi.org/10.1016/j.jsc.2008.09.001
17. Tropical Resultants for Curves and Stable Intersection
    Revista Matemática Iberoamericana, 24(3) (2008), pp. 941-961
    https://doi.org/10.4171/RMI/561
18. Tropical Constructive Pappus' Theorem
    International Mathematics Research Notices, IMRN 2005:39 (2005) 2373-2389. ISSN 1073-7928
    https://doi.org/10.1155/IMRN.2005.2373

Research Articles in Conference Proceedings

1. Ultraquadrics associated to affine and projective automorphisms
   With: T. Recio, J.R. Sendra, C. Villarino.
   Procceedings del EACA 2014, pp 147-150, Barcelona http://www.ub.edu/eaca2014/program.html
2. On the separation of tropically convex sets
   With: T. Theobald, F. Santos.
   Proceedings of the XIII Encuentro en Álgebra Computacional y Aplicaciones, EACA 2012, pp 167-170, Alcalá de Henares, ISBN 978-84-8138-770-4
3. Superficies regladas racionales reales (Spanish)
   With: C. Andradas, T. Recio, J.R. Sendra, C. Villarino.
   Proceedings of the XII Encuentro en Álgebra Computacional y Aplicaciones, EACA 2010, pp 40-44, Santiago de Compostela, ISBN 978-84-9887-518-8
4. El lugar singular de una hipersuperficie tropical (Spanish)
   With: A. Dickenstein.
   Proceedings of the XII Encuentro en Álgebra Computacional y Aplicaciones, EACA 2010, pp 113-117, Santiago de Compostela, ISBN 978-84-9887-518-8
5. Defining a framework to deduce incidence theorems in tropical geometry
   Proceedings of the seventh International Workshop on Automated Deduction in Geometry, ADG 2008, pp 102-110
6. An Ostrowski-like irreducibility test using tropical geometry
   With: C. D'Andrea.
   Proceedings of the XI encuentro en álgebra computacional y aplicaciones, EACA 2008, pp 61-64
7. Tropical Plane Geometric Constructions
   Electronic Procceedings of MEGA 2007
8. Fast Computation of the Implicit Ideal of a Hypercircle
   With: J.R. Sendra, T. Recio, C. Villarino.
   Procceedings of AGGM 2006, pp 258-265
9. Constructive Proof of Extended Kapranov theorem
   Actas de X Encuentro en Álgebra Computacional y Aplicaciones EACA2006, ISBN: 84-611-2311-5, pp 178-181, http://arxiv.org/abs/0810.4907
10. Computing the Algebraic Counterpart of a Tropical Plane Geometric Construction
    Procceedings in Transgressive Computing 2006, ISBN: 84-689-8381-0, pp 357-364

Other Publications

1. Manual de Hipercirculos (Spanish)
   With: J.R. Sendra, T. Recio, C. Villarino.
   Contribuciones científicas en honor de Mirian Andrés Gómez. Laureano Lambán, Ana Romero y Julio Rubio (Editores), Universidad de La Rioja. Servicio de Publicaciones Logroño, 2010, ISBN 978-84-96487-50-5
2. Software Matemático Libre (Spanish)
   With: M. A. Abanades, J. Escribano, F. Botana.
   La Gaceta de la RSME, Vol 12(2), 2009 pag 325-346

Thesis

• Two Tools in Algebraic Geometry: Construction of Configurations in Tropical Geometry and Hypercircles for the Simplification of Parametric Curves(1.5MB)
  2007, Universidad de Cantabria/Université de Rennes I. In english with an introduction is Spanish and French

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Software

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