My current research interest is Tropical Algebra and Geometry.
 See my research papers (some on arXiv) regarding tropical issues:
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). 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 techniques to draw algebraic curves. Here are some misprints and errors