Professor of Geometry and Topology, Department of Mathematics, Statistics and Computational Science, Universidad de Cantabria, and Corresponding Academician of the Real Academia de Ciencias Exactas, Físicas y Naturales (Spain).
Since 2019, Editor-in-Chief of Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales: Serie A: Matemáticas, RACSAM, edited by Springer. It is a Q1 journal of JCR Science (Mathematics): 56/325 (2019), 29/330 (2020), 26/332 (2021), 15/329 (2022).
Reviewer of Mathematical Reviews (American Mathematical Society) since 1995, and Reviewer of zbMATH Open (edited by the European Mathematical Society, the Heidelberg Academy of Sciences and Humanities, and FIZ Karlsruhe) since 2021.
He is interested in a wide range of topics around Geometry. First of all, in structures on manifolds, such as complex, paracomplex, quaternionic, symplectic, etc. and in the applications of these ones to Mathematical Physics. He is also interested in Analysis on manifolds: jets bundles, connections, etc., and in metrics on manifolds: semi-Riemannian, neutral, Finsler, etc.
Author of more than 50 papers published in International Journals, such as Proceedings of the Amer. Math. Soc., Differential Geometry and Appl., Topology and its Appl., Houston Math. Journal, RACSAM, Acta Math. Hungarica, Publ. Math. Debrecen, Czechoslovak Math. J., Carpathian Journal of Math., Mediterr. J. Math., Atti Sem. Mat. Fis. Modena, Rend. Mat. Appl., Riv. Mat. Univ. Parma, Turkish J. Mathematics, Hacettepe Journal of Math. and Stat, Balkan J. Geom. Appl., Bull. Malaysian Math. Sci. Society, Journal of Geometry and Physics, Journal of Physics A: Math. and General, Journal of Math. Physics, International Journal of Geometric Methods in Modern Physics, Computer Aided Geometric Design.
Graduate courses on: Linear Algebra, Affine and Projective Geometries, Geometry of Curves and Surfaces, Differential Geometry (Manifolds and Bundles), Riemannian Geometry, General Topology, Algebraic Topology, Differential Topology.
Postgraduate courses on: Polynomic Structures on Manifolds, Geometry of Submanifolds, Fibre Bundles and Connections, Semi-Riemannian Geometry, Complex Differential Geometry, Holonomy, Algebras and Differential Geometry, Hyperbolic Geometry, History of Mathematics.
Organizing committee member of the project ESTALMAT-Cantabria (Mathematical encouragement program for 12-14 aged children).
Past Positions in Universidad de Cantabria
2012-2014 Vice-Chancellor of Academic Affaires
2008-2012 Head of Post-Graduate Programs and Life Long Learning
2004-2008 Vice-Dean of the Faculty of Sciences
2003-2004 Assistant Head of the Department of Mathematics, Statistics and Computation