Mario Fuentes Rumí

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 Matemáticas), in Merida, Mexico, under the mentorship of José Cantarero.

• Feb 2023 - Aug  2023   Postdoctoral researcher at the University of Malaga.

• 2019 - 2023   Predoctoral fellow 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. In Advances in Mathematics (Vol. 402, p. 108359). Elsevier BV. https://doi.org/10.1016/j.aim.2022.108359

•  Fuentes, M. (2022). Classification of fiber sequences with a prescribed holonomy action. In Topology and its Applications (Vol. 317, p. 108185). Elsevier BV. https://doi.org/10.1016/j.topol.2022.108185

•  Félix, Y., Fuentes, M., & Murillo, A. (2024). Realization of Lie algebras of derivations and moduli spaces of some rational homotopy types. In Algebraic & Geometric Topology (Vol. 24, Issue 4, pp. 2285–2305). Mathematical Sciences Publishers. https://doi.org/10.2140/agt.2024.24.2285

• Fuentes, M. (2024). The equivariant K- and KO-theory of certain classifying spaces via an equivariant Atiyah-Hirzebruch spectral sequence. In Journal of Algebra and Its Applications. World Scientific Pub Co Pte Ltd. https://doi.org/10.1142/s0219498826500581

• Félix, Y., Fuentes, M., & Murillo, A. (2024). A Survey on Applications of a New Approach to Quillen Rational Homotopy Theory. In Cutting-edge mathematics (Vol. 13, pp. 62–80). https://doi.org/10.1007/978-3-031-62025-6_4

Accepted

•  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 

• Félix, Y., Fuentes, M., & Murillo, A. (2024). A Lie characterization of the Bousfield-Kan Q-completion and Q-good spaces. https://doi.org/10.48550/arXiv.2407.02812

Talks

•  October 2024  Complete (curved) Lie algebras as models of spaces. Rencontre 2024 de Topologie algébrique, Université Toulouse III - Paul Sabatier.

•  July 2024   Modelos de Lie de los espacios topológicos y su no linealidad. Encuentro de estudiantes de posgrado de la red de álgebra no-conmutativa, Universidad de Almería.

• July 2024   Modelos de Lie de los espacios topológicos y su no linealidad. VI Encuentro Conjunto RSME-SMM, Valencia.

• 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 algébraique. 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.