Toke Meier Carlsen

Toke Meier Carlsen

I worked as a professional mathematician from 2001 to 2022. I now work as a software developer, but still do a little bit of mathematical research in my spare time. Below is a list of my research publications and some of my research talks.


  1. Conjugacy of local homeomorphisms via groupoids and C*-algebras.
    With Becky Armstrong, Kevin Aguyar Brix and Søren Eilers.
    arXiv:2105.00479, 19 pages.

  2. Shift equivalence through the lens of Cuntz-Krieger algebras.
    With Adam Dor-On and Søren Eilers.
    arXiv:2011.10320, 36 pages.

  3. Symbolic Dynamics, Partial Dynamical Systems, Boolean Algebras and C*-algebras Generated by Partial Isometries.
    arXiv:math/0604165, 55 pages.

Peer-reviewed research papers

  1. Condition (K) for Boolean dynamical systems.
    With Eun Ji Kang.
    J. Aust. Math. Soc., 112 (2022), 145–169.

  2. Orbit equivalence of higher-rank graphs.
    With James Rout.
    J. Operator Theory, 86 (2021), 395–424.

  3. Reconstruction of groupoids and C*-rigidity of dynamical systems.
    With Efren Ruiz, Aidan Sims and Mark Tomforde.
    Adv. Math., 390 (2021), 107923.

  4. Cuntz-Krieger algebras and one-sided conjugacy of shifts of finite type and their groupoids.
    With Kevin Aguyar Brix.
    J. Aust. Math. Soc., 109 (2020), 289–298.

  5. C*-algebras, groupoids and covers of shift spaces.
    With Kevin Aguyar Brix.
    Trans. Amer. Math. Soc. Ser. B 7 (2020), 134–185.

  6. Gauge-invariant ideals of C*-algebras of Boolean dynamical Systems.
    With Eun Ji Kang.
    J. Math. Anal. Appl. 488 (2020), 124037, 27 pages.

  7. Flow Equivalence of G-SFTs.
    With Mike Boyle and Søren Eilers.
    Trans. Amer. Math. Soc. 373 (2020), 2591–2657.

  8. Topological freeness for C*-correspondences.
    With Eduard Ortega and Bartosz Kwaśniewski.
    J. Math. Anal. Appl. 473 (2019), 749–785.

  9. Flow equivalence and orbit equivalence for shifts of finite type and isomorphism of their groupoids.
    With Søren Eilers, Eduard Ortega and Gunnar Restorff.
    J. Math. Anal. Appl. 469 (2019), 1088–1110.

  10. Orbit equivalence of graphs and isomorphism of graph groupoids.
    With Marius Lie Winger.
    Math. Scand. 123 (2018), 239–248.

  11. Flow equivalence of sofic shifts.
    With Mike Boyle and Søren Eilers.
    Isr. J. Math. 225 (2018), 111–146.

  12. Diagonal-preserving graded isomorphisms of Steinberg algebras.
    With James Rout.
    Commun. Contemp. Math. 20 (2018), 25 pages.

  13. *-isomorphism of Leavitt path algebras over ℤ.
    Adv. Math. 324 (2018), 326–335.

  14. Diagonal-preserving gauge-invariant isomorphisms of graph C*-algebras.
    With James Rout.
    J. Funct. Anal. 273 (2017), 2981–2993.

  15. C*-algebras associated to Boolean dynamical systems.
    With Eduard Ortega and Enrique Pardo.
    J. Math. Anal. Appl. 450 (2017), 727–768.

  16. Strong classification of purely infinite Cuntz-Krieger algebras.
    With Gunnar Restorff and Efren Ruiz.
    Trans. Amer. Math. Soc. B 4 (2017), 1–30.

  17. Equivalence and stable isomorphism of groupoids, and diagonal-preserving stable isomorphisms of graph C*-algebras and Leavitt path algebras.
    With Efren Ruiz and Aidan Sims.
    Proc. Amer. Math. Soc. 145 (2017), 1581–1592.

  18. Flow equivalence and isotopy for subshifts.
    With Mike Boyle and Søren Eilers.
    Dyn. Syst. 32 (2017), 305–325.

  19. Graph algebras and orbit equivalence.
    With Nathan Brownlowe and Michael F. Whittaker.
    Ergodic Theory Dynam. Systems 37 (2017), 389–417.

  20. C*-algebras of labelled graphs III - K-theory computations.
    With Teresa Bates and David Pask.
    Ergodic Theory Dynam. Systems 37 (2017), 337–368.

  21. On Hong and Szymanski’s description of the primitive-ideal space of a graph algebra.
    With Aidan Sims.
    Operator Algebras and Applications, Volume 12 of the series “Abel Symposium” (2016), 109–126.

  22. Partial actions and KMS states on relative graph C*-algebras.
    With Nadia Larsen.
    J. Funct. Anal. 271 (2016), 2090–2132.

  23. The primitive ideals of the Cuntz-Krieger algebra of a row-finite higher-rank graph with no sources.
    With Sooran Kang, Jacob Shotwell and Aidan Sims.
    J. Funct. Anal. 266 (2014), 2570–2589.

  24. An introduction to the C*-algebra of a one-sided shift space.
    Operator Algebra and Dynamics, Springer Proceedings in Mathematics & Statistics, Volume 58 (2013), 63–88.

  25. Simple Cuntz-Pimsner rings.
    With Eduard Ortega and Enrique Pardo.
    J. Algebra 371 (2012), 367–390.

  26. Index maps in the K-theory of graph algebras.
    With Søren Eilers and Mark Tomforde.
    J. K-Theory 9 (2012), 385–406.

  27. The structure of the C*-algebra of a locally injective surjection.
    With Klaus Thomsen.
    Ergodic Theory Dynam. Systems 32 (2012), no. 2, 1226–1248.

  28. Algebraic Cuntz-Pimsner rings.
    With Eduard Ortega.
    Proc. London Math. Soc. (3) 103 (2011), no. 4, 601–653.

  29. Co-universal algebras associated to product systems, and gauge-invariant uniqueness theorems.
    With Nadia S. Larsen, Aidan Sims and Sean Vittadello.
    Proc. London Math. Soc. (3) 103 (2011), no. 4, 563–600.

  30. On the K-theory of the C*-algebra associated to a one-sided shift space.
    With Sergei Silvestrov.
    Proc. Est. Acad. Sci. 59 (2010), no. 4, 272–279.

  31. On the Exel Crossed Product of Topological Covering Maps.
    With Sergei Silvestrov.
    Acta Appl. Math. 108 (2009), no. 3, 573–583.

  32. Cuntz-Pimsner C*-algebras associated with subshifts.
    Internat. J. Math. 19 (2008), no. 1, 47–70.

  33. C*-crossed Products and Shift Spaces.
    With Sergei Silvestrov.
    Expo. Math. 25 (2007), no. 4, 275–307.

  34. Dimension groups associated to β-expansions.
    With Teresa Bates and Søren Eilers.
    Math. Scand. 100 (2007), no. 2, 198–208.

  35. A graph approach to computing nondeterminacy in substitutional dynamical systems.
    With Søren Eilers.
    Theor. Inform. Appl. 41 (2007), no. 3, 285–306.

  36. Ordered K-groups associated to substitutional dynamics.
    With Søren Eilers.
    J. Funct. Anal. 238 (2006), no. 1, 99–117.

  37. Matsumoto K-groups associated to certain shift spaces.
    With Søren Eilers.
    Doc. Math 9 (2004), 639–671.

  38. Augmenting dimension group invariants for substitution dynamics.
    With Søren Eilers.
    Ergodic Theory Dynam. Systems 24 (2004), no. 4, 1015–1039.

  39. Some Remarks on the C*-algebras Associated with Subshifts.
    With Kengo Matsumoto.
    Math. Scand. 95 (2004), no. 1, 145–160.

  40. On C*-algebras Associated with Sofic Shifts.
    J. Operator Theory 49 (2003), no. 1, 203–212.

  41. A Useful Strengthening of the Stone-Weierstrass Theorem.
    With Søren Boel and Niels Richard Hansen.
    Amer. Math. Monthly 108 (2001), no.7, 642–643.


  1. Operator Algebras and Applications – The Abel Symposium 2015.
    Editors Toke M. Carlsen, Nadia S. Larsen, Sergey Neshveyev and Christian Skau.
    Volume 12 of the series “Abel Symposia” (2016), Springer International Publishing.

  2. Operator Algebra and Dynamics – Nordforsk Network Closing Conference, Faroe Islands, May 2012.
    Editors Toke M. Carlsen, Søren Eilers, Gunnar Restorff and Sergei D. Silvestrov.
    Springer Proceedings in Mathematics & Statistics, Volume 58 (2013), Springer International Publishing.


  1. C*-rigidity of topological dynamical systems.

  2. A short introduction to graph groupoids and their algebras.

  3. C*-rigidity of dynamical systems and étale groupoids.

  4. C*-algebras associated to shift spaces.


  1. Operator algebraic applications in symbolic dynamics.
    Ph.D. thesis, University of Copenhagen (2004).

  2. C*-algebras associated to general shift spaces.
    Master’s thesis, University of Copenhagen (2001).


  1. C*-rigidity of topological dynamical system.
    Danish-Norwegian Operator Algebras Meeting at Trondheim, 27 November 2021.

  2. C*-rigidity of topological dynamical systems.
    Operator Algebra Web-Seminar at Federal University of Santa Catarina, 9 November 2021.

  3. C*-rigidity of topological dynamical systems.
    South Atlantic Noncommutative Geometry Seminar (GeNoCAS), 28 September 2021.

  4. Cuntz-Krieger algebras, topological Markov shifts and groupoids.
    NYC noncommutative geometry seminar, 2 September 2020.

  5. Graph algebras, groupoids, and symbolic dynamics.
    Western Sydney University Abend Seminar, 14 May 2020.