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: 2024 | 2021 | 2020 | 2018 | 2017 | 2016 | 2014 | 2013 | 2011 | 2010
Number of items: 21.

2024

Brownlowe, N., Buss, A., Goncalves, D., Hume, J. B., Sims, A. and Whittaker, M. F. (2024) KK-duality for self-similar groupoid actions on graphs. Transactions of the American Mathematical Society, (Accepted for Publication)

2021

Walton, J. J. and Whittaker, M. F. (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, M. and Whittaker, M. F. (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, R., Goffeng, M., Mesland, B. and Whittaker, M. F. (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, M., Raeburn, I., Ramagge, J. and Whittaker, M. F. (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, J., Putnam, I. F. and Whittaker, M. F. (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, N., Pask, D., Ramagge, J., Robertson, D. and Whittaker, M. (2017) Zappa-Szép product groupoids and C*-blends. Semigroup Forum, 94(3), pp. 500-519. (doi: 10.1007/s00233-016-9775-z)

Brownlowe, N., Carlsen, T. M. and Whittaker, M. (2017) Graph algebras and orbit equivalence. Ergodic Theory and Dynamical Systems, 37(2), pp. 389-417. (doi: 10.1017/etds.2015.52)

Mampusti, M. and Whittaker, M. F. (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, R., Killough, D. B. and Whittaker, M. (2016) Dynamical correspondences for Smale spaces. New York Journal of Mathematics, 22, pp. 943-988.

Deeley, R. J., Killough, D. B. and Whittaker, M. F. (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, N. P., Webster, S. B.G. and Whittaker, M. (2016) Fractal dual substitution tilings. Journal of Fractal Geometry, 3(3), pp. 265-317. (doi: 10.4171/JFG/37)

Kumjian, A., Pask, D., Sims, A. and Whittaker, M. F. (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, D., Whitehead, B. and Whittaker, M. (2014) Cohomology of the pinwheel tiling. Journal of the Australian Mathematical Society, 97(2), pp. 162-179. (doi: 10.1017/S1446788714000275)

Laca, M., Raeburn, I., Ramagge, J. and Whittaker, M. (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, N., Ramagge, J., Robertson, D. and Whittaker, M. (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, A., Whitehead, B. and Whittaker, M. (2014) Twisted C*-algebras associated to finitely aligned higher-rank graphs. Documenta Mathematica, 19, pp. 831-866.

2013

Whittaker, M. (2013) Spectral triples for hyperbolic dynamical systems. Journal of Noncommutative Geometry, 7(2), pp. 563-582. (doi: 10.4171/JNCG/127)

2011

Frank, N. P. and Whittaker, M. (2011) A fractal version of the pinwheel tiling. Mathematical Intelligencer, 33(2), pp. 7-17. (doi: 10.1007/s00283-011-9212-9)

2010

Whittaker, M. (2010) C*-algebras of tilings with infinite rotational symmetry. Journal of Operator Theory, 64(2), pp. 299-319.

This list was generated on Thu Apr 18 17:32:02 2024 BST.
Jump to: Articles
Number of items: 21.

Articles

Brownlowe, N., Buss, A., Goncalves, D., Hume, J. B., Sims, A. and Whittaker, M. F. (2024) KK-duality for self-similar groupoid actions on graphs. Transactions of the American Mathematical Society, (Accepted for Publication)

Walton, J. J. and Whittaker, M. F. (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, M. and Whittaker, M. F. (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, R., Goffeng, M., Mesland, B. and Whittaker, M. F. (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, M., Raeburn, I., Ramagge, J. and Whittaker, M. F. (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, J., Putnam, I. F. and Whittaker, M. F. (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, N., Pask, D., Ramagge, J., Robertson, D. and Whittaker, M. (2017) Zappa-Szép product groupoids and C*-blends. Semigroup Forum, 94(3), pp. 500-519. (doi: 10.1007/s00233-016-9775-z)

Brownlowe, N., Carlsen, T. M. and Whittaker, M. (2017) Graph algebras and orbit equivalence. Ergodic Theory and Dynamical Systems, 37(2), pp. 389-417. (doi: 10.1017/etds.2015.52)

Mampusti, M. and Whittaker, M. F. (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, R., Killough, D. B. and Whittaker, M. (2016) Dynamical correspondences for Smale spaces. New York Journal of Mathematics, 22, pp. 943-988.

Deeley, R. J., Killough, D. B. and Whittaker, M. F. (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, N. P., Webster, S. B.G. and Whittaker, M. (2016) Fractal dual substitution tilings. Journal of Fractal Geometry, 3(3), pp. 265-317. (doi: 10.4171/JFG/37)

Kumjian, A., Pask, D., Sims, A. and Whittaker, M. F. (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, D., Whitehead, B. and Whittaker, M. (2014) Cohomology of the pinwheel tiling. Journal of the Australian Mathematical Society, 97(2), pp. 162-179. (doi: 10.1017/S1446788714000275)

Laca, M., Raeburn, I., Ramagge, J. and Whittaker, M. (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, N., Ramagge, J., Robertson, D. and Whittaker, M. (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, A., Whitehead, B. and Whittaker, M. (2014) Twisted C*-algebras associated to finitely aligned higher-rank graphs. Documenta Mathematica, 19, pp. 831-866.

Whittaker, M. (2013) Spectral triples for hyperbolic dynamical systems. Journal of Noncommutative Geometry, 7(2), pp. 563-582. (doi: 10.4171/JNCG/127)

Frank, N. P. and Whittaker, M. (2011) A fractal version of the pinwheel tiling. Mathematical Intelligencer, 33(2), pp. 7-17. (doi: 10.1007/s00283-011-9212-9)

Whittaker, M. (2010) C*-algebras of tilings with infinite rotational symmetry. Journal of Operator Theory, 64(2), pp. 299-319.

This list was generated on Thu Apr 18 17:32:02 2024 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.