My current research interest is Polytopes and Tropical Algebra and Geometry.
  See my research papers (most of them on arXiv) regarding tropical issues:
 Heres is a pdf file of my poster Alcoved polyhedra: new shapes for design, presented at CCMA 2019, Madrid, July 2019
Here is a pdf file of my  talk on Matrices commuting with a given normal  tropical matrix, given at Skolkovo, near Moscow, in August 2015.
Here is a pdf  of my talk on Volúmenes, politopos alcobados y matrices tropicales, given at Banach Spaces Workshop,   in UCM, Madrid, November, 28, 2017 (in Spanish)
Here is a talk I will give at U.Birmingham next week.

I have taken part in  Seminar on History of  Mathematics, Facultad de Matemáticas, UCM, in 2013-2014, 2014-2015 and 2016-2017.  My talks were  Historia del Álgebra Lineal   Historia de las Curvas (talk 1 and talk 2) and Historia de los Poliedros. (All of them in Spanish).

I am a  participant in the research group  Operators, lattices and structure of Banach spaces, MTM 2016-76808-P supported by MINIECO and in the  UCM Group 910444 Geometría algebraica y analítica real, 2019.

Formerly I was interested in Real Algebraic Geometry. My Master thesis (UCM, 1984, advisor: J.M. Ruiz Sancho) dealt with Zariski-dense curves. In my Ph. D. thesis (Stanford University, 1988,  advisor: G.W. Brumfiel), I defined and studied spaces of  valuations on rings compatible with orderings (I called these spaces "real Riemann surfaces", following denotation by O. Zariski) and spaces of orderings together with involutions (called  "the complex spectrum of a ring"), similar to the real spectrum of M. Coste and M. F. Roy.  I tried to put these spaces in connection with several compactifications of algebraic varieties known then (due to G. Bergman, and to J. Morgan and P. Shalen). Bergman's paper is actually a precendent of Tropical Geometry.  Later on, I studied atypical values of real polynomial functions on the plane. Later, I pursued the task of making a few facts about real plane algebraic curves (well--known to experts) available to a wider audience. See my list of  related published papers:
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