Jordi Delgado
Department of Mathematics
Universitat Politècnica de Catalunya
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Universitat Politècnica de Catalunya

Dr. Jordi Delgado Updated on 24 March 2026

Professor lector – Universitat Politècnica de Catalunya

Research Identifiers

ORCID: 0000-0002-8365-8929; Scopus: 57195623588; ResearcherID: AAC-8997-2020; Ciência ID: 2C10-D843-805D

Research Interests

  • Geometric, combinatorial, and algorithmic group theory
  • Automata-theoretic methods in algebra
  • Subgroups and homomorphisms of free and related groups: semidirect extensions, RAAGs, and fundamental groups of graphs of groups
  • Subgroups of discrete groups via Stallings automata and generalizations
  • Decision problems in discrete groups

MSC Classification

03Dxx, 20Axx, 20Exx, 20Fxx

Contact

  • Universitat Politècnica de Catalunya
  • Department of Mathematics
  • EPSEM, FME
  • Av. de les Bases de Manresa, 61, 73, 08242 Manresa, Barcelona
  • jorge.delgado@upc.edu,
  • (+34) 938777302

Main Education

  • PhD in Mathematics, Universitat Politècnica de Catalunya (UPC) (2017)
  • MSc in Advanced Mathematics and Mathematical Engineering, Universitat Politècnica de Catalunya (UPC) (2011)
  • Licentiate in Mathematics, Universidad Nacional de Educación a Distancia (UNED) (2009)

Complementary Education

  • Gestió de la recerca, Universitat Politècnica de Catalunya (UPC) (2025)
  • Curs STEAM d’Iniciació a la Docència Universitària, Universitat Politècnica de Catalunya (UPC) (2024)
  • Group cohomology and Bieri Strebel-Neumann-Renz invariants, University of the Basque Country, UPV/EHU (2021)
  • Groups, languages, and automata, University of the Basque Country, UPV/EHU (2021)
  • Summer School on Logic and Algorithms in Group Theory, Hausdorff Research Institute for Mathematics (HIM) (2018)
  • Computational Group Theory with GAP, University of the Basque Country (UPV/EHU) (2018)
  • Groups of intermediate growth in Seville, Institute of Research in Mathematics at the University of Seville (IMUS) (2017)
  • Young GAGTA 2017 mini-courses, University of the Basque Country UPV/EHU (2017)
  • Algorithmic group theory, Barcelona Graduate School of Mathematics (2016)
  • Continuous Writing Improvement towards Academic Publication, Escola Superior d’Enginyeries Industrial, Aeroespacial i Audiovisual de Terrassa (UPC) (2016)
  • Course on Spectral sequences, Instituto de Ciencias Matemáticas (ICMAT) (2015)
  • Introductory Course on homological Algebra, Instituto de Ciencias Matemáticas (ICMAT) (2015)
  • Workshop on scientific writing, Escola Politècnica Superior d’Enginyeria de Manresa (UPC) (2013)
  • Advanced course: summer school on automorphism of free groups, Centre de recerca matemàtica (CRM) (2012)
  • Research programme on Automorphisms of Free Groups, Centre de recerca matemàtica (CRM) (2012)
  • Automorphisms of right-angled Artin groups, Centre de recerca matemàtica (CRM) (2012)
  • Geometric structures on surfaces and geodesic currents, Centre de recerca matemàtica (CRM) (2012)
  • Locally finite graphs of finite tree width and virtually free groups, Centre de recerca matemàtica (CRM) (2012)
  • Hyperbolic groups and straight-line programs, Centre de recerca matemàtica (CRM) (2012)
  • Fixed points of virtually free group homomorphisms, Centre de recerca matemàtica (CRM) (2012)
  • Course on partially commutative groups, Facultat de Matemàtiques i Estadística (FME) (2011)
  • Course on hyperbolic groups, Facultat de Matemàtiques i Estadística (FME) (2011)
  • Course on train tracks, Facultat de Matemàtiques i Estadística (FME) (2009)

Grants

  • Ajuts d’iniciació a la recerca ALECTORS-2024 (II), Universitat Politècnica de Catalunya, Universitat Politècnica de Catalunya (2025)
  • Ajuts d’iniciació a la recerca ALECTORS-2024, Universitat Politècnica de Catalunya, Universitat Politècnica de Catalunya (2024)
  • María Zambrano grant, Spanish Government (Ministerio de Universidades), Universitat Politècnica de Catalunya (2022)
  • Fellowship for the trimester program in Logic and Algorithms in Group Theory, Hausdorff Institute for Mathematics (HIM), University of Bonn (2018)
  • Postdoctoral grant UID/MAT/00144/2013, FCT/MCTE, Fundação para a Ciência e Tecnologia, Ministério da Ciência, Tecnologia e Ensino Superior, Portugal, Centre of Mathematics of the University of Porto (CMUP) (2018)
  • AAD_2013 grant (ECO/181/2013), AGAUR, Generalitat de Catalunya (Catalan Government), Generalitat de Catalunya (2013)
  • Research grant FPI-UPC 81-727, Universitat Politècnica de Catalunya, Universitat Politècnica de Catalunya (2012)
  • Grant BPE-UPC 2011, Universitat Politècnica de Catalunya, Department of Applied Mathematics III, Escola Politècnica Superior d’Enginyeria de Manresa (EPSEM) (2011)

Awards

  • Borsa Ferran Sunyer i Balaguer 2017, Ferran Sunyer i Balaguer Foundation & Birkhäuser, Institut d’Estudis Catalans (2017)
  • Évariste Galois Prize 2012 (accesit), Societat Catalana de Matemàtiques, Institut d’Estudis Catalans (2012)

Positions

  • Professor Lector, Universitat Politècnica de Catalunya (UPC) (Feb 2024 – Present)
  • María Zambrano researcher, Universitat Politècnica de Catalunya (UPC) (Feb 2022 – Jan 2024)
  • Postdoctoral researcher, University of the Basque Country (UPV/EHU) (Dec 2019 – Dec 2021)
  • Postdoctoral researcher, Universidade do Porto (Jul 2018 – Dec 2019)
  • Visiting researcher, University of the Basque Country (UPV/EHU) (Jan 2018 – May 2018)
  • BFSB Postdoctoral researcher, Ferran Sunyer i Balaguer Foundation (Sep 2017 – Dec 2017)
  • Investigador en formació FPI-UPC, Universitat Politècnica de Catalunya (Mar 2014 – Mar 2016)
  • FPI scholarship, Universitat Politècnica de Catalunya (Mar 2012 – Mar 2014)
  • BPE scholarship, Universitat Politècnica de Catalunya (Feb 2011 – Apr 2011)

Research Projects

  • Geometric Methods in Group Theory (Sep 2022 – Aug 2026), Universitat Politècnica de Catalunya (UPC), funded by Agencia Estatal de Investigación (AEI); co-funded by FEDER, UE (Project PID2021-126851NB-I00).
  • Diophantine Geometry and Model Theory of Groups (Jun 2020 – May 2022), Universidad del País Vasco / Euskal Herriko Unibertsitatea (UPV/EHU), funded by Agencia Estatal de Investigación (AEI) (Project PID2019-107444GA-I00).
  • Geometric Methods in Group Theory (Jan 2018 – Dec 2022), Universitat Politècnica de Catalunya (UPC), funded by Agencia Estatal de Investigación (AEI); co-funded by FEDER, UE (Project MTM2017-82740-P).
  • Groups, Topology and Applications (Jan 2016 – Dec 2020), Universidad del País Vasco / Euskal Herriko Unibertsitatea (UPV/EHU), funded by Gobierno Vasco / Basque Government (Project IT974-16).
  • Red Española de Teoría de Grupos (Dec 2015 – Nov 2017), Universitat Politècnica de Catalunya (UPC), funded by Ministerio de Economía y Competitividad (MINECO) / Spanish Government (Project MTM2015-71830-REDT).
  • Geometric Methods in Group Theory (Jan 2015 – Dec 2017), Universitat Politècnica de Catalunya (UPC), funded by Ministerio de Economía y Competitividad (MINECO) / Spanish Government (Project MTM2014-54896-P).
  • Geometric Methods in Group Theory (Jan 2012 – Dec 2014), Universitat Politècnica de Catalunya (UPC), funded by Ministerio de Economía y Competitividad (MINECO) / Spanish Government (Project MTM2011-25955).

Research stays

  • Universitat Politècnica de Catalunya (UPC), Manresa, Spain (Sep 2021 – Dec 2021). Algorithmic problems for Droms groups.
  • Universitat Politècnica de Catalunya (UPC), Manresa, Spain (Jun 2019 – Aug 2019). Secret sharing and Howson’s property.
  • Hausdorff Research Institute for Mathematics (HIM), Bonn, Germany (Sep 2018). Trimester program in Logic and Algorithms in Group Theory.
  • University of the Basque Country, Leioa, Spain (Jan 2018 – May 2018). Logical aspects of Artin groups of finite type.
  • Centre de Recerca Matemàtica (CRM), Bellaterra, Barcelona (Sep 2017 – Dec 2017). Subgroups of RAAGs.
  • The Graduate Center (CUNY), NYC, New York (Oct 2015 – Dec 2015). A free-group based secret-sharing scheme.
  • The Graduate Center (CUNY), NYC, New York (Jun 2015 – Jul 2015). Algorithmic recognition of Z-extensions.
  • The Graduate Center (CUNY), NYC, New York (Oct 2013). The automorphism group of a rigid polycyclic group.
  • Centre de Recerca Matemàtica (CRM), Bellaterra, Barcelona (Sep 2012 – Dec 2012). Research programme on automorphisms of free groups: algorithms, geometry and dynamics.

Publications

Research Papers

  1. A. Carvalho, J. Delgado. Orbit problems for free-abelian times free groups and related families. Journal of Algebra and its Applications. Vol. 25, N. 05, 2650002 (2026) DOI: 10.1142/S0219498826500027.
  2. J. Delgado, M. Linton, J. Lopez de Gamiz, M. Roy, P. Weil. The finitely generated intersection property in fundamental groups of graphs of groups. Preprint: https://arxiv.org/abs/2512.12635.
  3. J. Delgado, M. Linton, J. Lopez de Gamiz, M. Roy, P. Weil. Pullbacks and intersections in categories of graphs of groups. Preprint: https://arxiv.org/abs/2508.04362.
  4. J. Delgado, M. Roy, E. Ventura. Quotient-saturated groups. Journal of Pure and Applied Algebra. Vol. 229, N. 9, 108053 (2025) DOI: 10.1016/j.jpaa.2025.108053.
  5. A. Carvalho, J. Delgado. Free-abelian by free groups: homomorphisms and algorithmic explorations. Kyoto Journal of Mathematics. (2025)
  6. J. Delgado, M. Roy, E. Ventura. Intersection configurations in free and free times free-abelian groups. Proceedings of the Royal Society of Edinburgh Section A: Mathematics. Vol. 154, N. 5, pp. 1552-1582 (2024) DOI: 10.1017/prm.2023.79.
  7. A. Carvalho, J. Delgado. Decidability of the Brinkmann Problems for endomorphisms of the free group. Archiv der Mathematik. V. 123, No. 3, 233-240 (2024) DOI: 10.1007/s00013-024-02029-2.
  8. J. Delgado, E. Ventura, A. Zakharov. Relative order and spectrum in free and related groups. Communications in Contemporary Mathematics. Vol. 26, N. 01, 2250066 (2024) DOI: 10.1142/S0219199722500663.
  9. J. Delgado, E. Ventura. Stallings automata for free-times-abelian groups: intersections and index. Publicacions Matemàtiques. Vol. 66, N. 2, pp. 789-830 (2022) DOI: 10.5565/PUBLMAT6622209.
  10. J. Delgado, E. Ventura. A list of applications of Stallings automata. Transactions on Combinatorics. Vol. 11, N. 3, pp. 181-235 (2022) DOI: 10.22108/toc.2021.130387.1905.
  11. J. Delgado, E. Ventura. Autòmats d’Stallings, un camí d’anada i tornada. Butlletí de la Societat Catalana de Matemàtiques. Vol. 37, N. 1, pp. 5-59 (2022) DOI: 10.2436/20.2002.01.102.
  12. J. Delgado, P. Silva. On the lattice of subgroups of a free group: complements and rank. journal of Groups, Complexity, Cryptology. Vol. 12, N. 1, pp. 1-24 (2020) DOI: 10.46298/jgcc.2020.12.1.6059.
  13. J. Delgado, E. Ventura, A. Zakharov. Intersection problem for Droms RAAGs. International Journal of Algebra and Computation. Vol. 28, N. 07, pp. 1129-1162 (2018) DOI: 10.1142/S0218196718500509.
  14. B. Cavallo, J. Delgado, D. Kahrobaei, E. Ventura. Algorithmic recognition of infinite cyclic extensions. Journal of Pure and Applied Algebra. Vol. 221, N. 9, pp 2157-2179 (2017) DOI: 10.1016/j.jpaa.2016.10.008.
  15. J. Delgado. Some characterizations of Howson PC-groups. Reports@SCM. Vol 1, N. 1, pp. 33-38 (2014) DOI: 10.2436/20.2002.02.3.
  16. J. Delgado, E. Ventura. Algorithmic problems for free-abelian times free groups. Journal of Algebra. Vol. 391, N. 1, pp. 256-283 (2013) DOI: 10.1016/j.jalgebra.2013.04.033.

Other Publications

  1. J. Delgado, E. Ventura. Stallings’ automata. In Languages and Automata: GAGTA BOOK 3 (Chapter 3). Ed. B. Steinberg. De Gruyter. pp. 95-160. (2024-10). Link.
  2. J. Delgado. Whitehead Problems for Words in (\mathbb{Z}^m \times F_n). In Extended Abstracts Fall 2012. Ed. J. González-Meneses, M. Lustig, E. Ventura. Trends in Mathematics. Springer International Publishing. pp. 35-38. (2014-06-11). Link.

Theses

  1. J. Delgado. Extensions of Free Groups: Algebraic, Geometric, and Algorithmic Aspects. (PhD thesis, Universitat Politècnica de Catalunya (UPC)). Link. (2017-09-15).
  2. J. Delgado. Problemes algorísmics en grups lliures per lliure-abelià. (Master’s thesis, Universitat Politècnica de Catalunya (UPC)). Link. (2011-01-01).

Teaching Material

  1. Introduction to Stallings Automata and the Geometry of Subgroups of Free Groups. Introduction to Mathematical Research, (2025).
  2. Àlgebra lineal. Grau en Enginyeria d’Automoció, (2025).
  3. Introduction to Stallings automata. Master in Advanced Mathematics and Mathematical Engineering, (2025).
  4. Introducció a l’àlgebra lineal. Grau en Enginyeria, (2024).
  5. Stallings automata and applications. BGSMath graduate course, (2023).
  6. Integració a l’espai. Grau en Enginyeria, (2022).
  7. Probabilitat i estadística. Grau en Enginyeria, (2015).
  8. Nombres Reals, propietats algebraiques i conceptes bàsics. (2011).

Divulgative Material

  1. Algú en dóna més?. Anem x + mates (2025).
  2. Sobre les espatlles de gegants. Anem x + mates (2024).
  3. Fins a l’infinit… i més enllà?. Anem x + mates (2023).
  4. Infinit com el mar?. Anem x + mates (2022).
  5. Incertesa, backgammon i altres delícies. Anem x + mates (2020).
  6. Sopa de nombres. 7 de mates (2018).
  7. L’infinit és més gran del que et penses. 7 de mates (2017).

Talks

Research Talks

  1. On two notions of ‘saturation’ for groups. 9th European Congress of Mathematics (European Mathematical Society, 2024-07-19). School of Engineering of the University of Seville, Seville, Spain.
  2. On multiple intersections of subgroups. Encontro Nacional da SPM 2024 (Sociedade Portuguesa de Matemática, 2024-07). Universidade do Minho, Braga, Portugal.
  3. A tale of intersections. II Encuentro Conjunto RSME-UMA (RSME-UMA, 2022-12-13).Ronda, Spain.
  4. Relative order and spectrum: three questions and two answers. ICMAT Algebra Seminar (2022-03-17). Instituto de Ciencias Matemáticas (ICMAT), Madrid, Spain.
  5. Applications of Stallings automata: old and new. Encontro Nacional SPM 2021 (Sociedade Portuguesa de Matemática, 2021-07).Portugal (online event).
  6. On relative order and spectrum in groups. GAGTA 2021 (GAGTA, 2021-06).Edinburgh, UK (online event). Event URL: https://sites.google.com/view/gagta2020.
  7. Relative order and spectrum in free and related groups. UPV/EHU Algebra Seminar (2021-05-19).Leioa, Spain.
  8. On the complements and rank of the subgroups of the free group. Semigroups, Automata and Languages Seminar (2019-11-29). Centro de Matemática Universidade do Porto, Porto, Portugal.
  9. From algebra to geometry (and back). CMUP Post-doc meeting (2019-05). Centro de Matemática Universidade do Porto, Porto, Portugal.
  10. On the intersection problem for free-abelian by free groups. Algorithmic Problems in Group Theory (2019-03). Leibniz Center for Informatics, Schloss Dagstuhl, Germany.
  11. Stallings automata for extensions by free groups. Algebra and Logic Group Seminar (Universidade Nova de Lisboa, 2018-11-19). Sala de Seminários - Edifício VII, Lisbon, Portugal.
  12. Stallings foldings for free extensions. Semigroups, Automata and Languages Seminar (2018-11). Centro de Matemática Universidade do Porto, Porto, Portugal.
  13. A geometric description for subgroups of abelian-by-free groups. Thirteenth Barcelona Weekend in Group Theory (2018-04-27). room A2, Centre de Recerca Matemàtica, Barcelona, Spain.
  14. Enriched Stallings automata. UPV/EHU Algebra Seminar (2018-01). Facultad de Ciencias de la UPV/EHU, Leioa, Spain.
  15. Extending Stallings automata. Joint meeting of the Edinburgh Mathematical Society and Societat Catalana de Matemàtiques (Edinburgh Mathematical Society & Societat Catalana de Matemàtiques, 2017-09). International Centre for Mathematical Sciences (ICMS), Edinburgh, Scotland.
  16. Enriched automata and subgroups of free-abelian by free groups. Pure Math seminar (2017-09). University of Newcastle upon Tyne, Newcastle, UK.
  17. Extensions of free groups: algebraic, geometric and algorithmic aspects. PhD defense (Universitat Politècnica de Catalunya, 2017-09). Facultat de Matemàtiques i Estadística de la Universitat Politècnica de Catalunya, Barcelona, Spain.
  18. On the undecidability of the BNS invariant. 4º Congreso De Jóvenes Investigadores (2017-09). Universitat de València, Valencia, Spain.
  19. Stallings automata for Fn⋉Zm. Groups of intermediate growth in Seville (2017-07). Instituto Universitario de Investigación de Matemáticas (IMUS), Seville, Spain.
  20. Intersection problem for Droms groups. Geometric and Asymptotic Group Theory with Applications (GAGTA11) (GAGTA, 2017-06). Bizkaia Aretoa UPV/EHU, Bilbao, Spain.
  21. Membership problem for free-abelian by free groups. GrupsBCN seminar 2017 (GrupsBCN, 2017-06). Facultat de Matemàtiques i Estadística de la Universitat Politècnica de Catalunya, Barcelona, Spain.
  22. Algorithmic problems for partially commutative groups. Congreso Bienal de la Real Sociedad Matemática Española (RSME, 2017-01). Facultad de Educación de la Universidad de Zaragoza, Zaragoza, Spain.
  23. Representing Subgroups of [Free-abelian]-by-Free Groups and their Intersections. XI Encuentro en Teoría de Grupos (Red de Teoria de Grupos, 2016-09). Facultat de Matemàtiques i Estadística de la Universitat Politècnica de Catalunya, Barcelona, Spain.
  24. Exploding pullbacks & Intersections within Free-abelian times Free Groups. Geometric and Asymptotic Group Theory with Applications (GAGTA10) (GAGTA, 2016-06). Stevens Institute of Technology, NYC, New York, USA.
  25. Recognizing Z-extensions. New York Applied Algebra Colloquium (2015-11-30). The Graduate Center (CUNY), NYC, New York, USA.
  26. Stallings Graphs and Pullbacks for Zm×Fn. Algebra and Cryptography Seminar (2015-11). The Graduate Center (CUNY), NYC, New York, USA.
  27. Enriched Pullbacks and the Intersection Problem. Geometric and probabilistic methods in group theory and dynamical systems (2015-11). Texas A&M University (TAMU), College Station, Texas, USA.
  28. Stallings Foldings for Free-abelian times Free Groups. Geometric and Asymptotic Group Theory with Applications (GAGTA9) (GAGTA, 2015-09). CIRM (Luminy), Marseille, France.
  29. On the algorithmic recognition of certain classes of groups. GC Cryptography Student Seminar (2015-07). The Graduate Center (CUNY), NYC, New York, USA.
  30. Solvability and Unsolvability Results for Certain Cyclic Extensions. X Encuentro en Teoría de Grupos (Red de Teoria de Grupos, 2014-10). Instituto Universitario de Investigación de Matemáticas (IMUS), Sevilla, Spain.
  31. Isomorphism Problem for Unique Z-extensions. Geometric and Asymptotic Group Theory with Applications (GAGTA8) (2014-07). University of Newcastle, Newcastle, Australia.
  32. Direct Product of Free-abelian and Free Groups: Algebraic and Algorithmic Aspects. New York Applied Algebra Colloquium (2013-10-25). The Graduate Center (CUNY), NYC, New York, USA.
  33. Computing Intersections in Zm×Fn. Algebra and Cryptography Seminar (2013-10). The Graduate Center (CUNY), NYC, New York, USA.
  34. El Problema de la Intersecció a Zm×Fn. GrupsBCN seminar (GrupsBCN, 2013-10). Centre de Recerca Matemàtica (CRM), Bellaterra, Spain.
  35. Finite Index Problem for Free-Abelian times Free Groups. Geometric and Asymptotic Group Theory with Applications (GAGTA7, 2013) (2013-05). City College (CUNY), NYC, New York, USA.
  36. About Howson Property for Zm×Fn. IX Encuentro en Teoría de Grupos (2012-06). Instituto de Ciencias Matemáticas (ICMAT), Madrid, Spain.
  37. Whitehead problems for free times free-abelian groups. Seminari de teoria de grups (GrupsBCN, 2012). Centre de Recerca Matemàtica, Bellaterra, Spain.
  38. Subgroup Intersection Problem for Fn×Zm. Geometric and Asymptotic Group Theory with Applications (GAGTA5, 2011) (2011-07). Escola Politècnica Superior d’Enginyeria de Manresa (EUPM), Manresa, Spain.

Divulgative Talks

  1. Algú en dóna més?. Programa anem x + mates (FEEMCAT, 2025-02). Escola Politècnica Superior d’Enginyeria de Manresa (EPSEM), Manresa, Spain.
  2. Sobre les espatlles de gegants…. Programa anem x + mates (FEEMCAT, 2024-02). Escola Politècnica Superior d’Enginyeria de Manresa (EPSEM), Manresa, Spain.
  3. Fins a l’infinit… i més enllà?. Programa anem x + mates (FEEMCAT, 2023-02). Escola Politècnica Superior d’Enginyeria de Manresa (EPSEM), Manresa, Spain.
  4. Infinit com el mar?. Programa anem x + mates (FEEMCAT, 2022-02). Escola Politècnica Superior d’Enginyeria de Manresa (EPSEM), Manresa, Spain.
  5. Incertesa, backgammon i altres delícies. Programa anem x + mates (FEEMCAT, 2020-03). Escola Politècnica Superior d’Enginyeria de Manresa (EPSEM), Manresa, Spain.
  6. Sopa de nombres. Programa anem x + mates (2017) (FEEMCAT). Escola Politècnica Superior d’Enginyeria de Manresa (EPSEM), Manresa, Spain.
  7. Sopa de nombres. Programa 7demates (2017-18) (7demates). Escola Politècnica Superior d’Enginyeria de Manresa (EPSEM), Manresa, Spain.
  8. L’infinit és més gran del que et penses. Diada de la Ciència (2017) (Escola Daina-Isard). Escola Daina-Isard, Olesa de Montserrat, Spain.
  9. L’infinit és més gran del que et penses. Programa anem x + mates (2017) (FEEMCAT). Escola Politècnica Superior d’Enginyeria de Manresa (EPSEM), Manresa, Spain.
  10. L’infinit és més gran del que et penses. Programa 7demates (2016-17) (7demates). Escola Politècnica Superior d’Enginyeria de Manresa (EPSEM), Manresa, Spain.

Organization of Scientific Events

  • Eighteenth Barcelona Weekend in Group Theory. (GrupsBCN), May 2025, Facultat de Matemàtiques i Estadística (UPC), Barcelona, Spain.
  • Seventeenth Barcelona Weekend in Group Theory. (GrupsBCN), May 2024, Facultat de Matemàtiques i Estadística (UPC), Barcelona, Spain.
  • Sixteenth Barcelona Weekend in Group Theory. (GrupsBCN), May 2023, Facultat de Matemàtiques i Estadística (UPC), Barcelona, Spain.
  • Nineteenth Barcelona Weekend in Group Theory. (GrupsBCN), March 2026, Escola Politècnica Superior d’Enginyeria de Manresa (UPC), Manresa, Spain.
  • Fifteenth Barcelona Weekend in Group Theory. (GrupsBCN), June 2022, Facultat de Matemàtiques i Estadística (UPC), Barcelona, Spain.
  • Geometric and Asymptotic Group Theory with Applications (GAGTA5). (GAGTA), Jul 2011, Escola Politècnica Superior d’Enginyeria de Manresa (UPC), Manresa, Manresa, Spain.

Participation in Scientific Events

Conferences

  1. Nineteenth Barcelona Weekend in Group Theory. grupsBCN, Manresa, Spain (2026-03).
  2. Geometric and Asymptotic Group Theory with Applications (GAGTA 2025). Hoboken, USA (2025-06).
  3. Eighteenth Barcelona Weekend in Group Theory. grupsBCN, Barcelona, Spain (2025-05).
  4. 9th European Congress of Mathematics. European Mathematical Society, Seville, Spain (2024-07).
  5. Encontro Nacional da SPM 2024. Sociedade Portuguesa de Matemática, Braga, Portugal (2024-07).
  6. Seventeenth Barcelona Weekend in Group Theory. grupsBCN, Barcelona, Spain (2024-05).
  7. 4th Workshop on Geometric, Algebraic and Probabilistic Combinatorics. GAPCOMB, Montserrat, Spain (2023-07).
  8. Sixteenth Barcelona Weekend in Group Theory. grupsBCN, Barcelona, Spain (2023-05).
  9. II Encuentro Conjunto RSME-UMA. RSME-UMA, Ronda, Spain (2022-12).
  10. 3rd Workshop on Geometric, Algebraic and Probabilistic Combinatorics (GAPCOMB). GAPCOMB, Montserrat, Spain (2022-07).
  11. Fifteenth Barcelona Weekend in Group Theory. grupsBCN, Barcelona, Spain (2022-06).
  12. Groups in Madrid 2021. Autonomous University of Madrid, Campus Cantoblanco UAM, Spain (2021-06).
  13. Geometric and Asymptotic Group Theory with Applications (GAGTA14). GAGTA, Edinburgh, UK (Online event) (2021-06).
  14. GTA Gran Bilbao II. Facultad de Ciencias y Tecnología, University of the Basque Country, Leioa, Spain (2020-02).
  15. Fourteenth Barcelona Weekend in Group Theory. grupsBCN, Barcelona, Spain (2019-05).
  16. CMUP Post-doc meeting. Centro de Matemática Universidade do Porto, Porto, Portugal (2019-05).
  17. Algorithmic Problems in Group Theory. Leibniz Center for Informatics, Schloss Dagstuhl, Germany (2019-03).
  18. Semigroups, Automata and Languages Seminar. Centro de Matemática Universidade do Porto, Porto, Portugal (2018-11).
  19. Algebra and Logic Group Seminar. Centre of Mathematics and Applications Universidade Nova de Lisboa, Lisbon, Portugal (2018-11).
  20. XII Encuentro de Teoría de Grupos. Universidad de Zaragoza, Zaragoza, Spain (2018).
  21. Thirteenth Barcelona Weekend in Group Theory. grupsBCN, Barcelona, Spain (2018).
  22. Groups in Madrid 2017. Instituto de Ciencias Matemáticas (ICMAT), Madrid, Spain (2017).
  23. Joint meeting of the Edinburgh Mathematical Society and Societat Catalana de Matemàtiques. International Centre for Mathematical Sciences (ICMS), Edinburgh, Scotland (2017).
  24. 4º Congreso De Jóvenes Investigadores. Universitat de València, Valencia, Spain (2017).
  25. Geometric and Asymptotic Group Theory with Applications (GAGTA11). Bizkaia Aretoa UPV/EHU, Bilbao, Spain (2017).
  26. Twelfth Barcelona Weekend in Group Theory. grupsBCN, Barcelona, Spain (2017).
  27. Barcelona Mathematical Days 2017. Institut d’Estudis Catalans (IEC), Barcelona, Spain (2017).
  28. Congreso Bienal de la Real Sociedad Matemática Española 2017. Facultad de Educación de la Universidad de Zaragoza, Zaragoza, Spain (2017).
  29. XI Encuentro en Teoría de Grupos. Facultat de Matemàtiques i Estadística de la UPC, Barcelona, Spain (2016).
  30. Geometric and Asymptotic Group Theory with Applications (GAGTA10). Stevens Institute of Technology, NYC, USA (2016).
  31. Eleventh Barcelona Weekend in Group Theory. grupsBCN, Barcelona, Spain (2016).
  32. Algebra and Cryptography Seminar. The Graduate Center (CUNY), NYC, USA (2015).
  33. Geometric and probabilistic methods in group theory and dynamical systems. Texas A&M University (TAMU), College Station, Texas, USA (2015).
  34. New York Applied Algebra Colloquium. The Graduate Center (CUNY), NYC, USA (2015).
  35. Geometric and Asymptotic Group Theory with Applications (GAGTA9). CIRM, Marseille, France (2015).
  36. GC Cryptography Student Seminar. The Graduate Center (CUNY), NYC, USA (2015).
  37. Growth, Symbolic Dynamics and Combinatorics of Words. École normale supérieure, Paris, France (2015).
  38. Edinburgh Mathematical Society - Societat Catalana de Matemàtiques joint meeting. Institut d’Estudis Catalans (IEC), Barcelona, Spain (2015).
  39. Tenth Barcelona Weekend in Group Theory. grupsBCN, Barcelona, Spain (2015).
  40. Workshop on homological algebra. Instituto de Ciencias Matemáticas (ICMAT), Madrid, Spain (2015).
  41. Barcelona Mathematical Days 2014. Institut d’Estudis Catalans (IEC), Barcelona, Spain (2014).
  42. X Encuentro en Teoría de Grupos. Instituto Universitario de Investigación de Matemáticas (IMUS), Sevilla, Spain (2014).
  43. Geometric and Asymptotic Group Theory with Applications (GAGTA8). University of Newcastle, Newcastle, Australia (2014).
  44. Ninth Barcelona Weekend in Group Theory. grupsBCN, Barcelona, Spain (2014).
  45. New York Group Theory Seminar. The Graduate Center (CUNY), NYC, USA (2013).
  46. Algebra and Cryptography Seminar. The Graduate Center (CUNY), NYC, USA (2013).
  47. New York Applied Algebra Colloquium. The Graduate Center (CUNY), NYC, USA (2013).
  48. Geometric and Asymptotic Group Theory with Applications (GAGTA7). City College (CUNY), NYC, USA (2013).
  49. Eighth Barcelona Weekend in Group Theory. grupsBCN, Barcelona, Spain (2013).
  50. Conference on Automorphisms of Free Groups. Bellaterra, Spain (2012).
  51. Geometric and Asymptotic Group Theory with Applications (GAGTA6). GAGTA, Düsseldorf, Germany (2012).
  52. IX Encuentro en Teoría de Grupos. Red Ibérica de Teoría de Grupos, Madrid, Spain (2012).
  53. Seventh Barcelona Weekend in Group Theory. grupsBCN, Barcelona, Spain (2012).
  54. Geometric and Asymptotic Group Theory with Applications (GAGTA5). GAGTA, Manresa, Spain (2011).
  55. Sixth Barcelona Weekend in Group Theory. grupsBCN, Barcelona, Spain (2011).
  56. Fifth Barcelona Weekend in Group Theory. grupsBCN, Barcelona, Spain (2010).

Seminars

  • GrupsBCN seminar. GrupsBCN, Centre de Recerca Matematica & Facultat de Matemàtiques i Estadística, Universitat Politècnica de Catalunya, Barcelona, Spain (2011 - present).
  • Algebra Seminar. Department of Mathematics UPV/EHU, Department of Mathematics UPV/EHU, Leioa, Spain (2018 - 2021).
  • Semigroups, Automata and Languages Seminar. Centro de Matemática, Universidade do Porto, Centro de Matemática, Universidade do Porto, Porto, Portugal (2018 - 2019).
  • New York Group Theory Seminar (Magnus Seminar). Graduate Center, CUNY, Graduate Center, CUNY, New York, USA (2015).

Teaching

Graduate Courses

  • Non-Commutative Algebra. Master in Advanced Mathematics and Mathematical Engineering (Universitat Politècnica de Catalunya). Facultat de Matemàtiques i Estadística (UPC), Barcelona, Spain (2025-09).
  • Non-Commutative Algebra. Master in Advanced Mathematics and Mathematical Engineering (Universitat Politècnica de Catalunya). Facultat de Matemàtiques i Estadística (UPC), Barcelona, Spain (2024-09).
  • Stallings Automata and Applications. BGSMath Advanced Graduate Course (BGSMath). Centre de Recerca Matemàtica, Online course, Spain (2023-01).
  • Non-Commutative Algebra. Master in Advanced Mathematics and Mathematical Engineering (Universitat Politècnica de Catalunya). Facultat de Matemàtiques i Estadística (UPC), Barcelona, Spain (2022-09).

Undergraduate Courses

  • Matemàtiques III. Grau en Enginyeria (Universitat Politècnica de Catalunya). Escola Politècnica Superior d’Enginyeria de Manresa (UPC), Manresa, Spain (2025-2026).
  • Àlgebra. Grau en Enginyeria d’Automoció (Universitat Politècnica de Catalunya). Escola Politècnica Superior d’Enginyeria de Manresa (UPC), Manresa, Spain (2025-2026).
  • Discrete Mathematics and Optimization. Bachelors degree in Bioinformatics (Universitat Politècnica de Catalunya). Barcelona School of Informatics (FIB), Barcelona, Spain (2024-2025).
  • Àlgebra. Grau en Enginyeria d’Automoció (Universitat Politècnica de Catalunya). Escola Politècnica Superior d’Enginyeria de Manresa (UPC), Manresa, Spain (2024-2025).
  • Matemàtiques II. Grau en Enginyeria (Universitat Politècnica de Catalunya). Escola Politècnica Superior d’Enginyeria de Manresa (UPC), Manresa, Spain (2023-2024).
  • Matemàtiques I. Grau en Enginyeria (Universitat Politècnica de Catalunya). Escola Politècnica Superior d’Enginyeria de Manresa (UPC), Manresa, Spain (2023-2024).
  • Matemàtiques I. Grau en Enginyeria (Universitat Politècnica de Catalunya). Escola Politècnica Superior d’Enginyeria de Manresa (UPC), Manresa, Spain (2022-2023).
  • Matemàtiques II. Grau en Enginyeria (Universitat Politècnica de Catalunya). Escola Politècnica Superior d’Enginyeria de Manresa (UPC), Manresa, Spain (2021-2022).
  • Probability and Statistics. Grau en Enginyeria (Universitat Politècnica de Catalunya). Escola d’Enginyeria de Terrassa (UPC), Terrassa, Spain (2014-2015).
  • Statistics. Grau en Enginyeria (Universitat Politècnica de Catalunya). Escola Politècnica Superior d’Enginyeria de Manresa (UPC), Manresa, Spain (2013-2014).
  • Matemàtiques I. Grau en Enginyeria (Universitat Politècnica de Catalunya). Escola Politècnica Superior d’Enginyeria de Manresa (UPC), Manresa, Spain (2012-2013).
  • Statistics. Grau en Enginyeria (Universitat Politècnica de Catalunya). Escola Politècnica Superior d’Enginyeria de Manresa (UPC), Manresa, Spain (2012-2013).
  • Scientific Methodology and Biostatistics. Fundació universitària del Bages (Fundació universitària del Bages). Fundació universitària del Bages, Manresa, Spain (2011-2012).

Other Courses

  • Introduction to Stallings Automata and the Geometry of Subgroups of Free Groups. Barcelona Introduction to Mathematical Research (BGSMath). Centre de Recerca Matemàtica, Campus Bellaterra & online, Spain (2025-07).
  • Fonaments de Matemàtiques Preuniversitaries. Programa d’accés a la Universitat (Universitat Politècnica de Catalunya). Escola Politècnica Superior d’Enginyeria de Manresa (UPC), Manresa, Spain (2012-2013).

Direction and Mentoring

  • Codirector of TFG thesis: Covering spaces. Bachelor in Mathematics. Facultat de Matemàtiques i Estadística (UPC). Student: Raul Toribio. In progress (since 2026).
  • Codirector of MSc thesis: Embeddings between Droms groups. Master in Advanced Mathematics and Mathematical Engineering. Facultat de Matemàtiques i Estadística (UPC). Student: Bernat Coderch. In progress (since 2026).
  • Codirector of PhD thesis: TBA. Doctoral Program in Mathematics. Facultat de Matemàtiques i Estadística (UPC). Student: Lluis Carmona. In progress (since 2026).
  • Codirector of PhD thesis: Intersection configurations in some rational extensions. Doctoral Program in Mathematics. Facultat de Matemàtiques i Estadística (UPC). Student: Antoni Massegú. In progress (since 2025).
  • Codirector of MSc thesis: Free by free-abelian groups: isomorphisms and algorithmic questions. Master in Advanced Mathematics and Mathematical Engineering. Facultat de Matemàtiques i Estadística (UPC). Student: Lluis Carmona. 10/10 - MH (2026).
  • Director of TFG thesis: Extending Stallings automata: A graph-theoretic approach to intersections beyond free groups. Bachelor in Mathematics. Facultat de Matemàtiques i Estadística (UPC). Student: Leila Kerroum. 9.5/10 - MH (2025).
  • Director of MSc thesis: Counting subgroups using Stallings automata and generalizations. Master in Advanced Mathematics and Mathematical Engineering. Facultat de Matemàtiques i Estadística (UPC). Student: Paloma López Larios. 10/10 - MH (2023).
  • Mentor of Summer School. Barcelona Introduction to Mathematical Research 2023 Summer Program. UPC. Students: Edgar Moreno, Kamil Przybyszewsk. completed (2023).

Other mathematical activities

Journal Edition

  • Assistant editor of Notícies de la Societat Catalana de Matemàtiques (2019-2021)

Refereeing and Review

  • Reviewer for American Mathematical Society (Mathematical Reviews / MathSciNet) (2019-present)

Scientific Committees

  • Examination committee member for the PhD thesis entitled Spaces of left-preorders on groups, Doctoral Program in Mathematical Research, Universidad Complutense de Madrid, candidate: Iván Chércoles Cuesta (2025-07).
  • Examination committee member for the Master’s thesis entitled Groups Acting on Trees: Thompson, Grigorchuk and Röver, Master in Advanced Mathematics and Mathematical Engineering, Facultat de Matemàtiques i Estadística, Universitat Politècnica de Catalunya (UPC), candidate: Àlex Garcia Herranz (2024).
  • Examination committee member for the Master’s thesis entitled Generalizations of word and conjugacy problems in Right Angled Artin Groups, Master in Advanced Mathematics and Mathematical Engineering, Facultat de Matemàtiques i Estadística, Universitat Politècnica de Catalunya (UPC), candidate: Javier Enrique Mejia Esquivel (2024-06-26).
  • Examination committee member for the Master’s thesis entitled Counting subgroups using Stallings automata and generalizations, Master in Advanced Mathematics and Mathematical Engineering, Facultat de Matemàtiques i Estadística, Universitat Politècnica de Catalunya (UPC), candidate: Paloma López Larios (2023-08-31).
  • Examination committee member for the PhD proposal, Doctoral Program in Mathematics, Universitat Politècnica de Catalunya (UPC), candidate: M. Roy (2018).

Divulgation

  • Outreach contributor of Anem x + matemàtiques program (2016-present).
  • Outreach contributor of 7demates program (2016-2019).
  • Translator (Spanish to Catalan) of the Intermatia interactive mathematical platform program (2020-2024).

Professional Associations and Memberships

  • Member of BarCeloNa Group Theory (GrupsBCN) research group, Barcelona (Jan 2013 – Present).
  • Member of Geometric, Algebraic and Probabilistic Combinatorics (GAPCOMB) research group, UPC (Jan 2022 – Present).
  • Member of BGSMath Postdoctoral Community (Jan 2022 – Present).
  • Member of Groups, Topology and Applications (GTA) research group, Bilbao (Jan 2020 – Dec 2021).
  • Member of European Mathematical Society (EMS) (Jan 2017 – Present).
  • Member of Societat Catalana de Matemàtiques (SCM) (Jan 2015 – Present).

Languages

English, Spanish, and Catalan.