I am a Post Doctoral Research Associate in Pure Mathematics at the University of Manchester. Previously, I was a PostDoc in Saarbrücken (Universität des Saarlandes), Milan (Politecnico di Milano) and Porto after obtaining my doctorate in Theoretical Computer Science in Stuttgart.

I work in the interdisciplinary area between Informatics/Computer Science and Mathematics and have contributed to both fields. My main research focus lies in the application of algebraic methods (in particular: semigroup and group theory) to this area.

Research Interests

I primiarly work on the decidability and complexity of algorithmic questions over groups and semigroups and attached questions on the structure of such objects. Of particular importance to me, are self-similar structures and algebraic objects connected to automaton theory (in particular, automaton groups and semigroups). Additionally, I investigate varieties of finite monoids/semigroups connected to formal language theory and their attached profinite objects to describe them using logic and combinatorial methods. I also work on structural semigroup theory with an emphasis on inverse semigroups and recently started to work on equations over groups.

But I am always happy to explore further areas of Computer Science and Mathematics.

Education & Career

Publications

see also ORCID (all publications), MathSciNet (Mathematics publications) and dblp (Computer Science publications)

Highlights

  • paper on the freeness problem for automaton semigroups at MFCS 2024 (invited to the special issue)
  • paper constructing an automaton group with PSpace-complete word problem in the STACS 2020 special issue
  • paper on infinite automaton (semi)groups having infinite orbits in Journal of Algebra
  • book chapter on the word problem for automaton groups
  • doctoral thesis

All Publications (chronologically, newest first)

Peer Reviewed

  1. Equations in wreath products
    Journal Paper Semigroup Forum (2025)
    with Laurent Bartholdi, Ruiwen Dong and Leon Pernak
    10.1007/s00233-025-10511-8 2410.04905 [math.GR]
  2. The Freeness Problem for Automaton Semigroups
    Conference Paper 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)
    with Daniele D’Angeli and Emanuele Rodaro, invited to the special issue
    10.4230/LIPIcs.MFCS.2024.44 2402.01372 [cs.FL]
  3. The Word Problem for Finitary Automaton Groups
    Conference Paper 25th International Conference on Descriptional Complexity of Formal Systems (DCFS 2023)
    with Maximilian Kotowsky, invited to the special issue
    10.1007/978-3-031-34326-1_7 2302.10670 [cs.FL]
  4. An Automaton Group with PSpace-Complete Word Problem
    Journal Paper Theory of Computing Systems 67.1 (2023)
    with Armin Weiß, special issue for STACS 2020 conference version
    10.1007/s00224-021-10064-7 1906.03424 [cs.FL]
  5. On the Orbits of Automaton Semigroups and Groups
    Journal Paper Algebra and Discrete Mathematics 33.1 (2022)
    with Daniele D’Angeli, Dominik Francoeur and Emanuele Rodaro
    10.12958/adm1692 2007.10273 [cs.FL]
  6. Erratum to “On the Orbits of Automaton Semigroups and Groups”
    Journal Paper Israel Journal of Mathematics 245.2 (2021)
    with Daniele D’Angeli and Emanuele Rodaro corrected paper
    s11856-021-2206-1 1712.07408v3 [cs.FL]
  7. On Orbits and the Finiteness of Bounded Automaton Groups
    Journal Paper International Journal of Algebra and Computation 31.06 (2021)
    Special Issue on Papers From the Conference “Semigroups and Groups, Automata, Logics (SandGAL 2019)”
    with Ievgen Bondarenko
    10.1142/S0218196721400087 1912.06897 [math.GR]
  8. On the structure theory of partial automaton semigroups
    Journal Paper Semigroup Forum 101 (2020)
    with Daniele D’Angeli and Emanuele Rodaro
    10.1007/s00233-020-10114-5 1811.09420 [cs.FL]
  9. Infinite automaton semigroups and groups have infinite orbits
    Journal Paper Journal of Algebra 553 (2020)
    with Daniele D’Angeli, Dominik Francoeur and Emanuele Rodaro
    10.1016/j.jalgebra.2020.02.014 1903.00222 [cs.FL]
  10. An Automaton Group with PSpace-Complete Word Problem
    Conference Paper 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)
    with Armin Weiß, invited to the special issue journal version
    10.4230/LIPIcs.STACS.2020.6 1906.03424 [cs.FL]
  11. Orbit Expandability of Automaton Semigroups and Groups
    Journal Paper Theoretical Computer Science 809 (2020)
    with Daniele D’Angeli and Emanuele Rodaro
    10.1016/j.tcs.2019.12.037 1812.07359 [cs.FL]
  12. On the Orbits of Automaton Semigroups and Groups
    Journal Paper Israel Journal of Mathematics 237.1 (2020)
    with Daniele D’Angeli and Emanuele Rodaro erratum
    10.1007/s11856-020-1972-5 1712.07408 [cs.FL]
  13. The Word Problem for Omega-Terms over the Trotter-Weil Hierarchy
    Journal Paper Theory of Computing Systems 62.3 (2018)
    with Manfred Kufleitner, special issue for CSR 2016 conference version
    10.1007/s00224-017-9763-z 1509.05364
  14. On the complexity of the word problem for automaton semigroups and automaton groups
    Journal Paper Advances in Applied Mathematics 90 (2017)
    with Daniele D’Angeli and Emanuele Rodaro
    10.1016/j.aam.2017.05.008 1611.09541 [cs.FL]
  15. The Word Problem for Omega-Terms over the Trotter-Weil Hierarchy (Extended Abstract)
    Conference Paper 11th International Computer Science Symposium in Russia (CSR 2016)
    with Manfred Kufleitner, invited to the special issue journal version
    10.1007/978-3-319-34171-2_17 1509.05364 [cs.FL]

Preprints & Non-Peer Reviewed Works

  1. The Word Problem for (ω−1)-Terms over DAb
    Preprint 2024
    with Jorge Almeida and Manfred Kufleitner
    2411.08523 [cs.FL]
  2. The Word Problem for Automaton Groups
    Book Chapter Chapter 6 of Automata and Languages: GAGTA BOOK 3
    De Gruyter, 2024
    with Armin Weiß, Ed. by Benjamin Steinberg
    10.1515/9783110984323-006 978-3-11-099642-5
  3. The Finiteness Problem for Automaton Semigroups of Extended Bounded Activity
    Preprint 2024
    with Daniele D’Angeli and Emanuele Rodaro
    2406.20056 [cs.FL]
  4. Preserving self-similarity in free products of semigroups
    Preprint 2024
    with Tara Macalister Brough and Janette Welker
    2003.12810v3 [math.GR]
  5. Every numerical semigroup arises as an automaton monoid
    Preprint 2024
    with Tara Macalister Brough and Alan J. Cain
    2303.12715 [math.GR]
  6. The Self-Similarity of Free Semigroups and Groups
    Proceedings Paper Logic, Algebraic system, Language and Related Areas in Computer Science; RIMS Kôkyûroku 2229 (2022)
    with Emanuele Rodaro
    2205.10248 [math.GR]
  7. Two-Variable Ehrenfeucht-Fraisse Games over Omega-Terms
    Preprint 2014
    with Manfred Kufleitner
    1411.0593 [cs.LO]

Theses

  • Doctoral Thesis
    Automaton Structures – Decision Problems and Structure Theory
    Universität Stuttgart, Advisor: Volker Diekert
    10.18419/opus-11267
  • Diploma Thesis
    Das Wortproblem für Omega-Terme über Zweivariablenlogik
    Universität Stuttgart, in German, Advisor: Manfred Kufleitner, Examiner: Volker Diekert
    10.18419/opus-3431
  • Studienarbeit (Senior Thesis)
    Kaskadenzerlegung spezieller Automatenklassen
    Universität Stuttgart, in German, Advisor: Manfred Kufleitner, Examiner: Volker Diekert
    10.18419/opus-3170

Talks

Date Title & Location
2025-03-12 Solving Spherical Equations in Wreath Products of Abelian Groups External Seminar Talk
Algebra, Geometry and Topology (MAXIMALS) seminar
Heriot-Watt University, Edinburgh, UK
2025-02-07
& 2025-02-21 		An introduction to contracting automaton semigroups and monoids Mini Course
Semigroup Theory Seminar
University of Manchester, UK
2024-10-18 A Ranker-Based Description for DAb with Applications Internal Seminar Talk
Semigroup Theory Seminar
University of Manchester, UK
2024-08-26 The Freeness Problem for Automaton Semigroups Cs Conference Talk
49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)
Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia
2024-08-22 The Word and Separation Problem for DAb External Seminar Talk
Max Planck Institute for Software Systems (MPI-SWS), Kaiserslautern, Germany
2024-06-21 Decision Problems for Automaton Semigroups and Groups Invited Workshop Talk
North British Semigroups and Applications Network (NBSAN) Satellite Meeting to the 75th British Mathematical Colloquium (BMC 2024)
University of Manchester, UK
2024-02-05 Recent Developments on Decision Problems for Automaton Groups and Semigroups Contributed Maths Talk
Geometric and Asymptotic Group Theory with Applications (GAGTA) 2024
Centre International de Rencontres Mathématiques (CIRM), Marseille, France
2023-12-15 Decision Problems for Automaton Groups and Monoids of Bounded Activity External Seminar Talk
Noon-Seminar
Universität des Saarlandes (Saarbrücken), Germany
2023-07-06 The Word Problem for Finitary Automaton Groups Cs Conference Talk
25th International Conference on Descriptional Complexity of Formal Systems (DCFS 2023)
Universität Potsdam, Germany
2022-11-14 Decidability Results and Open Problems for Automaton Structures External Seminar Talk
Seminario Al@Bicocca
Università degli Studi di Milano-Bicocca, Italy (hybrid)
2022-07-18 Decision Problems for Automaton Semigroups Contributed Maths Talk
Encontro Nacional, Sociedade Portuguesa de Matemática (ENSPM 2022)
Instituto Politécnico de Tomar, Portugal (online)
2022-04-22 Eine Ranker-Beschreibung für DAb External Seminar Talk
Oberseminar der Theoretischen Informatik
Institut für Formale Methoden der Informatik, Universität Stuttgart, Germany
2022-03-22 A Combinatorial Description for DAb Internal Seminar Talk
Seminar on Semigroups, Automata and Languages
Centro de Matemática, Universidade do Porto, Portugal (online)
2021-12-10 Automaton and Non-Automaton Semigroups Invited Maths Talk
Research Seminar Program 2021
Centro de Matemática, Universidade do Porto, Portugal
2021-11-12 Automata and Algebra Invited Maths Talk
CMUP New Members Meeting (Part 1)
Centro de Matemática, Universidade do Porto, Portugal
2021-02-01 Variants of the Word Problem for Automaton Structures External Seminar Talk
Algebra and Logic Seminar
Centro de Matemática e Aplicações, Universidade NOVA de Lisboa, Portugal (online)
2020-11-06 Automaton Structures: Structure Theory and Decision Problems External Seminar Talk
Seminar on Semigroups, Automata and Languages
Centro de Matemática, Universidade do Porto, Portugal (online)
2020-04-17 An Automaton Group with PSpace-Complete Word Problem External Seminar Talk
Automata Seminar
Institut de Recherche en Informatique Fondamentale, Université de Paris, France (online)
2020-03-13 Infinite Automaton Semigroups and Groups Have Infinite Orbits Contributed Cs Talk
37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)
Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier/Université de Montpellier, France
2020-03-11 An Automaton Group with PSpace-Complete Word Problem Cs Conference Talk
37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)
Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier/Université de Montpellier, France
2019-06-10 Automaton Structures: Decision Problems and Structure Results Contributed Maths Talk
Semigroups and Groups, Automata, Logics (SandGAL)
Cremona Campus, Politecnico di Milano, Italy
2019-02-11 Inverse and Partial Automaton Semigroups Invited Workshop Talk
Workshop on Groups, Automata and Graphs
Technische Universität Graz, Austria
2017-11-13 Decision Problems and Automaton Structures External Seminar Talk
Strukturtheorie-Seminar
Institut für Diskrete Mathematik, Technische Universität Graz, Austria
2015-03-20 The Word Problem for Omega Terms over Two Variable Logic External Seminar Talk
Seminar on Semigroups, Automata and Languages
Centro de Matemática, Universidade do Porto, Portugal (online)