Areas of Interest
- Noncommutative Geometry
- The field with one element
- Groupoids and convolution algebras
- Quantum Groups
- Deformation Theory
Preprints and works in progress
- Projective geometry for blueprints (with O. Lorscheid) - Comptes Rendus - Mathématique 350, 455-458 (2012). DOI: 10.1016/j.crma.2012.05.001.
- Mapping F_un-land: An overview of geometries over the field with one element (with O. Lorscheid) - In Noncommutative Geometry, Arithmetic, and related topics, proceedings of the 21st meeting of the JAMI, 241-265 (2011).
- On the classification of twisting maps between $K^n$ and $K^m$ (with P. Jara, G. Navarro and D. Stefan) - Journal of Algebra and Representation Theory, (2010) DOI: 10.1007/s10468-010-9222-x.
- Torified varieties and their geometries over F_1 (with O. Lorscheid) - Mathematische Zeitschrift, (2009) DOI: 10.1007/s00209-009-0638-0.
- Factorization structures with a 2-dimensional factor (with O. Cortadellas and G. Navarro) - Journal of the London Mathematical Society, 81 (1), 1-23 (2010); DOI: 10.1112/jlms/jdp055.
- On the classification and properties of noncommutative duplicates (with G. Navarro) - K-Theory, 38 (2), 223-234 (2008). DOI: 10.1007/s10977-007-9017-y, MathReview: MR2366562
- A note on generalized path algebras (with R. Ibañez-Cobos and G. Navarro) - Revue Roumaine de Mathèmatiques Pures et Appliquèes, 53 (1), 25-36 (2008). MathReview: MR2449185
- A connection for product manifolds in noncommutative geometry - International Mathematics Research Notices IMRN 2008 (7), Art. ID rnn005 (2008). DOI: 10.1093/imrn/rnn005, MathReview: MR2428304
- General twisting of algebras (with F. Panaite and F. Van Oystaeyen) - Advances in Mathematics, 212 (1), 315-337 (2007). DOI: 10.1016/j.aim.2006.10.003, MathReview: MR2319771
- On iterated twisted tensor products of algebras (with P. Jara, F. Panaite and F. Van Oystaeyen) - International Journal of Mathematics, 19 (9), 1053-1101 (2008). DOI: 10.1142/S0129167X08004996, MathReview: MR2458561
- Invariance under twisting (with P. Jara, F. Panaite, and F. Van Oystaeyen) - Proceedings of the "New techniques in Hopf algebras" conference, Koninklijke Vlaamse Academie van België voor Wetenschappen en Kunsten, KVAB D/2007/455/10, 85-104 (2007). MathReview: MR2395678
- Cuadrados mágicos de números primos (Magic squares of primes) - Gaceta de la Real Sociedad Matemática Española (1999).
Talks and Posters
- Twisted tensor products and Hochschild cohomology of Koszul rings - Talk at the Algebra session of the 1st Joint Conference of the Belgian, Royal Spanish and Luxembourg Mathematical Societies, University of Liege, June 2012.
- Noncommutative geometry of finte groups - Talk at the Noncommutative Geometry workshop of the British Mathematical Colloquium, University of Kent, April 2012 (Slides).
- Network theory and analysis of football strategies - Talk and poster at the Physics of Sports conference, Ecole Polytechnique Paris, April 2012 (Poster and Slides).
- Geometry over the field with one element - invited mini-course at Categories, Geometry and Physics Jairo Charris Seminar 2011, Universidad Sergio Arboleda, Santa Marta (Colombia), August 2011.
- Crystals, clusters and combinatorial aspects of geometries over the field with one element - invited talk at Noncommutative Geometry and Arithmetic JAMI Conference 2011, Johns Hopkins University, Baltimore, Maryland (USA), March 2011.
- Crystals and intrinsic geometries over the field with one element - invited talk at Noncommutative geometry and applications to number theory workshop, Ohio State University, Columbus, Ohio (USA), April 2010.
- Cyclotomy and the field with one element - invited talk at Low dimensional topology and number theory II, University of Tokyo (Japan), March 2010.
- Geometry of monoids - invited talk at Focused workshop on F1-geometry, University of Granada (Spain), November 2010.
- Torified schemes: a new family of varieties over F_1 - invited talk at the Seventh anual Spring Institute on Noncommutative Geometry and Operator Algebras: Geometry over F1, Noncommutative Geometry and Zeta, at Vanderbilt University, Nashville, Tennessee (USA), May 2009.
- Noncommutative Geometry of the Standard Model - talk at the "Postdoc Spring School: Field Theory, String Theory and Gromov-Witten Invariants", Max Planck Institute for Mathematics, Bonn (Germany), April 2008
- Inner deformations of algebras - short communication at the "International Conference on Noncommutative Rings and Geometry in honour of Freddy Van Oystaeyen", Almeria, September 2007 - Slides
- On the classification of factorization structures of low dimension - short communication at the "XIIth International Conference in Representation of Algebras", Torun, August 2007 - Slides
- Connections over twisted tensor products of algebras - short communication at the "International Colloquium on Integrable Systems and Quantum symmetries", Prague, June 2007 - Slides
- A product connection in noncommutative geometry - Poster at the "New Trend in Noncommutative Geometry" workshop, Cambridge, December 2006
- Invariance under twisting - Short communication at the "New techniques in Hopf algebras and graded ring theory" meeting, Brussels, September 2006 - Slides
- Twisted tensor products in noncommutative geometry - Poster at the "International Congress of Mathematicians", Madrid, August 2006
- Iterated twisted tensor products of algebras - Short communication at the "Algebras and Coalgebras" conference, Cairo, March 2006 - Slides
- Dominios de Mori. Ejemplos - Short communication at the "I Encuentro de Grupos de Investigación de Álgebra de Andalucía", Almería, October 2002
- Factorization Structures. A Cartesian Product for Noncommutative Geometry - PhD Thesis, Universidad de Granada, 2007. ISBN 978-84-338-4337-1.
- Twisted Tensor Products in Noncommutative Geometry - Master Thesis IAMD "Noncommutative Algebra and Geometry", Antwerp, 2006
- A Goodearl-Letzter Stratification Theory for the Noncommutative Planes and Spheres - IAMD "Noncommutative Algebra and Geometry" short project. Advised by T. Lenagan (2005)
- On ring theoretic properties of noncommutative planes and spheres - IAMD "Noncommutative Algebra and Geometry" short project. Advised by F. Van Oystaeyen (2005)
- Aspectos algebraicos en Geometría no Conmutativa - DEA report, Granada, 2005.