Professor Mike Whittaker

  • Professor of Mathematics (Mathematics)

telephone: 0141 330 5181
email: Mike.Whittaker@glasgow.ac.uk
pronouns: He/him/his

Office: Room 329, Mathematics and Statistics Building, University of Glasgow, University Place, Glasgow, Q12 8SQ

Import to contacts

ORCID iDhttps://orcid.org/0000-0003-1293-0080

Biography

Personal Website: https://www.mikewhittaker.org/home

Research interests

My primary research interest is the connection between topological dynamical systems and operator algebras. Starting with a dynamical system we construct C*-algebras that are used to ascertain dynamical invariants in a noncommutative framework. Some of my specific interests in this area include hyperbolic dynamical systems called Smale spaces, self-similar group actions, graph and k-graph algebras, and aperiodic substitution tilings. Using the noncommutative geometry program, developed by Alain Connes, we have used these algebras to construct K-theoretic invariants including Poincaré duality classes, KMS equilibrium states, and spectral triples. I have been particularly interested in dynamical systems that are fractal in nature, with comprehensible local structure but chaotic global behaviour. Aperiodic tilings are extremely useful for further understanding this type of phenomenon and serve as a geometric model for self-similar dynamical systems.

Research groups

Publications

List by: Type | Date

Jump to: 2025 | 2024 | 2021 | 2020 | 2018 | 2017 | 2016 | 2014 | 2013 | 2011 | 2010
Number of items: 23.

2025

Hume, Jeremy B. and Whittaker, Michael F. ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2025) Katsura-Exel-Pardo self-similar actions, Putnam's binary factors, and their limit spaces. Journal of the Australian Mathematical Society, (Accepted for Publication)

2024

Gerontogiannis, Dimitris Michail, Whittaker, Michael F. ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 and Zacharias, Joachim ORCID logoORCID: https://orcid.org/0000-0003-1186-3816 (2024) A geometric representative for the fundamental class in KK-duality of Smale spaces. Journal of Functional Analysis, 287(2), 110455. (doi: 10.1016/j.jfa.2024.110455)

Brownlowe, Nathan, Buss, Alcides, Goncalves, Daniel, Hume, Jeremy B., Sims, Aidan and Whittaker, Michael F. ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2024) KK-duality for self-similar groupoid actions on graphs. Transactions of the American Mathematical Society, (doi: 10.1090/tran/9183) (Early Online Publication)

2021

Walton, James J. and Whittaker, Michael F. ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2021) An aperiodic tile with edge-to-edge orientational matching rules. Journal of the Institute of Mathematics of Jussieu, (doi: 10.1017/S1474748021000517) (Early Online Publication)

2020

Easo, P. et al. (2020) The Cuntz-Toeplitz algebras have nuclear dimension one. Journal of Functional Analysis, 279(7), 108690. (doi: 10.1016/j.jfa.2020.108690)

Mampusti, Michael and Whittaker, Michael F. ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2020) An aperiodic monotile that forces nonperiodicity through dendrites. Bulletin of the London Mathematical Society, 52(5), pp. 942-959. (doi: 10.1112/blms.12375)

2018

Deeley, Robin, Goffeng, Magnus, Mesland, Bram and Whittaker, Michael F. ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2018) Wieler solenoids, Cuntz-Pimsner algebras and K-theory. Ergodic Theory and Dynamical Systems, 38(8), pp. 2942-2988. (doi: 10.1017/etds.2017.10)

Laca, Marcelo, Raeburn, Iain, Ramagge, Jacqui and Whittaker, Michael F. ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2018) Equilibrium states on operator algebras associated to self-similar actions of groupoids on graphs. Advances in Mathematics, 331, pp. 268-325. (doi: 10.1016/j.aim.2018.03.030)

2017

Kaminker, Jerome, Putnam, Ian F. and Whittaker, Michael F. ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2017) K-theoretic duality for hyperbolic dynamical systems. Journal für die Reine und Angewandte Mathematik (Crelles Journal), 2017(730), pp. 263-299. (doi: 10.1515/crelle-2014-0126)

Brownlowe, Nathan, Pask, David, Ramagge, Jacqui, Robertson, David and Whittaker, Michael ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2017) Zappa-Szép product groupoids and C*-blends. Semigroup Forum, 94(3), pp. 500-519. (doi: 10.1007/s00233-016-9775-z)

Brownlowe, Nathan, Carlsen, Toke Meier and Whittaker, Michael ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2017) Graph algebras and orbit equivalence. Ergodic Theory and Dynamical Systems, 37(2), pp. 389-417. (doi: 10.1017/etds.2015.52)

Mampusti, Michael and Whittaker, Michael F. ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2017) Fractal spectral triples on Kellendonk's C*-algebra of a substitution tiling. Journal of Geometry and Physics, 112, pp. 224-239. (doi: 10.1016/j.geomphys.2016.11.010)

2016

Deeley, Robin, Killough, D. Brady and Whittaker, Michael ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2016) Dynamical correspondences for Smale spaces. New York Journal of Mathematics, 22, pp. 943-988.

Deeley, Robin J., Killough, D. Brady and Whittaker, Michael F. ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2016) Functorial properties of Putnam's homology theory for Smale spaces. Ergodic Theory and Dynamical Systems, 36(5), pp. 1411-1440. (doi: 10.1017/etds.2014.134)

Frank, Natalie Priebe, Webster, Samuel B.G. and Whittaker, Michael ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2016) Fractal dual substitution tilings. Journal of Fractal Geometry, 3(3), pp. 265-317. (doi: 10.4171/JFG/37)

Kumjian, Alex, Pask, David, Sims, Aidan and Whittaker, Michael F. ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2016) Topological spaces associated to higher-rank graphs. Journal of Combinatorial Theory, Series A, 143, pp. 19-41. (doi: 10.1016/j.jcta.2016.04.005)

2014

Frettlöh, Dirk, Whitehead, Benjamin and Whittaker, Michael ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2014) Cohomology of the pinwheel tiling. Journal of the Australian Mathematical Society, 97(2), pp. 162-179. (doi: 10.1017/S1446788714000275)

Laca, Marcelo, Raeburn, Iain, Ramagge, Jacqui and Whittaker, Michael ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2014) Equilibrium states on the Cuntz-Pimsner algebras of self-similar actions. Journal of Functional Analysis, 266(11), pp. 6619-6661. (doi: 10.1016/j.jfa.2014.03.003)

Brownlowe, Nathan, Ramagge, Jacqui, Robertson, David and Whittaker, Michael ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2014) Zappa–Szép products of semigroups and their C*-algebras. Journal of Functional Analysis, 266(6), pp. 3937-3967. (doi: 10.1016/j.jfa.2013.12.025)

Sims, Aidan, Whitehead, Benjamin and Whittaker, Michael ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2014) Twisted C*-algebras associated to finitely aligned higher-rank graphs. Documenta Mathematica, 19, pp. 831-866.

2013

Whittaker, Michael ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2013) Spectral triples for hyperbolic dynamical systems. Journal of Noncommutative Geometry, 7(2), pp. 563-582. (doi: 10.4171/JNCG/127)

2011

Frank, Natalie Priebe and Whittaker, Michael ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2011) A fractal version of the pinwheel tiling. Mathematical Intelligencer, 33(2), pp. 7-17. (doi: 10.1007/s00283-011-9212-9)

2010

Whittaker, Michael ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2010) C*-algebras of tilings with infinite rotational symmetry. Journal of Operator Theory, 64(2), pp. 299-319.

This list was generated on Sun Jun 15 07:27:08 2025 BST.
Jump to: Articles
Number of items: 23.

Articles

Hume, Jeremy B. and Whittaker, Michael F. ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2025) Katsura-Exel-Pardo self-similar actions, Putnam's binary factors, and their limit spaces. Journal of the Australian Mathematical Society, (Accepted for Publication)

Gerontogiannis, Dimitris Michail, Whittaker, Michael F. ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 and Zacharias, Joachim ORCID logoORCID: https://orcid.org/0000-0003-1186-3816 (2024) A geometric representative for the fundamental class in KK-duality of Smale spaces. Journal of Functional Analysis, 287(2), 110455. (doi: 10.1016/j.jfa.2024.110455)

Brownlowe, Nathan, Buss, Alcides, Goncalves, Daniel, Hume, Jeremy B., Sims, Aidan and Whittaker, Michael F. ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2024) KK-duality for self-similar groupoid actions on graphs. Transactions of the American Mathematical Society, (doi: 10.1090/tran/9183) (Early Online Publication)

Walton, James J. and Whittaker, Michael F. ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2021) An aperiodic tile with edge-to-edge orientational matching rules. Journal of the Institute of Mathematics of Jussieu, (doi: 10.1017/S1474748021000517) (Early Online Publication)

Easo, P. et al. (2020) The Cuntz-Toeplitz algebras have nuclear dimension one. Journal of Functional Analysis, 279(7), 108690. (doi: 10.1016/j.jfa.2020.108690)

Mampusti, Michael and Whittaker, Michael F. ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2020) An aperiodic monotile that forces nonperiodicity through dendrites. Bulletin of the London Mathematical Society, 52(5), pp. 942-959. (doi: 10.1112/blms.12375)

Deeley, Robin, Goffeng, Magnus, Mesland, Bram and Whittaker, Michael F. ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2018) Wieler solenoids, Cuntz-Pimsner algebras and K-theory. Ergodic Theory and Dynamical Systems, 38(8), pp. 2942-2988. (doi: 10.1017/etds.2017.10)

Laca, Marcelo, Raeburn, Iain, Ramagge, Jacqui and Whittaker, Michael F. ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2018) Equilibrium states on operator algebras associated to self-similar actions of groupoids on graphs. Advances in Mathematics, 331, pp. 268-325. (doi: 10.1016/j.aim.2018.03.030)

Kaminker, Jerome, Putnam, Ian F. and Whittaker, Michael F. ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2017) K-theoretic duality for hyperbolic dynamical systems. Journal für die Reine und Angewandte Mathematik (Crelles Journal), 2017(730), pp. 263-299. (doi: 10.1515/crelle-2014-0126)

Brownlowe, Nathan, Pask, David, Ramagge, Jacqui, Robertson, David and Whittaker, Michael ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2017) Zappa-Szép product groupoids and C*-blends. Semigroup Forum, 94(3), pp. 500-519. (doi: 10.1007/s00233-016-9775-z)

Brownlowe, Nathan, Carlsen, Toke Meier and Whittaker, Michael ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2017) Graph algebras and orbit equivalence. Ergodic Theory and Dynamical Systems, 37(2), pp. 389-417. (doi: 10.1017/etds.2015.52)

Mampusti, Michael and Whittaker, Michael F. ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2017) Fractal spectral triples on Kellendonk's C*-algebra of a substitution tiling. Journal of Geometry and Physics, 112, pp. 224-239. (doi: 10.1016/j.geomphys.2016.11.010)

Deeley, Robin, Killough, D. Brady and Whittaker, Michael ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2016) Dynamical correspondences for Smale spaces. New York Journal of Mathematics, 22, pp. 943-988.

Deeley, Robin J., Killough, D. Brady and Whittaker, Michael F. ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2016) Functorial properties of Putnam's homology theory for Smale spaces. Ergodic Theory and Dynamical Systems, 36(5), pp. 1411-1440. (doi: 10.1017/etds.2014.134)

Frank, Natalie Priebe, Webster, Samuel B.G. and Whittaker, Michael ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2016) Fractal dual substitution tilings. Journal of Fractal Geometry, 3(3), pp. 265-317. (doi: 10.4171/JFG/37)

Kumjian, Alex, Pask, David, Sims, Aidan and Whittaker, Michael F. ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2016) Topological spaces associated to higher-rank graphs. Journal of Combinatorial Theory, Series A, 143, pp. 19-41. (doi: 10.1016/j.jcta.2016.04.005)

Frettlöh, Dirk, Whitehead, Benjamin and Whittaker, Michael ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2014) Cohomology of the pinwheel tiling. Journal of the Australian Mathematical Society, 97(2), pp. 162-179. (doi: 10.1017/S1446788714000275)

Laca, Marcelo, Raeburn, Iain, Ramagge, Jacqui and Whittaker, Michael ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2014) Equilibrium states on the Cuntz-Pimsner algebras of self-similar actions. Journal of Functional Analysis, 266(11), pp. 6619-6661. (doi: 10.1016/j.jfa.2014.03.003)

Brownlowe, Nathan, Ramagge, Jacqui, Robertson, David and Whittaker, Michael ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2014) Zappa–Szép products of semigroups and their C*-algebras. Journal of Functional Analysis, 266(6), pp. 3937-3967. (doi: 10.1016/j.jfa.2013.12.025)

Sims, Aidan, Whitehead, Benjamin and Whittaker, Michael ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2014) Twisted C*-algebras associated to finitely aligned higher-rank graphs. Documenta Mathematica, 19, pp. 831-866.

Whittaker, Michael ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2013) Spectral triples for hyperbolic dynamical systems. Journal of Noncommutative Geometry, 7(2), pp. 563-582. (doi: 10.4171/JNCG/127)

Frank, Natalie Priebe and Whittaker, Michael ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2011) A fractal version of the pinwheel tiling. Mathematical Intelligencer, 33(2), pp. 7-17. (doi: 10.1007/s00283-011-9212-9)

Whittaker, Michael ORCID logoORCID: https://orcid.org/0000-0003-1293-0080 (2010) C*-algebras of tilings with infinite rotational symmetry. Journal of Operator Theory, 64(2), pp. 299-319.

This list was generated on Sun Jun 15 07:27:08 2025 BST.

Grants

EPSRC First Grant 2018-2020

Supervision

Postdoctoral supervision:

Jamie Walton 2018-2020.

PhD supervision:

Dimitris Gerontogiannis 2016-2021
Ismail Ozkaraca 2016-2021
Luke Ito 2015-2019
Michael Mampusti 2013-2019

Teaching

I currently lecture and coordinate Maths 1.