Real Geometry studies many of the objects and structures arising from the mathematical modelling of physical and technological processes, that is, it studies those objects defined through equalities and inequalities involving real valued functions (polynomial, Nash, analytic, differentiable, semialgebraic, constructible, etc.). This subject also includes the construction and development of the suitable structures to analyze those objects, as well as the relevant computational methods: algorithms and complexity. Our research lines include "Rings of Semialgebraic Functions", "O-minimality", "Polynomial, regular and Nash images of Rn", "Real Analytic Geometry", "Real algebraic curves", "Sums of squares and Knot Theory", "Constructibility and algorithms".
By the nature of the studied objects, the approached problems and the used techniques, all our research lines can be included in the so-called Real Algebraic and Analytic Geometry (Mathematical Subject Classification: 14Pxx). Important research European and North-American groups and independent researchers of other countries (for instance: Japan, Brasil, Chile, etc.) have worked in this field for more than 40 years. It is worthwhile mentioning that our group collaborate with several of these international research groups.