Theses

  • On the complexity of the endomorphism problem in free groups 
        (PhD thesis, Rutgers University, USA, 2005)
     
  • Algorithmic, asymptotic and combinatorial facets of the Diophantine Problem in groups 
        (Habilitation, Fribourg University, Switzerland, 2013)
     

    Papers

  • Polynomial-time complexity for instances of the endomorphism problem in free groups 
        (International Journal of Algebra and Computation, Vol.17, No.2, 289-328, 2007) CRM Preprint (pdf)

  • Two examples in the Galois theory of free groups, CRM Preprint (pdf)
       with Warren Dicks    (Journal of Algebra, Vol. 305, Issue 1, 540-547, 2006)

  • Characterization of non-minimal tree actions,
        with Lisa Carbone    (Rev. Roumaine Math. Pures Appl., Tome 52, 4, 377-388, 2007)

  • Restricted walks in regular trees,
        with Sasa Radomirovic (Electronic Journal of Combinatorics, Vol. 13, R93, 2006) CRM Preprint (pdf)

  • Automorphism group and canonical form algorithms for finite solvable groups,
        with M. Slattery and M. Smith (Preprint 2006)

  • The equation xp yq = zr and groups that act freely on Λ-trees,
        with N. Brady, A. Martino and S. O Rourke (Transactions of the AMS, 361, 223-236, 2009) CRM Preprint (pdf)

  • Generic intersections of subgroups in free groups and the Hanna Neumann Conjecture,
        with A. Martino and E. Ventura CRM Preprint 2007(pdf)

  • The monomorphism problem in free groups,
        with A. Ould Houcine (Archiv der Mathematik, Volume 94, Issue 5, Page 423-436, 2010) older version on arxiv

  • On Lyndon's equation in some HNN-extensions and Lambda-free groups,
        with B. Fine and G. Rosenberger. (Journal of Group Theory, Vol.14, 333-339, 2011)

  • On the asymptotics of visible elements and homogeneous equations in surface groups,
        with Y. Antolin Pichel and N. Viles (Groups, Geometry and Dynamics, 6, Issue 4, 619-638, 2012) arxiv

  • Rapid Decay is Preserved by Graph Products,
        with Derek F. Holt and Sarah Rees (Journal of Topology and Analysis, Vol. 5, No. 2, 225 - 237, 2013) arxiv

  • Rapid decay and Baum-Connes for large type Artin groups,
        with Derek F. Holt and Sarah Rees (Trans. Amer. Math. Soc., 368, 6103-6129, 2016) arxiv

  • Geodesic growth in right-angled and even Coxeter groups,
        with Yago Antolin (European Journal of Combinatorics, 34, 859-874, 2013) arxiv

  • Conjugacy growth series and languages in groups,
        with Susan Hermiller (Trans. Amer. Math. Soc. 366, 2803-2825, 2014) arxiv

  • The surface group conjecture: Cyclically pinched and conjugacy pinched one-relator groups,
        with B. Fine and G. Rosenberger pdf (Results in Mathematics, Volume 64, Issue 1, 175 - 184, 2013)

  • Classes of Groups Generalizing a Theorem of Benjamin Baumslag,
        with B. Fine and G. Rosenberger pdf (Comm. in Algebra, 44:656 - 667, 2016)

  • Sofic groups: graph products and graphs of groups,
        with Derek F. Holt and Sarah Rees (Pacific Journal of Mathematics, Vol. 271, No. 1, 53-64, 2014) arxiv

  • Conjugacy languages in groups,
        with Derek Holt, Susan Hermiller and Sarah Rees (Israel Journal of Mathematics, 211, 311-347, 2016) arxiv

  • Finite generating sets of relatively hyperbolic groups and applications to geodesic languages,
        with Yago Antolin, (Trans. Amer. Math. Soc., Volume 368, Number 11, 7965-8010, 2016) arxiv

  • Permutations of context-free, ET0L and indexed languages,
        with Tara Brough, Murray Elder and Georg Zetzsche (Discrete Mathematics & Theoretical Computer Science, vol 17:3, 167-178, 2016) arxiv

  • Solution sets for equations over free groups are EDT0L languages,
        with Volker Diekert and Murray Elder (conference version, ICALP 2015, Kyoto) arxiv

  • Geodesic growth of right-angled Coxeter groups based on trees,
        with Alex Kolpakov (Journal of Algebraic Combinatorics, 44(2), 249-264, 2016) arxiv

  • Solution sets for equations over free groups are EDT0L languages,
        with Volker Diekert and Murray Elder (journal version, IJAC, 26:5, 843-886, 2016) arxiv

  • Formal conjugacy growth in acylindrically hyperbolic groups,
        with Yago Antolin, (Int. Math. Res. Notices, 1, 1-37, 2017) arxiv

  • The generalised word problem in hyperbolic and relatively hyperbolic groups,
        with Derek F. Holt and Sarah Rees (J. of Algebra, Vol.516, 149-171, 2018) arxiv

  • Applications of L systems to group theory,
        with Murray Elder and Michal Ferov (IJAC, Vol.28, No.2, 309-329, 2018) arxiv

  • Free subgroups of free products and combinatorial hypermaps,
        with Alexander Kolpakov (Discrete Mathematics, Vol. 342, 1415 - 1433, 2019) arxiv

  • The conjugacy ratio of groups,
        with Charles Cox and Armando Martino (Proc. of the Edinburgh Math. Soc., Vol. 62, 895-911, 2019) arxiv

  • Three-dimensional maps and subgroup growth,
        with Remi Bottinelli and Alexander Kolpakov (submitted) arxiv

  • Equations in groups that are virtually direct products,
        with Derek F. Holt and Sarah Rees (J. of Algebra, Vol.545, 88-99, 2020) arxiv

  • Solution sets to systems of equations in hyperbolic groups are EDT0L in PSPACE,
        with Murray Elder (conference version, ICALP 2019, Greece) arxiv

  • The conjugacy growth of the soluble Baumslag-Solitar groups,
        with Alex Evetts and Meng-Che 'Turbo' Ho (New York Journal of Mathematics, 2020) arxiv

  • The complexity of solution sets to equations in hyperbolic groups,
        with Murray Elder (Israel Journal of Maths, to appear) arxiv

  • The Post Correspondence Problem and equalisers for certain free group and monoid morphisms,
        with Alan Logan (ICALP 2020) arxiv

  • Fixed points and stable images of endomorphisms for the free group of rank two,
        with Alan Logan (submitted) arxiv

    Manuscripts

  • Decompositions of finitely generated groups   (Report about JSJ decompostions)
  • Representation theory and combinatorics   (Undergraduate Honors Thesis)

    PhD Theses Supervised

    Julie Brönnimann (Neuchâtel, 2016): Geodesic Growth of Groups

    Valentin Mercier (Neuchâtel, 2017): Conjugacy Growth Series in Groups

    Alex Evetts (Heriot-Watt, 2020): Aspects of Growth in Finitely Generated Groups

    Master Theses Supervised

    Michele Feltz (Fribourg, 2010):  On the Conjugacy Problem in Groups and its Variants

    Karin Comino (Fribourg, 2011):  Struktur und Wachstum von Graph Produkten

    Fabio Teles (Neuchâtel, 2016): Problèmes de Décision

    Charles Ashford (Heriot-Watt, 2017): At the Limit of Computability: Turing Machines and Unsolvable Problems

    Philoktitis Abel Velegrakis (Heriot-Watt, 2018): Coxeter groups: measuring the symmetry of shapes and spaces