Professor of Mathematics
University of Glasgow
e-mail: Mike.Whittaker at glasgow.ac.uk
Office: 329 Maths and Stats Building
Postal Address:
School of Mathematics and Statistics
University of Glasgow
University Place
Glasgow, G12 8QQ
United Kingdom
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.
Supervision:
Postdoctoral:
2018-2020: Dr Jamie Walton, funded by EPSRC First Grant.
Doctoral:
2024-present: Lorna Richardson, joint supervisor (with Jim Belk),
2024-present: Susanna Terron, joint supervisor (with Rachael Boyd),
2021-present: Jeremy Hume, second supervisor (with Xin Li),
2016-2021: Dr Dimitrios Gerontogiannis, supervisor (with Joachim Zacharias),
Thesis: Ahlfors regularity, extensions by Schatten ideals and a geometric fundamental class of Smale space C*-algebras using dynamical partitions of unity2016-2021: Dr Ismail Ozkaraca, supervisor
Thesis: An application of space filling curves to substitution tilings2015-2019: Dr Luke J. Ito, second supervisor (with Joachim Zacharias)
Thesis: Almost finiteness of groupoid actions and Z-stability of C*-algebras associated to tilings2013-2019: Dr Michael Mampusti, adjunct supervisor (with David Pask and Aidan Sims)
Thesis: Equilibrium states and Cuntz-Pimsner algebras on Mauldin-Williams graphs
Grants:
2018-2020: EPSRC First Grant, Application of space filling curves to substitution tilings, £101,091
Organisation and service:
Editorial boards:
2020-present: Editor of the London Mathematical Society Newsletter
Service:
2024-present: Co-organiser of the Scottish Dynamics Network
2023-present: Co-organiser of the Grimm Network in Aperiodic Order
2019-present: Convener of the Research Support Fund, Edinburgh Mathematical Society
2018-present: Trustee of the Glasgow Mathematical Journal Trust
2018-2023: Member of the Outer Assessment Panel Irish Research Council
Colloquia and seminars:
2016-2020: School of Mathematics and Statistics Distinguished Lecture Series, University of Glasgow
2016-2018: Analysis Seminar, University of Glasgow
2011-2015: Operator Algebras Seminar, University of Wollongong
Conferences organised:
May 26-30, 2025: EdinSeaG: Noncommutativity along the North Sea, International Centre for Mathematical Sciences, Edinburgh.
July 20-21, 2023: Hatfest: Celebrating the discovery of an aperiodic monotile, Grimm Network, University of Oxford, Oxford.
July 18, 2023: Grimm Network Research Meeting, The Open University, Milton Keynes.
June 19-23, 2023: Algebras, Geometry, and C*-algebras, International Centre for Mathematical Sciences, Edinburgh.
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.