Dr Mike Whittaker

  • Lecturer in Pure Mathematics (Mathematics)

telephone: 0141 330 5181
email: Mike.Whittaker@glasgow.ac.uk

Office: Room 329
Mathematics and Statistics Building
University of Glasgow
University Place

Research interests

Personal website

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 all by: Type | Date

Jump to: 2017 | 2016 | 2015 | 2014 | 2013 | 2011 | 2010
Number of items: 16.

2017

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)

Deeley, R., Goffeng, M., Mesland, B. and Whittaker, M. F. (2017) Wieler solenoids, Cuntz-Pimsner algebras and K-theory. Ergodic Theory and Dynamical Systems, (doi:10.1017/etds.2017.10) (Early Online Publication)

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)

2015

Kaminker, J., Putnam, I. and Whittaker, M. (2015) K-theoretic duality for hyperbolic dynamical systems. Journal für die Reine und Angewandte Mathematik (Crelles Journal), (doi:10.1515/crelle-2014-0126) (Early Online Publication)

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 Tue Jul 25 18:13:43 2017 BST.
Jump to: Articles
Number of items: 16.

Articles

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)

Deeley, R., Goffeng, M., Mesland, B. and Whittaker, M. F. (2017) Wieler solenoids, Cuntz-Pimsner algebras and K-theory. Ergodic Theory and Dynamical Systems, (doi:10.1017/etds.2017.10) (Early Online Publication)

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)

Kaminker, J., Putnam, I. and Whittaker, M. (2015) K-theoretic duality for hyperbolic dynamical systems. Journal für die Reine und Angewandte Mathematik (Crelles Journal), (doi:10.1515/crelle-2014-0126) (Early Online Publication)

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 Tue Jul 25 18:13:43 2017 BST.

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