Biography:
David Alfaya has a PhD in Mathematics from Universidad Autónoma de Madrid (UAM). He has a Bachelor Degree in Mathematics (2013, First National Bachelor Prize in Science Area) and he is a Computer Science Engineer (2013, First National Bachelor Prize in Engineering and Architecture Area), with a Master in Mathematics and Applications (2014) and a Master in Research and Innovation in Communications and Information Technologies (2015) from UAM. He obtained his PhD in 2018, developing his predoctoral research at ICMAT (Instituto de Ciencias Matemáticas del Consejo Superior de Investigaciones Científicas). He enjoyed two JAE Intro undergraduate research scholarships in 2011 and 2012 at ICMAT. Between 2012 and 2013 he worked at the Information Retrieval Group at UAM. From 2014 to 2018 he was a predoctoral researcher at ICMAT with a La Caixa-Severo Ochoa grant and from 2018 to 2019 he worked as Associated Collaborator Professor at ICAI. In 2019 he was a postdoctoral researcher at ICMAT and since 2020 he has been an Assistant Collaborator Professor at the Department of Applied Mathematics of ICAI and Associate Researcher at IIT. His research interests spread through several fields of pure and applied mathematics. Within the framework of Algebraic Geometry, his main lines of work share an interest in the study of the geometry of moduli spaces (specially moduli of decorated bundles including, among others, Higgs bundles, connections and parabolic structures). On the other hand, he also develops research lines in Information Retrieval, Information Geometry, Blockchain technologies and interactions between Artificial Intelligence and Mathematics.
Areas of interest:
Pure and applied mathematics. Study of the geometry of moduli spaces (specially moduli of decorated bundles including, among others, Higgs bundles, connections and parabolic structures). Information Retrieval, Information Geometry, Blockchain technologies and interactions between Artificial Intelligence and Mathematics.
D. Alfaya, L.A. Calvo, A. Martínez de Guinea García, J. Rodrigo, A. Srinivasan, "Markoff m-Triples with k-Fibonacci Components", Mediterranean Journal of Mathematics, Vol. 22, nº. 3, pp. 76, May 2025. [Online: April 2025] doi: 10.1007/s00009-025-02845-y
D. Alfaya, I. Biswas, T.L. Gómez, S. Mukhopadhyay, "Torelli theorem for moduli stacks of vector bundles and principal G-bundles", Journal of Geometry and Physics, Vol. 207, pp. 105350, January 2025. [Online: October 2024] doi: 10.1016/j.geomphys.2024.105350
D. Alfaya, I. Biswas, P. Kumar, A. Singh, "Parabolic vector bundles and Lie algebroid connections", Canadian Journal of Mathematics, doi: 10.4153/S0008414X25101983 In press: December 2025.
D. Alfaya, I. Biswas, F.X. Machu, "Pullback and direct image of parabolic Higgs bundles and parabolic connections with symplectic and orthogonal structures", Illinois Journal of Mathematics, Vol. 70, nº. 1, pp. 53 - 76, April 2026. [Online: May 2026] doi: 10.1215/00192082-12506444
A. Polo-Molina, D. Alfaya, J. Portela, "A Mathematical Certification for Positivity Conditions in Neural Networks With Applications to Partial Monotonicity and Trustworthy AI", IEEE Transactions on Neural Networks and Learning Systems, Vol. 37, nº. 2, pp. 981 - 996, February 2026. [Online: October 2025] doi: 10.1109/TNNLS.2025.3614431
D. Alfaya, L.A. Calvo, A. Martínez de Guinea García, J. Rodrigo, A. Srinivasan, "A classification of Markoff-Fibonacci m-triples", Fibonacci Quarterly, Vol. 63, nº. 3, pp. 517 - 541, 2025. [Online: July 2025] doi: 10.1080/00150517.2025.2481607
D. Alfaya, L.A. Calvo, A. Martínez de Guinea García, J. Rodrigo, A. Srinivasan, "Markoff m-Triples with k-Fibonacci Components", Mediterranean Journal of Mathematics, Vol. 22, nº. 3, pp. 76, May 2025. [Online: April 2025] doi: 10.1007/s00009-025-02845-y
D. Alfaya, I. Biswas, T.L. Gómez, S. Mukhopadhyay, "Torelli theorem for moduli stacks of vector bundles and principal G-bundles", Journal of Geometry and Physics, Vol. 207, pp. 105350, January 2025. [Online: October 2024] doi: 10.1016/j.geomphys.2024.105350
D. Alfaya, C. Pauly, "Hitchin map for the moduli space of Λ-modules in positive characteristic", Journal of Algebra, Vol. 634, pp. 306 - 335, November 2023. [Online: July 2023] doi: 10.1016/j.jalgebra.2023.07.012
D. Alfaya, I. Biswas, "Pullback and direct image of parabolic connections and parabolic Higgs bundles", International Mathematics Research Notices, Vol. 2023, nº. 22, pp. 19546 - 19591, November 2023. [Online: August 2023] doi: 10.1093/imrn/rnad193
D. Alfaya, "Simplification of λ-ring expressions in the Grothendieck ring of Chow motives", Applicable Algebra in Engineering, Communication and Computing, Vol. 33, nº. 6, pp. 599 - 628, December 2022. [Online: June 2022] doi: 10.1007/s00200-022-00558-3
D. Alfaya, "Automorphism group of the moduli space of parabolic vector bundles with fixed degree", Bulletin des Sciences Mathématiques, Vol. 175, pp. 103112, March 2022. [Online: January 2022] doi: 10.1016/j.bulsci.2022.103112
D. Alfaya, T.L. Gómez, "Automorphism group of the moduli space of parabolic bundles over a curve", Advances in Mathematics, Vol. 393, pp. 108070, December 2021. [Online: November 2021] doi: 10.1016/j.aim.2021.108070
D. Alfaya, M. Oliva Calero, E. Alonso, S. Cano Casanova, J. Rodrigo, M. Villanueva Pesqueira, "Maths Team Contest: Refinement and extension of teaching methodologies", in Good practices in teaching: Comillas 2022-23, Madrid, Spain: Ed. Servicio de Publicaciones de la Universidad Pontificia Comillas, 2024, pp. 213-218, doi: 10.14422/9788484687627.029