My current research interest is Tropical Algebra and Geometry.
  See my research papers (most of them on arXiv) regarding tropical issues:

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)

I have taken part in  Seminar on History of  Mathematics, 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).

I am a  participant in the research group  Operators, lattices and structure of Banach spaces, MTM 2016-76808.

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