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Toke Meier Carlsen

Toke Meier Carlsen

professari í støddfrøði
Náttúruvísindadeildin

Samband

Telefon:+298 292566
tokemc(at)setur.fo

About Toke

I was born and raised in Copenhagen, Denmark, and I got my PhD from the University of Copenhagen in 2004 with Søren Eilers as my advisor. I have been a professor of mathematics at the University of the Faroe Islands since June 2015.

Before that, I was first an associate professor (2008-2012) and since a full professor (2012-2015) at the Norwegian University of Science and Technology (NTNU). I have also been a postdoc at Institut Mittag-Leffler (2004), NTNU (2004-2005), University of Münster (2005-2006), University of Newcastle, Australia (2006-2007), University of Wollongong (2007), and an assistant professor at the University of Southern Denmark (2008).

My area of research is the interplay between C*-algebras and symbolic dynamics.


Recent publications
  • Diagonal-preserving graded isomorphisms of Steinberg algebras (with James Rout)
    arXiv:1611.09749, 20 pages. [pdf]

  • Flow equivalence and orbit equivalence for shifts of finite type and isomorphism of their groupoids (with Søren Eilers, Eduard Ortega and Gunnar Restorff)
    arXiv:1610.09945, 19 pages. [pdf]

  • Orbit equivalence of graphs and isomorphism of graph groupoids (with Marius Lie Winger)
    Accepted for publication in Math. Scand., 9 pages. [pdf]

  • Diagonal-preserving gauge-invariant isomorphisms of graph C*-algebras (with James Rout)
    arXiv:1610.00692, 12 pages. [pdf]

  • Strong classification of purely infinite Cuntz-Krieger algebras (with Gunnar Restorff and Efren Ruiz)
    Accepted for publication in Trans. Amer. Math. Soc., 28 pages. [pdf]

  • 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)
    Accepted for publication in Proc. Amer. Math. Soc., published online (2016), 11 pages. [pdf] [url]

  • *-isomorphism of Leavitt path algebras over Z
    arXiv:1601.00777, 8 pages. [pdf]

  • Flow Equivalence of G-SFTs (with Mike Boyle and Søren Eilers)
    arXiv:1512.05238, 50 pages. [pdf]

  • 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. [pdf] [url]

  • Flow equivalence of sofic shifts (with Mike Boyle and Søren Eilers)
    Accepted for publication in Israel J. Math., 30 pages. [pdf]

  • Flow equivalence and isotopy for subshifts (with Mike Boyle and Søren Eilers)
    Accepted for publication in Dynamical Systems, published online (2016), 21 pages. [pdf] [url]

  • C*-algebras associated to Boolean dynamical systems (with Eduard Ortega and Enrique Pardo)
    Accepted for publication in J. Math. Anal. Appl., 43 pages. [pdf]

  • Partial actions and KMS states on relative graph C*-algebras (with Nadia S. Larsen)
    J. Funct. Anal. 271 (2016), 2090–2132. [pdf] [url]

Editorial publications
  1. 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 58 (2013), Springer International Publishing. [url]

  2. 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. [url]

Research

My research is mainly related to C*-algebras constructed from dynamical systems or combinatorial structures, such as
  • C*-algebras associated with subshifts,
  • graph C*-algebras,
  • C*-algebras of higher rank graphs,
  • groupoid C*-algebras,
  • Cuntz-Pimsner algebras, and
  • C*-algebras associated with product systems of Hilbert bimodules.
I am also interested in algebraic analogous of these kinds of C*-algebras such as
  • Leavitt path algebras,
  • Steinberg algebras, and
  • Cuntz-Pimsner ring,
and their relationship with the corresponding C*-algebras. I also study symbolic dynamical systems in their own right.


Research supervision
  • Postdoc supervisor for Antoine Julien, September 2012 – April 2014.
  • Postdoc supervisor for Eduard Ortega, August 2010 – June 2012.
  • Postdoc supervisor for Jacob Shotwell, September 2009 – February 2010.
  • Main Ph.D. advisor for Siri-Malén Høynes, August 2009 – September 2014.
  • Main Ph.D. advisor for Martin Wanvik, August 2008 – August 2015.
  • Secondary Ph.D. advisor for Magnus Norling, August 2009 – May 2013.
  • Secondary Ph.D. advisor for Tron Omland, August 2008 – June 2013.
  • Master project advisor for Marius Winger, January 2014 – June 2015.
  • Research internship supervisor for Laurie Mézeret, May 2010 – July 2010.

Publications

Below is a list of my publications. The list is also available as a pdf-file.

Notice that for some of the papers, the version available as a pdf-file (which you get be clicking the pdf-icon [pdf]) might be different from the published version of the paper (which you get to by clicking the url-icon [url]). The copyrights of the papers belong to the publishing journals.

Publications in peer-reviewed journals
  1. A Useful Strengthening of the Stone-Weierstrass Theorem (with Søren Boel and Niels Richard Hansen)
    Amer. Math. Monthly 108 (2001), no.7, 642–643. [pdf] [url]

  2. On C*-algebras Associated with Sofic Shifts J. Operator Theory 49 (2003), no. 1, 203–212. [pdf] [url]

  3. Some Remarks on the C*-algebras Associated with Subshifts (with Kengo Matsumoto)
    Math. Scand. 95 (2004), no. 1, 145–160. [pdf] [url]

  4. Augmenting dimension group invariants for substitution dynamics (with Søren Eilers)
    Ergodic Theory Dynam. Systems 24 (2004), no. 4, 1015–1039. [pdf] [url]

  5. Matsumoto K-groups associated to certain shift spaces (with Søren Eilers)
    Doc. Math 9 (2004), 639-671. [pdf] [url]

  6. Ordered K-groups associated to substitutional dynamics (with Søren Eilers)
    J. Funct. Anal. 238 (2006), no. 1, 99–117. [pdf] [url]

  7. A graph approach to computing nondeterminacy in substitutional dynamical systems (with Søren Eilers)
    Theor. Inform. Appl. 41 (2007), no. 3, 285–306. [pdf] [url]

  8. Dimension groups associated to ß-expansions (with Teresa Bates and Søren Eilers)
    Math. Scand. 100 (2007), no. 2, 198–208. [pdf] [url]

  9. C*-crossed Products and Shift Spaces (with Sergei Silvestrov)
    Expo. Math. 25 (2007), no. 4, 275–307. [pdf] [url]

  10. Cuntz-Pimsner C*-algebras associated with subshifts
    Internat. J. Math. 19 (2008), no. 1, 47–70. [pdf] [url]

  11. On the Exel Crossed Product of Topological Covering Maps (with Sergei Silvestrov)
    Acta Appl. Math. 108 (2009), no. 3, 573–583. [pdf] [url]

  12. 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. [pdf] [url]

  13. 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. [pdf] [url]

  14. Algebraic Cuntz-Pimsner rings (with Eduard Ortega)
    Proc. London Math. Soc. (3) 103 (2011), no. 4, 601–653. [pdf] [url]

  15. The structure of the C*-algebra of a locally injective surjection (with Klaus Thomsen)
    Ergodic Theory Dynam. Systems 32 (2012), no. 2, 1226-1248. [pdf] [url]

  16. Index maps in the K-theory of graph algebras (with Søren Eilers and Mark Tomforde)
    J. K-Theory 9 (2012), no. 2, 385–406. [pdf] [url]

  17. Simple Cuntz-Pimsner rings (with Eduard Ortega and Enrique Pardo)
    J. Algebra 371 (2012), 367–390. [pdf] [url]

  18. An introduction to the C*-algebra of a one-sided shift space
    Springer Proceedings in Mathematics & Statistics, 58 (2013), 63–88. [pdf] [url]

  19. 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. [pdf] [url]

  20. Partial actions and KMS states on relative graph C*-algebras (with Nadia S. Larsen)
    J. Funct. Anal. 271 (2016), 2090–2132. [pdf] [url]

  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. [pdf] [url]

  22. Graph algebras and orbit equivalence (with Nathan Brownlowe and Michael F. Whittaker)
    Accepted for publication in Ergodic Theory Dynam. Systems, published online (2015), 29 pages. [pdf] [url]

  23. C*-algebras of labelled graphs III - K-theory computations (with Teresa Bates and David Pask)
    Accepted for publication in Ergodic Theory Dynam. Systems, published online (2015), 32 pages. [pdf] [url]

  24. Flow equivalence and isotopy for subshifts (with Mike Boyle and Søren Eilers)
    Accepted for publication in Dynamical Systems, published online (2016), 21 pages. [pdf] [url]

  25. 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)
    Accepted for publication in Proc. Amer. Math. Soc., published online (2016), 11 pages. [pdf] [url]

  26. Flow equivalence of sofic shifts (with Mike Boyle and Søren Eilers)
    Accepted for publication in Israel J. Math., 30 pages. [pdf]

  27. Strong classification of purely infinite Cuntz-Krieger algebras (with Gunnar Restorff and Efren Ruiz)
    Accepted for publication in Trans. Amer. Math. Soc., 28 pages. [pdf]

  28. C*-algebras associated to Boolean dynamical systems (with Eduard Ortega and Enrique Pardo)
    Accepted for publication in J. Math. Anal. Appl., 43 pages. [pdf]

  29. Orbit equivalence of graphs and isomorphism of graph groupoids (with Marius Lie Winger)
    Accepted for publication in Math. Scand., 9 pages. [pdf]




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

  2. Flow Equivalence of G-SFTs (with Mike Boyle and Søren Eilers)
    arXiv:1512.05238, 50 pages. [pdf]

  3. *-isomorphism of Leavitt path algebras over Z
    arXiv:1601.00777, 8 pages. [pdf]

  4. Diagonal-preserving gauge-invariant isomorphisms of graph C*-algebras (with James Rout)
    arXiv:1610.00692, 12 pages. [pdf]

  5. Flow equivalence and orbit equivalence for shifts of finite type and isomorphism of their groupoids (with Søren Eilers, Eduard Ortega and Gunnar Restorff)
    arXiv:1610.09945, 23 pages. [pdf]

  6. Diagonal-preserving graded isomorphisms of Steinberg algebras (with James Rout)
    arXiv:1611.09749, 20 pages. [pdf]



Editorial publications
  1. 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 58 (2013), Springer International Publishing. [url]

  2. 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. [url]


Theses
  1. C*-algebras associated to general shift spaces
    Master's thesis. [pdf]

  2. Operator Algebraic Applications in Symbolic Dynamics
    PhD thesis. [pdf]


Notes
  1. C*-algebras associated to shift spaces
    arXiv:0808.0301, 31 pages. [pdf]

Teaching

Below is a list of courses I have taught at the University of the Faroe Islands, the Norwegian University of Science and Technology (NTNU), and the University of Southern Denmark.

In addition, I have been lecturing at the University of Copenhagen, and been a TA at the University of Copenhagen and at the University of Maryland.

My teaching portfolio contains a complete description of my teaching and my pedagogical education.
  • Mathematics 1 (20 ECTS), BSc in Energy and Environmental Engineering, University of the Faroe Islands, fall 2015 – spring 2016.
  • Mathematics 2 (5 ECTS), BSc in Energy and Environmental Engineering, University of the Faroe Islands, spring 2015.
  • Calculus 1 (7.5 ECTS), Master’s degree in engineering, Norwegian University of Science and Technology, fall 2013.
  • Calculus 3 (7.5 ECTS), Master’s degree in engineering, Norwegian University of Science and Technology, spring 2013.
  • Calculus 3 (7.5 ECTS), Master’s degree in engineering, Norwegian University of Science and Technology, fall 2012.
  • Functional analysis (7.5 ECTS), Master’s degree in engineering, Norwegian University of Science and Technology, spring 2011.
  • Calculus 1 (7.5 ECTS), Master’s degree in engineering, Norwegian University of Science and Technology, fall 2010.
  • C*-crossed products (7.5 ECTS), PhD program in mathematics, Norwegian University of Science and Technology, spring 2010.
  • K-theory for C*-algebras (7.5 ECTS), PhD program in mathematics, Norwegian University of Science and Technology, fall 2009.
  • Calculus 1 (7.5 ECTS), Master’s degree in engineering, Norwegian University of Science and Technology, fall 2009.
  • Functional analysis (7.5 ECTS), Master’s degree in engineering, Norwegian University of Science and Technology, spring 2009.
  • Operator algebra (7.5 ECTS), PhD program in mathematics, Norwegian University of Science and Technology, fall 2008.
  • Calculus 1 (7.5 ECTS), Master’s degree in engineering, Norwegian University of Science and Technology, fall 2008.
  • Differential Equations, bachelor programme in Mathematics, University of Southern Denmark, spring 2008.
Samband
Fróðskaparsetur Føroya
J.C. Svabos gøta 14
FO-100 Tórshavn
Tel.: +298 352500
Faks: +298 352501
setur(at)setur.fo