Ian David Morris

(he / him)

  School of Mathematical Sciences
Queen Mary, University of London
Mile End Road
London E1 4NS

profile for Ian Morris at MathOverflow, Q&A for professional mathematicians

Who I am:

I am currently a Reader in Mathematics at Queen Mary, University of London, where I have been working since September 2020. From January 2012 to August 2020 I held a permanent position at the University of Surrey, first as Lecturer and then as Senior Lecturer, and previously to that I held postdoctoral positions at the University of Rome Tor Vergata, at the University of Warwick, at the University of Manchester, and at the Erwin Schrödinger Institute in Vienna. Still earlier I studied at Warwick for my undergraduate degree and received my PhD in 2006 from the University of Manchester where I was supervised by Dr. Charles Walkden.

At Queen Mary I am currently the director of the Mathematics MSc, the deputy director of postgraduate research studies, and the official local representative of the London Mathematical Society.

My core area of mathematical expertise is ergodic theory, but a recurring theme in my research has been the application of ergodic theory to problems in other areas of mathematical analysis. At various times this has included fractal geometry, the joint spectral characteristics of sets of matrices and linear operators, the analysis of number-theoretic algorithms and the metric geometry of measurable subsets of the plane. In the last few years I have been particularly engaged in developing the thermodynamic formalism of linear cocycles, motivated principally by its applications to the dimension theory of self-affine fractals and non-conformal repelling sets. More recently I have developed interests in the general properties of fiber-bunched linear cocycles and in the use of ergodic theory to understand marginal instability phenomena in switched differential and difference equations.

I would be interested to hear from potential PhD students who would like to study any of these topics, especially if from the perspective of ergodic theory.

My Erdős number is 3, by three routes: Morris → Hare → Shallit → Erdős; Morris → Lee → Vaughan → Erdős; and Morris → Jenkinson → Mauldin → Erdős.

Who I am not:

More people share my name than you might expect:
Grants held:

September 2017 - July 2022: Principal Investigator for Leverhulme Trust Research Project Grant RPG-2016-194 "Lower bounds for Lyapunov exponents", £267,776.

July 2014 - June 2016: Principal Investigator for EPSRC First Grant EP/L026953/1, "Distributional analysis of GCD algorithms via the ergodic theory of random dynamical systems", £91,795.

Postgraduate and postdoctoral supervision:


My earlier preprint “Dominated splittings for semi-invertible operator cocycles on Hilbert space” (arXiv 1403.0824) contained a critical error and I encourage researchers not to cite it.


At the time of writing my publications are as follows:
  1. On dense intermingling of exact overlaps and the open set condition.
  2. Submitted. (arXiv)
  3. On affine iterated function systems which robustly admit an invariant affine subspace.
  4. Proceedings of the American Mathematical Society, to appear. (arXiv)
  5. A converse statement to Hutchinson's theorem and a dimension gap for self-affine measures (with Çağrı Sert).
  6. Journal of the European Mathematical Society, to appear. (arXiv)
  7. Fast approximation of the affinity dimension for dominated affine iterated function systems.
  8. Annales Fennici Mathematici 47 (2022) 645-694. (arXiv) (Mathematica code)
  9. Marginally unstable discrete-time linear switched systems with highly irregular trajectory growth.
  10. Systems and Control Letters 163 (2022) 105216. (arXiv)
  11. Fast approximation of the p-radius, matrix pressure or generalised Lyapunov exponent for positive and dominated matrices.
  12. SIAM Journal on Matrix Analysis and Applications 43 (2022) 178-198. (arXiv)
  13. How long is the Chaos Game? (with Natalia Jurga)
  14. Bulletin of the London Mathematical Society 53 (2021) 1749-1765. (arXiv)
  15. A strongly irreducible affine iterated function system with two invariant measures of maximal dimension (with Çağrı Sert).
  16. Ergodic Theory and Dynamical Systems 41 (2021) 3417-3438. (arXiv)
  17. Totally ergodic matrix equilibrium states have the Bernoulli property.
  18. Communications in Mathematical Physics 387 (2021) 995-1050. (arXiv)
  19. Lq-spectra of self-affine measures: closed forms, counterexamples and split binomial sums (with Jonathan Fraser, Lawrence Lee and Han Yu).
  20. Nonlinearity 34 (2021) 6331-6357.(arXiv)
  21. Prevalent uniqueness in ergodic optimisation.
  22. Proceedings of the American Mathematical Society 149 (2021) 1631-1639. (arXiv)
  23. Domination, almost additivity and thermodynamical formalism for planar matrix cocycles (with Balázs Bárány and Antti Käenmäki).
  24. Israel Journal of Mathematics 239 (2020) 173-214. (arXiv)
  25. Analyticity of the affinity dimension for planar iterated function systems with matrices which preserve a cone (with Natalia Jurga).
  26. Nonlinearity 33 (2020) 1572-1593. (arXiv)
  27. Effective estimates on the top Lyapunov exponent for random matrix products (with Natalia Jurga).
  28. Nonlinearity 32 (2019) 4117-4146. (arXiv)
  29. Characterization of dominated splittings for operator cocycles acting on Banach spaces (with Alex Blumenthal).
  30. Journal of Differential Equations 267 (2019) 3977-4013. (arXiv)
  31. A necessary and sufficient condition for a matrix equilibrium state to be mixing.
  32. Ergodic Theory and Dynamical Systems 39 (2019) 2223-2234. (arXiv)
  33. An explicit formula for the pressure of box-like affine iterated function systems.
  34. Journal of Fractal Geometry 6 (2019) 127-141. (arXiv)
  35. On equality of Hausdorff and affinity dimensions, via self-affine measures on positive subsystems (with Pablo Shmerkin).
  36. Transactions of the American Mathematical Society 371 (2019) 1547-1582. (arXiv)
  37. Lyapunov-maximising measures for pairs of weighted shift operators.
  38. Ergodic Theory and Dynamical Systems 39 (2019) 225-247. (arXiv)
  39. Some observations on Käenmäki measures.
  40. Annales Academiæ Scientiarum Fennicæ 43 (2018) 945-960. (arXiv)
  41. Ergodic properties of matrix equilibrium states.
  42. Ergodic Theory and Dynamical Systems 38 (2018) 2295-2320. (arXiv)
  43. Equilibrium states of generalised singular value potentials and applications to affine iterated function systems (with Jairo Bochi).
  44. Geometric and Functional Analysis 28 (2018) 995-1028. (arXiv)
  45. Structure of equilibrium states on self-affine sets and strict monotonicity of affinity dimension (with Antti Käenmäki).
  46. Proceedings of the London Mathematical Society 116 (2018) 929-956. (arXiv)
  47. Generic properties of the lower spectral radius for some low-rank pairs of matrices.
  48. Linear Algebra and its Applications 524 (2017) 35-60. (arXiv)
  49. On Falconer's formula for the generalised Rényi dimension of a self-affine measure.
  50. Annales Academiæ Scientiarum Fennicæ 42 (2017) 227-238. (arXiv)
  51. An inequality for the matrix pressure function and applications.
  52. Advances in Mathematics 302 (2016) 280-308. (arXiv)
  53. A rigorous version of R. P. Brent's model for the binary Euclidean algorithm.
    Advances in Mathematics 290 (2016) 73-143. (arXiv)
  54. Continuity properties of the lower spectral radius (with Jairo Bochi).
    Proceedings of the London Mathematical Society 110 (2015) 477-509. (arXiv)
  55. A note on configurations in sets of positive density which occur at all large scales.
    Israel Journal of Mathematics 207 (2015) 719-738. (arXiv)
  56. Extremal sequences of polynomial complexity (with Kevin G. Hare and Nikita Sidorov).
    Mathematical Proceedings of the Cambridge Philosophical Society 155 (2013) 191-205.
  57. Mather sets for sequences of matrices and applications to the study of joint spectral radii.
    Proceedings of the London Mathematical Society 107 (2013) 121-150. (pdf)
  58. On a Devil's staircase associated to the joint spectral radii of a family of pairs of matrices (with Nikita Sidorov).
    Journal of the European Mathematical Society 15 (2013) 1747-1782.
  59. A new sufficient condition for the uniqueness of Barabanov norms.
    SIAM Journal on Matrix Analysis and Applications 33 (2012) 317-324. (pdf)
  60. The generalised Berger-Wang formula and the spectral radius of linear cocycles.
    Journal of Functional Analysis 262 (2012) 811-824. (pdf)
  61. An explicit counterexample to the Lagarias-Wang finiteness conjecture (with Kevin G. Hare, Nikita Sidorov and Jacques Theys).
    Advances in Mathematics 226 (2011) 4667-4701. (pdf)
  62. A rapidly-converging lower bound for the joint spectral radius via multiplicative ergodic theory.
    Advances in Mathematics 225 (2010) 3425-3445. (pdf)
  63. Criteria for the stability of the finiteness property and for the uniqueness of Barabanov norms.
    Linear Algebra and its Applications 443 (2010) 1301-1311. (pdf)
  64. Ergodic optimization for generic continuous functions.
    Discrete and Continuous Dynamical Systems 27 (2010) 383-388. (pdf)
  65. The Conze-Guivarc'h-Mañé lemma for intermittent maps of the circle.
    Ergodic Theory and Dynamical Systems 29 (2009) 1603-1611 (pdf)
  66. Lyapunov optimizing measures for C1 expanding maps of the circle (with Oliver Jenkinson).
    Ergodic Theory and Dynamical Systems 28 (2008) 1849-1860 (pdf)
  67. Approximating the maximum ergodic average via periodic orbits (with David Collier).
    Ergodic Theory and Dynamical Systems 28 (2008) 1081-1090 (pdf)
  68. Maximizing measures of generic Hölder continuous potentials have zero entropy.
    Nonlinearity 21 (2008) 993-1000 (pdf)
  69. A sufficient condition for the subordination principle in ergodic optimization.
    Bulletin of the London Mathematical Society 39 (2007) 214-220 (pdf)
  70. Entropy for zero-temperature limits of Gibbs-equilibrium states for countable-alphabet subshifts of finite type.
    Journal of Statistical Physics 126 (2007) 315-324 (pdf)