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Luis Felipe Tabera Alonso


Dpto. de Matemáticas, Estadística y Computación
Facultad de Ciencias
Avda. Los Castros, s/n.
39005 Santander
Spain
mail: taberalf (at) unican (dot) es
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Last update, November 2013

Forthcomming Events

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Docencia / Teaching

2012-2013 Álgebra Lineal y Discreta
Álgebra Lineal
Procesado Geométrico
Geometría Proyectiva y Algebraica
2011-2012 Álgebra Lineal y Discreta
Álgebra Lineal
Álgebra Avanzada
Álgebra Conmutativa
Composición de documentos con LaTeX
2010-2011 Álgebra lineal y discreta
Álgebra Lineal
Matemáticas III
Álgebra Avanzada
Composición de documentos con LaTeX
Procesado Geométrico
2009-2010 Matemáticas I
Matemáticas III
Álgebra Lineal
Álgebra Avanzada
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Preprints

  • On rational points on hypercircles (submitted)
  • On real tropical basis and real tropical discriminant (submitted)
  • On Tubular vs. Swung surfaces (submitted)
    With: T. Recio, J.R. Sendra, C. Villarino.
  • Geometry and algorithms for tropical geometry (in preparation)
    With: F. Santos and T. Theobald
  • Ultraquadrics associated to affine and projective automorphisms (submitted)
    With: T. Recio, J.R. Sendra, C. Villarino.
  • Tropical discriminants in positive characteristic (submitted)
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Articles

  • Reparametrizing swung surfaces over the reals
    With: C. Andradas, T. Recio, J.R. Sendra, C. Villarino. To appear in Applicable Algebra in Engineering, Communication and Computing
    http://dx.doi.org/10.1007/s00200-014-0215-6
  • Factoring analytic multivariate polynomials and non-standard Cauchy-Riemann conditions
    With: T. Recio, J.R. Sendra, C. Villarino. Mathematics and Computers in Simulation. Available online 1 June 2013
    http://dx.doi.org/10.1016/j.matcom.2013.03.013
  • Computing Hypercircles by Moving Hyperplanes
    Journal of Symbolic Computation. Volume 50, March 2013, Pages 450-464
    http://dx.doi.org/10.1016/j.jsc.2012.09.001
  • Singular Tropical Hypersurfaces
    With: A. Dickenstein. Discrete & Computational Geometry. Volume 47, Number 2 (2012), 430-453
    http://dx.doi.org/10.1007/s00454-011-9364-6
  • Optimal Affine Reparametrization of Rational Curves
    J. Symbolic Comput. 46(8) (2011), pp. 967-976
    http://dx.doi.org/10.1016/j.jsc.2011.04.001
  • Algorithmic Detection of Hypercircles
    With: J.R. Sendra, T. Recio, C. Villarino. Mathematics and Computers in Simulation, Volume 82(1) (2011), pp. 54-67
    http://dx.doi.org/10.1016/j.matcom.2010.07.017
  • 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
    http://dx.doi.org/10.1016/j.cagd.2010.12.001
  • 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
  • Tropical Plane Geometric Constructions: a Transfer Technique in Tropical Geometry
    Revista Matemática Iberoamericana, Volume 27, Number 1 (2011), 181-232.
  • Software Matemático Libre (Spanish)
    With: M. A. Abanades, J. Escribano, F. Botana. La Gaceta de la RSME, Vol 12(2), 2009 pag 325-346
  • Tropicalization and irreducibility of generalized Vandermonde determinants
    With: C. D'Andrea. Proceedings of the American Mathematical Society, 137(11), pp. 3647-3656. 2009
  • Generalizing Circles over Algebraic Extensions
    With: J.R. Sendra, T. Recio, C. Villarino. Mathematics of Computation 79 (2010), 1067-1089.
  • 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,
    http://dx.doi.org/10.1016/j.jsc.2008.09.001
  • Tropical Resultants for Curves and Stable Intersection
    Revista Matemática Iberoamericana, 24(3) (2008), pp. 941-961
  • Tropical Constructive Pappus' Theorem
    International Mathematics Research Notices, IMRN 2005:39 (2005) 2373-2389. ISSN 1073-7928
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Thesis

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Articles in Conference Proceedings

  • 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
  • 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
  • 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
  • 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
  • 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
  • Tropical Plane Geometric Constructions
    Electronic Procceedings of MEGA 2007
  • Fast Computation of the Implicit Ideal of a Hypercircle
    With: J.R. Sendra, T. Recio, C. Villarino. Procceedings of AGGM 2006, pp 258-265
  • 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
  • Computing the Algebraic Counterpart of a Tropical Plane Geometric Construction
    Procceedings in Transgressive Computing 2006, ISBN: 84-689-8381-0, pp 357-364
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Relevant Positions/Visits

2011 Institut Mittag Leffler, (Member of the Algebraic Geometry with a view towards applications program )
2009 Department of Mathematics, UC Berkeley (Postdoctoral researcher)
MSRI (Member of the tropical geometry program)
2008 IMDEA Matemáticas (Postdoctoral researcher in the prospective line in tropical geometry)
2007 Departament d'Àlgebra i Geometria, Universitat de Barcelona (Profesor Ayudante LOU)
2006 TU Kaiserslautern (Predoctoral short visit, 2 months)
2005 Institut Henri Poincaré (Participation in the trimester on real geometry, 3 months)
2003-2004 Université de Rennes I (Predoctoral position in the department of mathematics, 7 months)
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Projects/Grants

2012-2014 Algorithms and Applications in Algebraic Geometry (MTM2011-25816-C02). Main researcher Rafael Sendra, main researcher of subproject Tomas Recio. In this project I contribute studying algorithms for finding optimal parametrizations of rational varieties and several topics in tropical geometry.
2011 Workshop on tropical geometry (MTM2010-12192-E).
2011 Workshop on tropical geometry (2011ADC1005). Gobierno de Cantabria; consejería de educación, cultura y deporte. (Responsable)
2010 International Conference on real geometry, computer algebra and mathematical education (2010ADC0014). Gobierno de Cantabria; consejería de educación, cultura y deporte. (Responsable)
2009-2011 Algorithmic and Combinatorial Tools in Algebraic Geometry and Applications (MTM2008-04699-C03). Main researcher Rafael Sendra, main researcher of subproject Tomas Recio. In this project I contribute studying algorithms for finding optimal parametrizations of rational curves and several topics in tropical geometry.
2006-2012 Desarrollo del programa de actividad investigadora del equipo beneficiario: "MATHEMATICA" (CSD2006-00032)
2006-2007 Acción Integrada Hispano Austriaca. Soluciones de ecuaciones algebraicas y diferenciales. HU2005-0015. Main researcher Luis Narvaez Macarro
2005-2008 Resolución Simbólico Numérica de Problemas para Curvas y Superficies Reales (MTM2005-08690-C02-02). Main researcher Rafael Sendra, main researcher of subproject Tomas Recio. In this project I contribute studying algorithms for finding optimal parametrizations of rational curves and several topics in tropical geometry.
2004-2014 EACA Network, (MTM2004-21958-E, MTM2006-28242-E, MTM2009-06305-E and MTM2011-13133-E).
2003-2006 Real Algebraic and Analytic Geometry (HPRN-CT2001-00271). Main researcher Niels Schwartz.

Software

I enjoy using the Sage Computer math system. I am orgaizing a conference about the use of Sage in education together with F. Botana (U. Vigo) and M. Abanades (CES Felipe II Aranjuez). I contribute as a developerof the Sage library and have written a module on Hypercircles and reparametrization algorithms for Sage. Take a look at the Documentation!
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Previous Conferences

I have helped in the organization of the following conferences:
2012 III Jornada Sage/Python at the University of Vigo.
2011 I co-organized the tropical geometry workshop that took place at the CIEM.
2010 Real Geometry, Computer Algebra and Math Education (Recio 60)that took place at the CIEM.
2009 I helped with the organization of the Effective Methods in Algebraic Geometry , MEGA 2009 (webpage), that took place in U. Barcelona
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