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.

Preprints

  1. A Cuntz-Krieger Uniqueness theorem for C*-algebras of relative generalized Boolean dynamical systems.
    With Eun Ji Kang.
    arXiv:2305.09232, 26 pages.

  2. Ideal structure of C*-algebras of commuting local homeomorphisms.
    With Kevin Aguyar Brix and Aidan Sims.
    arXiv:2303.02313, 50 pages.

  3. Some results regarding the ideal structure of C*-algebras of étale groupoids.
    With Kevin Aguyar Brix and Aidan Sims.
    arXiv:2211.06126, 18 pages.

  4. Shift equivalence through the lens of Cuntz-Krieger algebras.
    With Adam Dor-On and Søren Eilers. Accepted for publication in Analysis & PDE.
    arXiv:2011.10320, 36 pages.

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

Peer-reviewed research papers

  1. Conjugacy of local homeomorphisms via groupoids and C*-algebras.
    With Becky Armstrong, Kevin Aguyar Brix and Søren Eilers. Ergodic Theory Dynam. Systems 43 (2023), 2516–2537.
    doi:10.1017/etds.2022.50   arXiv:2105.00479

  2. Condition (K) for Boolean dynamical systems.
    With Eun Ji Kang.
    J. Aust. Math. Soc., 112 (2022), 145–169.
    doi:10.1017/S1446788721000082   arXiv:1911.08238

  3. Orbit equivalence of higher-rank graphs.
    With James Rout.
    J. Operator Theory, 86 (2021), 395–424.
    doi:10.7900/jot.2020may06.2280   arXiv:1903.07179

  4. Reconstruction of groupoids and C*-rigidity of dynamical systems.
    With Efren Ruiz, Aidan Sims and Mark Tomforde.
    Adv. Math., 390 (2021), 107923.
    doi:10.1016/j.aim.2021.107923   arXiv:1711.01052

  5. 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.
    doi:10.1017/S1446788719000168   arXiv:1712.00179

  6. C*-algebras, groupoids and covers of shift spaces.
    With Kevin Aguyar Brix.
    Trans. Amer. Math. Soc. Ser. B 7 (2020), 134–185.
    doi:10.1090/btran/53   arXiv:1910.01938

  7. Gauge-invariant ideals of C*-algebras of Boolean dynamical Systems.
    With Eun Ji Kang.
    J. Math. Anal. Appl. 488 (2020), 124037, 27 pages.
    doi:10.1016/j.jmaa.2020.124037   Corrigendum   arXiv:1911.12172

  8. Flow Equivalence of G-SFTs.
    With Mike Boyle and Søren Eilers.
    Trans. Amer. Math. Soc. 373 (2020), 2591–2657.
    doi:10.1090/tran/7981   arXiv:1512.05238

  9. Topological freeness for C*-correspondences.
    With Eduard Ortega and Bartosz Kwaśniewski.
    J. Math. Anal. Appl. 473 (2019), 749–785.
    doi:10.1016/j.jmaa.2018.12.069   arXiv:1801.03142

  10. 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.
    doi:10.1016/j.jmaa.2018.09.056   arXiv:1610.09945

  11. Orbit equivalence of graphs and isomorphism of graph groupoids.
    With Marius Lie Winger.
    Math. Scand. 123 (2018), 239–248.
    doi:10.7146/math.scand.a-105087   arXiv:1610.09942

  12. Flow equivalence of sofic shifts.
    With Mike Boyle and Søren Eilers.
    Isr. J. Math. 225 (2018), 111–146.
    doi:10.1007/s11856-018-1644-x   arXiv:1511.03481

  13. Diagonal-preserving graded isomorphisms of Steinberg algebras.
    With James Rout.
    Commun. Contemp. Math. 20 (2018), 25 pages.
    doi:10.1142/S021919971750064X   arXiv:1611.09749

  14. *-isomorphism of Leavitt path algebras over ℤ.
    Adv. Math. 324 (2018), 326–335.
    doi:10.1016/j.aim.2017.11.018   arXiv:1601.00777

  15. Diagonal-preserving gauge-invariant isomorphisms of graph C*-algebras.
    With James Rout.
    J. Funct. Anal. 273 (2017), 2981–2993.
    doi:10.1016/j.jfa.2017.06.018   arXiv:1610.00692

  16. C*-algebras associated to Boolean dynamical systems.
    With Eduard Ortega and Enrique Pardo.
    J. Math. Anal. Appl. 450 (2017), 727–768.
    doi:10.1016/j.jmaa.2017.01.038   arXiv:1510.06718

  17. Strong classification of purely infinite Cuntz-Krieger algebras.
    With Gunnar Restorff and Efren Ruiz.
    Trans. Amer. Math. Soc. B 4 (2017), 1–30.
    doi:10.1090/btran/14   arXiv:1605.06153

  18. 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.
    doi:10.1090/proc/13321   arXiv:1602.02602

  19. Flow equivalence and isotopy for subshifts.
    With Mike Boyle and Søren Eilers.
    Dyn. Syst. 32 (2017), 305–325.
    doi:10.1080/14689367.2016.1207753   arXiv:1511.03478

  20. Graph algebras and orbit equivalence.
    With Nathan Brownlowe and Michael F. Whittaker.
    Ergodic Theory Dynam. Systems 37 (2017), 389–417.
    doi:10.1017/etds.2015.52   arXiv:1410.2308

  21. C*-algebras of labelled graphs III - K-theory computations.
    With Teresa Bates and David Pask.
    Ergodic Theory Dynam. Systems 37 (2017), 337–368.
    doi:10.1017/etds.2015.62   arXiv:1203.3072

  22. 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.
    doi:10.1007/978-3-319-39286-8_4   arXiv:1512.02850

  23. Partial actions and KMS states on relative graph C*-algebras.
    With Nadia Larsen.
    J. Funct. Anal. 271 (2016), 2090–2132.
    doi:10.1016/j.jfa.2016.07.001   arXiv:1311.0912

  24. 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.
    doi:10.1016/j.jfa.2013.08.029   arXiv:1305.6388

  25. 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.
    doi:10.1007/978-3-642-39459-1_4

  26. Simple Cuntz-Pimsner rings.
    With Eduard Ortega and Enrique Pardo.
    J. Algebra 371 (2012), 367–390.
    doi:10.1016/j.jalgebra.2012.08.005   arXiv:1110.6923

  27. Index maps in the K-theory of graph algebras.
    With Søren Eilers and Mark Tomforde.
    J. K-Theory 9 (2012), 385–406.
    doi:10.1017/is011004017jkt156   arXiv:1011.4154

  28. The structure of the C*-algebra of a locally injective surjection.
    With Klaus Thomsen.
    Ergodic Theory Dynam. Systems 32 (2012), no. 2, 1226–1248.
    doi:10.1017/S0143385711000216   arXiv:1011.0583

  29. Algebraic Cuntz-Pimsner rings.
    With Eduard Ortega.
    Proc. London Math. Soc. (3) 103 (2011), no. 4, 601–653.
    doi:10.1112/plms/pdq040   arXiv:0810.3254

  30. 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.
    doi:10.1112/plms/pdq028   arXiv:0906.4825

  31. 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.
    doi:10.3176/proc.2010.4.04

  32. On the Exel Crossed Product of Topological Covering Maps.
    With Sergei Silvestrov.
    Acta Appl. Math. 108 (2009), no. 3, 573–583.
    doi:10.1007/s10440-008-9372-6   arXiv:0811.0056

  33. Cuntz-Pimsner C*-algebras associated with subshifts.
    Internat. J. Math. 19 (2008), no. 1, 47–70.
    doi:10.1142/S0129167X0800456X   arXiv:math/0505503

  34. C*-crossed Products and Shift Spaces.
    With Sergei Silvestrov.
    Expo. Math. 25 (2007), no. 4, 275–307.
    doi:10.1016/j.exmath.2007.02.004   arXiv:math/0512488

  35. Dimension groups associated to β-expansions.
    With Teresa Bates and Søren Eilers.
    Math. Scand. 100 (2007), no. 2, 198–208.
    doi:10.7146/math.scand.a-15022

  36. A graph approach to computing nondeterminacy in substitutional dynamical systems.
    With Søren Eilers.
    Theor. Inform. Appl. 41 (2007), no. 3, 285–306.
    doi:10.1051/ita:2007020

  37. Ordered K-groups associated to substitutional dynamics.
    With Søren Eilers.
    J. Funct. Anal. 238 (2006), no. 1, 99–117.
    doi:10.1016/j.jfa.2005.12.028

  38. Matsumoto K-groups associated to certain shift spaces.
    With Søren Eilers.
    Doc. Math 9 (2004), 639–671.
    https://www.math.uni-bielefeld.de/documenta/vol-09/30.html

  39. Augmenting dimension group invariants for substitution dynamics.
    With Søren Eilers.
    Ergodic Theory Dynam. Systems 24 (2004), no. 4, 1015–1039.
    doi:10.1017/s0143385704000057

  40. Some Remarks on the C*-algebras Associated with Subshifts.
    With Kengo Matsumoto.
    Math. Scand. 95 (2004), no. 1, 145–160.
    doi:10.7146/math.scand.a-14453

  41. On C*-algebras Associated with Sofic Shifts.
    J. Operator Theory 49 (2003), no. 1, 203–212.
    http://www.mathjournals.org/jot/2003-049-001/2003-049-001-013.html   arXiv:math/0009147

  42. A Useful Strengthening of the Stone-Weierstrass Theorem.
    With Søren Boel and Niels Richard Hansen.
    Amer. Math. Monthly 108 (2001), no.7, 642–643.
    doi:10.2307/2695271

Books

  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.
    doi:10.1007/978-3-319-39286-8

  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.
    doi:10.1007/978-3-642-39459-1

Notes

  1. C*-rigidity of topological dynamical systems.
    pdf

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

  3. C*-rigidity of dynamical systems and étale groupoids.
    arXiv:1803.05326

  4. C*-algebras associated to shift spaces.
    arXiv:0808.0301

Theses

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

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

Talks

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

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

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

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

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