Research

Preprints

[1] Infinite Atomized Semilattices, with F. Martin-Maroto, A. Ricciardo and G. G. de Polavieja. [arXiv]

Publications

[7] A directed persistent homology theory for dissimilarity functions, with R. Sanchez-Garcia, Journal of Applied and Computational Topology. [Journal][arXiv][MathSciNet MR]

[6] Colouring simplicial complexes via the Lechuga-Murillo's model, Appl. Algebra Engrg. Comm. Comput. 33 (2022), 153–162. [Journal][arXiv][MathSciNet MR][zbMath]

[5] The ring of stable homotopy classes of self-maps of A(n,2)-polyhedra, Topology and its applications 290 (2021), 107607. [Journal][arXiv][MathSciNet MR][zbMath]

[4] Representability of permutation representations on coalgebras and the isomorphism problem, with C. Costoya and A. Viruel, Mediterr. J. Math. 17, 157 (2020). [Journal][arXiv][MathSciNet MR][zbMath]

[3] The group of self-homotopy equivalences of A(n,2)-polyhedra, with C. Costoya and A. Viruel, J. Group Theory 23 (2020), 575–591. [Journal][arXiv][MathSciNet MR][zbMath]

[2] Realisability problem in arrow categories, with C. Costoya and A. Viruel, Collect. Math. 71 (2020), 383–405. [Journal][arXiv][MathSciNet MR][zbMath]

[1] Homotopically rigid Sullivan algebras and their applications (with an Appendix by P. Lambrechts and D. Stanley), with C. Costoya and A. Viruel, Contemp. Math. 708 (2018), 103–121. [Journal][arXiv][MathSciNet MR][zbMath]

Positions held

2021- . Postdoctoral Fellow at the Fundação Champalimaud working with the Horizon 2020 Project "ALMA: Human Centric Algebraic Machine Learning", with the Collective Behaviour Lab led by G. de Polavieja.

2020-2021. Turing Research Fellow at the University of Southampton working on the Pilot Project "Automatic Detection of Genetic Oscillators" under the supervision of R. Sánchez-García.

2019-2020. Postdoctoral "Contrato Puente" of the Universidad de Málaga.

2015-2019. Predoctoral Fellow at the Universidad de Málaga with a Formación de Profesorado Universitario (FPU) grant of the Spanish Ministerio de Educación, Cultura y Deporte, under the supervision of C. Costoya and A. Viruel.

2014-2015. Contract associated to the Research Project "Representación homotópica de grupos" at the Universidade da Coruña, under the supervision of C. Costoya.

Contributed talks and seminars

• February 10, 2023, An introduction to Algebraic Machine Learning, Southampton Pure Math Colloquium, University of Southampton, (Southampton, United Kingdom).

• June 17th, 2022, An introduction to Algebraic Machine Learning, Métodos Categóricos y Homotópicos en Álgebra, Geometría, Topología y Análisis Funcional (Badajoz, Spain).

• September 14th, 2021, A directed persistent homology theory for dissimilarity functions, Annual meeting of the Centre for Topological Data Analysis, United Kingdom.

• January 27th, 2021, A directed persistent homology theory for dissimilarity functions, Bilbao Algebra Seminar (University of the Basque Country, Spain).

• November 8th, 2020, Una teoría de homología persistente dirigida para funciones de disimilitud, I Jornadas Topológicas Virtuales de la RET (Red Española de Topología, Online conference).

• October 12th, 2020, A directed persistent homology theory for dissimilarity functions, Topology Seminar (University of Southampton, United Kingdom).

• September 22nd, 2020, A directed persistent homology theory for dissimilarity functions, EPFL Applied Topology Seminar (École Polytechnique Fédérale de Lausanne, Switzerland).

• March 11th, 2020, On a Kahn's group realisability problem, Pure PGR Seminar (University of Southampton, United Kingdom).

• February 6th, 2020, On a Kahn's group realisability problem, Málaga & Topology Meeting 2020 (Universidad de Málaga, Spain).

• July 6th, 2019, Representación de grupos de permutaciones en coálgebras y el problema de isomorfismos, Métodos Categóricos y Homotópicos en Álgebra, Geometría y Topología 2019 (Universidade de Santiago de Compostela, Spain).

• May 20th, 2019, Realisability problem in arrow categories, parallel session at BYMAT 2019 "Bringing Young Mathematicians Together" (ICMAT, Madrid, Spain).

• February 5th, 2019, El problema de realizabilidad de grupos en categorías de flechas, Sesión Especial «Métodos homotópicos en álgebra, geometría y topología», Bienal RSME 2019 (Real Sociedad Matemática Española, Santander, Spain).

• October 23rd, 2018, The group realisability problem in topology, Workshop Tournesol Lille - Louvain-la-Neuve (Catholic University of Louvain, Belgium). 

• October 17th, 2018, El problema de realización de grupos en categorías de flechas, VII Encuentro de Jóvenes Topólog@s (Autonomous University of Barcelona, Spain).

• October 11th, 2018, Realising groups in arrow categories of graphs and spaces, Seminar of algebraic topology (Catholic University of Louvain, Belgium).

• April 10th, 2018, Realising groups as self-homotopy equivalences of A(n,2)-polyhedra, Seminari Baby Geometri (University of Pisa, Italy).

• March 21st, 2018, Self-homotopy equivalences of A(n,2)-polyhedra, Topology & Málaga Meeting (University of Málaga, Spain).

• October 3th, 2017, Self-homotopy equivalences of A(n,2)-polyhedra, Seminar of Topology (EPFL, Switzerland).

• July 4th, 2017, Homotopically rigid Sullivan algebras and their applications, Young Topologists Meeting 2017 (Stockholms Matematikcentrum, Sweden).

• June 30th, 2017, Self-homotopy equivalences of A(n,2)-polyhedra, Métodos Categóricos y Homotópicos en Álgebra, Geometría y Topología (University of Málaga, Spain).

• April 28th, 2017, Realising groups with highly connected DGAs, Seminar of Geometry and Topology (Adam Mickiewicz University in Poznan, Poland).

• July 21st, 2016, Highly connected inflexible manifolds, CIMPA Summer School in "Rational homotopy theory and its interactions" (International University of Rabat, Morocco).

• May 24th, 2016, Variedades inflexibles altamente conexas, Seminar of Geometry and Topology (Universidad Complutense de Madrid, Spain).

• May 19th, 2016, Variedades inflexibles altamente conexas, Seminar of Geometry (ICMAT-CSIC, Madrid, Spain).

• March 17th, 2016, Realizing groups with highly connected DGAs, Graphs and Groups in Galicia 2016 (University of A Coruña, Spain).

• June 30th, 2015,  Highly connected inflexible manifolds, 4th Spanish Young Topologists Meeting (Universidad Complutense de Madrid, Spain).

Poster sessions

• May 31st, 2023, Algebraic Machine Learning, Champalimaud Retreat (Champalimaud Foundation, Portugal). [Poster]

• October 19th, 2018, El problema de realización de grupos en categorías de flechas (in Spanish), XXV Encuentro de Topología (Autonomous University of Barcelona, Spain). [Poster]

• October 21st, 2016, Coloraciones de complejos simpliciales: Sobre el modelo de Lechuga-Murillo (in Spanish), XXIII Encuentro de Topología, Málaga (University of Malaga, Spain). [Poster]

Awards

• September 2022, Universidad de Málaga Doctoral Awards to the best thesis defended in the PhD programme in Mathematics in the academic year 2019-2020.

• October 2018, Red Española de Topología (RET) award to the best poster presented at the XXV Encuentro de Topología.

• October 2016, RET award to the best poster presented at the XXIII Encuentro de Topología.

• December 2015, Xunta de Galicia award for Excelence in Academic Performance for the studies of Degree in Mathematics at the University of Santiago de Compostela.

• November 2015, second prize of the XIV Certamen Universitario Arquimedes for young researchers, awarded for research made during my degree thesis.

• April 2015, University of Santiago de Compostela award for Excelence in Academic Performance for the studies of Degree in Mathematics.

Attended Summer Schools and Courses

• September 2023, Interactions of Proof Assistants and Mathematics, University of Regensburg, Regensburg, Germany.

• June 2023, ModML: Topics in Modern Machine Learning, Machine Learning Genoa Center, Genoa, Italy.

• August 2022, IBM Neuro-Symbolic AI Summer School.

• July 2021, Neuromatch Deep Learning.

Other merits

• November 2021, Received "Ayudante Doctor" professorship habilitation from the Spanish Ministerio de Universidades.

Theses

• 2019, PhD thesis, Realisability problems in Algebraic Topology, Universidad de Málaga. [RIUMA][Teseo]

• 2015, Master's thesis, Realisability of groups: on a Kahn's problem, Universidade de Santiago de Compostela. [Thesis]

• 2014, Degree thesis, Modelaxe de complexos simpliciais (in Galician), Universidade de Santiago de Compostela. [Thesis]