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 x^p y^q = z^r 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 (Manuscripta Mathematica, 168, pages 549–570 (2022)) 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 (ICALP 2019, 46th International Colloquium on Automata, Languages, and Programming) 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, 245, pages 869–920 (2021)) 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 (J. of Algebra, Vol. 591, 2022, 538 - 576) arxiv

Variations on the Post Correspondence Problem for free groups,
    with Alan Logan (DLT 2021, Developments in Language Theory pp 90–102) arxiv

Formal conjugacy growth in graph products I,
    with Susan Hermiller and Valentin Mercier (Groups, Geometry and Dynamics, Vol.17 (2023), no. 2, pp. 427–457) arxiv

Rational sets in virtually abelian groups: languages and growth,
    with Alex Evetts (L’Enseignement Mathematique, to appear 2023) arxiv

Group equations with abelian predicates,
    with Albert Garreta (Int. Math. Res. Notices, to appear 2024) arxiv

The Post Correspondence Problem: From Computer Science to Algebra,
    (LNCS, vol. 13608, Reachability Problems 2022, p. 28 - 36) publication

Post's correspondence problem for hyperbolic and virtually nilpotent groups,
    with Alex Levine and Alan Logan (Bulletin of the LMS, to appear 2024) arxiv

Languages, groups and equations,
    with Alex Levine (submitted 2023, to appear as Chapter in GAGTA book 3) arxiv

Effective equation solving, constraints and growth in virtually abelian groups,
    with Alex Evetts and Alex Levine (submitted 2023) arxiv

Formal conjugacy growth in graph products II,
    with Susan Hermiller and Valentin Mercier (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

Alex Levine (Heriot-Watt, 2022): Equations in groups, formal languages and complexity

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