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
1 and talk
2). (All of them in Spanish).
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
available to a wider audience. See my list of
related published papers:
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)
Ferrera) The asymptotic
values of a polynomial function on the real plane.J.
Pure Appl. Algebra 106 (1996), n. 3, 263--273. 26C99
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
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