Department: Álgebra, Geometría y Topología

Faculty: Ciencias Matemáticas

Centre/Institute: Instituto de Ciencias Matemáticas (ICMAT)

Area: Algebra

Research group: Geometría algebraica y analítica real


Personal web:

Doctor by the Universidad Complutense de Madrid with the thesis Sumas de cuadrados de gérmenes de función analítica 2001. Supervised by Dr. Jesús María Ruiz Sancho.

He is Professor (Catedrático) at the Departamento de Álgebra, Geometría y Topología of the Facultad de Ciencias Matemáticas (Universidad Complutense de Madrid). He obtained his PH. D. degree at Universidad Complutense de Madrid (2001) under the supervision of J.M. Ruiz and worked at Universidad Complutense de Madrid and Universidad Autónoma de Madrid (hold several type of contracts between them: a Ramon and Cajal contract). He has developed Research periods in: Duisburg (Germany), Pisa and Trento (Italy), Paris and Rennes (France) for more than 50 months. One of this periods was funded by Programa Salvador de Madariaga (2014-2015), others were supported by European Projects (HPRN-CT-2001-00271), national Spanish research grants or (competitive) local grants from the receptor universities. He had Ph.D. Students: Carlos Ueno (UCM), Antonio Carbone (Università di Trento). His research interests are inside Real Geometry concerning mainly: Hilbert’s 17th Problem, Quadratic Forms, Images of Nash maps, Images of polynomial and regular maps, Complex and Real Analytic Geometry, Smooth Approximation of continuous maps between triangulable spaces, Rings of continuous and differentiable semialgebraic functions, etc. He has authored and co-authored more than 50 papers. Some of them have appeared in the following journals: Trans. Amer. Math. Soc., Math. Ann., Ann. Sci. Ecole Norm. Sup., Comment. Math. Helv., J. reine angew. Math., Proc. Lond. Math. Soc., J. Eur. Math. Soc. (JEMS), Adv. Math., J. Inst. Math. Jussieu, Amer. J. Math., J. Geom. Anal., Selecta Math. (N.S.), J. Risk Insur., etc. For further information see: He has been main research of several national Spanish research grants: Current: PID2021-122752NB-I00 (period: 2022-2026). Previous: MTM2017-82105-P (period: 2018-2022, extended), MTM2008-00272 (period: 2009-2011), MTM2011-22435 (period: 2012-2015, extended), MTM2014-55565-P (period: 2015-2018, extended). Since December 2016 he is Associate Editor of Revista Matemática Complutense (