Mario Fuentes Rumí
Welcome to my website! I am a postdoctoral researcher at the Institut de Mathématiques de Toulouse. I recently defended my PhD thesis titled 'Lie models of classifying fibrations' under the guidance of Aniceto Murillo and Urtzi Buijs. Before my current position, I has been working as postdoctoral researcher at the Centro de Investigación en Matemáticas (CIMAT) in Merida, Mexico.
My research is centered around the following topics:
- Rational homotopy theory
- Complete (differential graded ) Lie algebras
- Maurer-Cartan simplicial sets
- Polyhedral products
- Equivariant K-theory
Through my research, I aim to deepen our understanding of the underlying algebraic structures of topological spaces and develop new mathematical tools to study them. Thank you for visiting my website!
Employment History
Jan 2024- Dec 2025 CIMI Postdoctoral researcher in the IMT (Institut de Mathématiques de Toulouse) in Toulouse, under the mentorship of Ricardo Campos
Sep 2023 - Dec 2023 Postdoctoral researcher in the CIMAT (Centro de Investigación en Matemáticas), in Merida, Mexico, under the mentorship of José Cantarero.
Feb 2023 - Aug 2023 Postdoctoral researcher at the University of Malaga.
2019 - 2023 Graduate student research fellowship FPU (competitive national predoctoral scholarship) at the University of Malaga.
2014 Research contract. JAE-Intro Scholarship. Introduction to Research for university students, Spanish National Research Council (CSIC). Complutense University of Madrid.
Education
2018 – 2023 Ph.D. in Mathematics, University of Malaga. Thesis titled 'Lie models of classifying fibrations', about rational homotopy theory and classifying spaces. Under the guidance of Professors Urtzi Buijs and Aniceto Murillo.
2016 – 2018 Master’s program in Mathematics, University of Bonn. The master's thesis was titled: 'Equivariant K-theory' and was carried on under the supervision of Dr. Irakli Patchkoria and Prof. Dr. Wolfgang.
2011 – 2016 BSc in Mathematics, Complutense University of Madrid.
2011 – 2016 BSc in Physics, Complutense University of Madrid.
Publications
Ph.D. Dissertation
Lie models of classifying fibrations
Articles
Félix, Y., Fuentes, M., & Murillo, A. (2022). Lie models of homotopy automorphism monoids and classifying fibrations. Advances in Mathematics, 402, 108359. https://doi.org/10.1016/j.aim.2022.108359
Fuentes, M. (2022). Classification of fiber sequences with a prescribed holonomy action. Topology and its Applications, 317, 108185. https://doi.org/10.1016/j.topol.2022.108185
Accepted
Félix, Y., Fuentes, M., & Murillo, A. (2022). Realization of Lie algebras of derivations and moduli spaces of some rational homotopy types. https://doi.org/10.48550/arXiv.2206.14124. To be published in Algebraic & Geometric Topology.
Félix, Y., Fuentes, M., & Murillo, A. (2022). All known realizations of complete Lie algebras coincide. https://doi.org/10.48550/arXiv.2207.10886. To be published in Algebraic & Geometric Topology.
Preprints
Félix, Y., Fuentes, M., & Murillo, A. (2023). Rational homotopy type of relative universal fibrations. https://doi.org/10.48550/arXiv.2311.14132
Fuentes, M., (2019). The equivariant K- and KO-theory of certain classifying spaces via an equivariant Atiyah-Hirzebruch spectral sequence. https://doi.org/10.48550/arXiv.1905.02972
Talks
March 2024 Derivations and moduli spaces of some rational homotopy types. Séminaire ALPE, Montpellier.
January 2024 ¡Todas las teorías de homotopía racional son compatibles! Congreso Bienal de la Real Sociedad Matemática Española, Pamplona.
September 2023 A proof of the Baues-Lemaire conjecture by means of complete Lie models. Iberoamerican and Pan Pacific International Conference on Topology and its Applications, Puebla.
August 2023 Introducción a las fibraciones universales y sus modelos de Lie. Coloquio FMAT-CIMAT, Universidad Autónoma de Yucatán.
July 2023 A proof of the Baues-Lemaire conjecture by means of complete Lie models. Young Topology Meeting, EPFL, Lausanne.
June 2023 Introducción a la homotopía racional clásica y moderna. CIMAT, Unidad Merida.
May 2023 Moduli spaces of some rational homotopy types. EPFL Topology Seminar, Lausanne
April 2023 Espacios de moduli de tipos de homotopía racional. Universidad complutense de Madrid.
March 2023 Lie models of classifying fibrations. Topological Activities. Stockholm.
March 2023 Modelos de Lie de fibraciones clasificantes. Seminario AGT. Centro de Investigación en Matemáticas, Guanajuato (online).
March 2023 Completando la homotopía racional. Graduate Mini course. Santiago de Compostela.
January 2023 Lie models of classifying spaces. University of Copenhagen (online).
October 2022 Álgebras de Lie de derivaciones y espacios de moduli. X Encuentro de Jóvenes Topólogos. Zaragoza.
September 2022 Lie models of classifying spaces. Classifying spaces in homotopy theory: in honour of Ran Levi’s 60th Birthday. ICMS, Bayes Centre, Edinburgh.
March 2022 Algebraic models for classifying spaces. Séminaire de topologie algébrique. Université catholique de Louvain.
October 2021 Grupos de autoequivalencias actuando nilpotentemente en la homología. Encuentro de Jóvenes Topólogos. Universidad de Sevilla.
July 2021 Rational homotopy, classifying spaces and self-homotopy equivalences. Young Topology Meeting 2021. Stockholm University (online).
June 2021 Homotopía racional, espacios clasificantes y autoequivalencias homotópicas. MCHAGT2021. Universidad de Sevilla.
March 2021 Homotopía racional con muchos ejemplos. Ciclo Junior de Topología. Universidad de Sevilla (online).
November 2020 H-fibraciones y espacios clasificantes. Jornadas Topológicas Virtuales (online).
June 2019 The equivariant K- and KO-theory of certain classifying spaces via an equivariant Atiyah-Hirzebruch spectral sequence. ECTR 2019 University of Sheffield.
February 2019 An equivariant generalization of the Atiyah-Hirzebruch spectral sequence and computations on equivariant K-theory. Topology & Málaga Meeting. University of Malaga.
Research stays
2020 Fields Institute for Research in Mathematical Sciences, Toronto. Attendance to the semester program Thematic Program on Toric Topology and Polyhedral Products which consists of several talks, workshops and seminars about these topics.
2022 Université catholique de Louvain, Louvain-la-Neuve. Research under the guidance of Professor Yves Félix.
Organizational experience
December 2022 Co-organizer of the conference II Encuentro conjunto RSME-UMA which took place in the city of Ronda, Malaga, Spain.
January 2023 Co-organizer of the Workshop Operads in Malaga, at the University of Malaga, Spain.
February 2023 Co-organizer of the parallel session 'Topología' in the conference VI Congreso de Jóvenes Investigadores de la Real Sociedad Matemática Española, in the university of Leon, Spain.