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Michael F. Whittaker
Lecturer in Pure Mathematics
School of Mathematics and Statistics
e-mail: Mike.Whittaker at glasgow.ac.uk
Office: 329 Maths and Stats Building
The Mathematics and Statistics Building
University of Glasgow
Glasgow, G12 8SQ
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.
- 2016-present: Ismail Ozkaraca, PhD candidate, supervisor
- 2016-present: Dimitrios Gerontogiannis, PhD candidate, supervisor (with Joachim Zacharias)
- 2015-present: Luke Hamblin, PhD candidate, second supervisor (with Joachim Zacharias)
- 2013-present: Michael Mampusti, PhD candidate, adjunct supervisor (with David Pask and Aidan Sims)
- 2016-2017: Catrice Chong, MSci, supervisor
- 2018-2020: EPSRC First Grant, Application of space filling curves to substitution tilings, £101,091
- June 2017: International Centre for Mathematical Sciences Conference Grant (joint with Nadia Larsen, Mark Lawson, and Christian Skau), in support of the conference Applications of Operator Algebras: Order, Disorder and Symmetry, £16,500
- December 2016: London Mathematical Society Workshop Grant, in support of the Workshop on Topological Dynamical Systems and Operator Algebras, £600
- August 2015: Edinburgh Mathematical Society Travel Grant, in support of a research visit by Charles Starling, £800
- 2013-2014: University of Wollongong International Links Grant (joint with Nathan Brownlowe and Aidan Sims, AUD15,000
- July 2014: AMSI Workshop Funding Grant and AustMS Special Interest Meeting Grant (joint with Murray Elder, Adam Sorensen, and Sam Webster), in support of the workshop Interactions between Operator Algebras and Dynamical Systems, AUD 9,950
Colloquia and seminars:
- June 26-30, 2017: Applications of Operator Algebras: Order, Disorder and Symmetry, International Centre for Mathematical Sciences, Edinburgh.
- March 24-25, 2017: Scottish Operator Algebras Research Meeting, University of Glasgow.
- December 2, 2016: Workshop on Topological Dynamical Systems and Operator Algebras, University of Glasgow.
- December 2-3, 2016: Scottish Operator Algebras Research Meeting, University of Glasgow.
- November 13, 2015: Scottish Operator Algebras Research Meeting, University of Glasgow.
- June 30 - July 4, 2014: Workshop on the Interactions Between Operator Algebras and Dynamical Systems, University of Wollongong.