My current research interest is Tropical Algebra and Geometry.

See my research
papers (most of them on arXiv) regarding tropical issues:

- (with J. Linde) Matrices commuting with a given normal tropical matrix, Linear Algebra Appl., 482 (2015), 101-121, ArXiv 1209:0660, MR 3365268, DOI 10.1016/j.laa.2015.04.032
- Distances on the tropical line determined by two points, Kybernetika, 50, n. 3, (2014), 408-435, ArXiv 1310.0174, MR 3245538
- On tropical Kleene star matrices and alcoved polytopes, Kybernetika, 49, n.6, (2013), 897-910, ArXiv 1210.1735, MR 3182647
- (with A. Jiménez) Characterizing the
convexity of the n-dimensional tropical simplex and the six
convex classes in R^3, (2011) ArXiv
1205.4162

- (with E. Lorenzo) An algorithm to
solve any tropical linear system A x=B x, Linear
Algebra Appl., 435, n.4, (2011), 884--901; MR 2807241

- Tropical linear maps on the plane, Linear Algebra Appl., 435, n.7, (2011), 1681--1710; doi:10.1016/j.laa.2010.07.031 (2010), MR2810666 (2012i:14075)
- (with M. Ansola) Tropical conics for the layman, in Tropical and Idempotent Mathematics, in G.L. Litvinov and S. N. Sergeev (eds.), Contemp. Math. 495 (2009) 87-101, MR2581514 (2011c:14160)
- (with M. Ansola)
A note on tropical triangles in the plane, Acta Math.
Sinica, Engl. series, v. 25, n. 11, (2009) 1775-1786, MR
2564942 (2010j:52078)

Here is a pdf of my talk
on Matrices commuting with a given normal tropical
matrix, given at Skolkovo, near Moscow, in August 2015.

*I have taken part in
Seminar on History of Mathematics, in Facultad de
Matemáticas, UCM, in 2013-2014 and 2014-2015. My
talks were Historia
del Álgebra Lineal and Historia de las Curvas*
(talk
1 and talk
2). (All of them in Spanish)

- Matrices de rotaciones, simetrías y roto-simetrías in A mathematical tribute to Professor José María Montesinos Amilibia, ISBN 978-84-608-1684-3, (2016), 559-564.
- Cómo obtener curvas con formas predeterminadas a partir de circunferencias Boletín Sociedad Puig--Adam, 85, (2010), 12--24, ArXiv 1307.7431
- Real plane algebraic curves.
*Expo. Math.*20 (2002), no. 4, 291--314. 14P05,**MR1940009****(2003h:14088)** - Multiplicidad de intersección y
resultantes. (Spanish)
*Mathematical contributions: volume in honor of Professor Enrique Outerelo Domínguez,*333--348, Homen. Univ. Complut.,*Editorial Complutense, Madrid,*2004. 14H50 (13P99),**MR2212975****(2006k:14052)** - Curvas algebraicas reales planas. (Spanish)
*Mathematical contributions: volume in honor of Joaquín Arregui Fernández,*249--263, Homen. Univ. Complut.,*Editorial Complutense, Madrid,*2000. 14P05, MR 1803907 - (with M.
Coste) Atypical
values at infinity of a polynomial function on the real
plane: an erratum, and an algorithmic criterion.
*J. Pure Appl. Algebra*162 (2001), n. 1, 23--35. 14P25 (14P20 26C99),**MR1844807**(2002f:14078) - (with J.
Ferrera) The asymptotic
values of a polynomial function on the real plane.
*J. Pure Appl. Algebra*106 (1996), n. 3, 263--273. 26C99 (14P99),**MR1298760****(95j:14076)** - (with J.
Ferrera)
Level curves of open polynomial functions
on the real plane.
*Comm. Algebra*22 (1994), n. 14, 5973--5981. 14P25 (26C05),**MR1298760****(95j:14076)** - A complex version of the Baer-Krull
theorems.
*Comm. Algebra*28 (2000), n. 8, 3727--3737. 12J15 (12J10 12L12),**MR1767584**(2001i:12010) - The complex spectrum of a ring.
*Real algebraic geometry and ordered structures (Baton Rouge, LA, 1996),*235--249, Contemp. Math., 253,*Amer. Math. Soc., Providence, RI,*2000. 13J30 (12D15),**MR1747588****(2001f:13039)** - Specializations and a local
homeomorphism theorem for real Riemann surfaces of rings.
*Pacific J. Math.*176 (1996), n. 2, 427--442. 14P10 (12D15),**MR1435000****(98b:14044)** - The compatible valuation rings of the
coordinate ring of the real plane.
*Recent advances in real algebraic geometry and quadratic forms (Berkeley, CA, 1990/1991; San Francisco, CA, 1991),*231--242, Contemp. Math., 155,*Amer. Math. Soc., Providence, RI,*1994. 13F30 (13A18),**MR1260710****(94k:13029)**

Prior to getting interested in Tropical Mathematics,
I devoted some years to write a text book
(undergraduate level) on plane
algebraic curves (complex and real). It is written in
Spanish. About half of the exercises in it are solved in full
detail. Also, I stress some simple techniques to draw
algebraic curves. Here are some misprints and errors