Mike Whittaker (he/him/his)
Professor of Mathematics
University of Glasgow
e-mail: Mike.Whittaker at glasgow.ac.uk
Office: 329 Maths and Stats Building
School of Mathematics and Statistics
University of Glasgow
Glasgow, G12 8QQ
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.
2016-2021: 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 unity
2016-2021: Dr Ismail Ozkaraca, supervisor
Thesis: An application of space filling curves to substitution tilings
2015-2019: Dr Luke J. Ito, second supervisor (with Joachim Zacharias)
Thesis: Almost finiteness of groupoid actions and Z-stability of C*-algebras associated to tilings
2013-2019: Dr Michael Mampusti, adjunct supervisor (with David Pask and Aidan Sims)
Thesis: Equilibrium states and Cuntz-Pimsner algebras on Mauldin-Williams graphs
Organisation and service:
2020-present: Editor of the London Mathematical Society Newsletter
2018-present: Trustee of the Glasgow Mathematical Journal Trust
2018-present: Member of the Outer Assessment Panel Irish Research Council
Colloquia and seminars:
2011-2015: Operator Algebras Seminar, University of Wollongong
July 20-21, 2023: Hatfest: Celebrating the discovery of an aperiodic monotile, Grimm Network, University of Oxford, Oxford.
March 24-25, 2017: Scottish Operator Algebras Research Meeting, 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.