Ian David Morris

  Mathematics Department
University of Surrey

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

Who I am:

I am currently a Senior Lecturer in the mathematics department of the University of Surrey, where I have been working since January 2012. I previously 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. Prior to all that 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.

In general I am interested in applications of ergodic theory and dynamical systems to other areas of mathematical analysis. I have previously worked on topics including symbolic dynamics, thermodynamic formalism, optimization problems in ergodic theory and applications of ergodic theory to combinatorics, but in recent years my research has been particularly dominated by connections between multiplicative ergodic theory and matrix analysis. My principal current focus is on applications of those two topics to the dimension theory of self-affine fractals.

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:

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.

September 2017 - September 2021: Principal Investigator for Leverhulme Trust Research Project Grant RPG-2016-194 "Lower bounds for Lyapunov exponents", £267,776.


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. A converse statement to Hutchinson's theorem and a dimension gap for self-affine measures (with Çağrı Sert).
  2. Preprint. (arXiv)
  3. A strongly irreducible affine iterated function system with two invariant measures of maximal dimension (with Çağrı Sert).
  4. Submitted. (arXiv)
  5. Fast approximation of the p-radius, matrix pressure or generalised Lyapunov exponent for positive and dominated matrices.
  6. Submitted. (arXiv)
  7. Analyticity of the affinity dimension for planar iterated function systems with matrices which preserve a cone (with Natalia Jurga).
  8. Submitted. (arXiv)
  9. Lq-spectra of self-affine measures: closed forms, counterexamples and split binomial sums (with Jonathan Fraser, Lawrence Lee and Han Yu).
  10. Submitted. (arXiv)
  11. Fast approximation of the affinity dimension for dominated affine iterated function systems.
  12. Submitted. (arXiv) (Mathematica code)
  13. A short proof that the number of division steps in the Euclidean algorithm is normally distributed.
    Preprint. (arXiv)
  14. Domination, almost additivity and thermodynamical formalism for planar matrix cocycles (with Balázs Bárány and Antti Käenmäki).
  15. Israel Journal of Mathematics, to appear. (arXiv)
  16. Effective estimates on the top Lyapunov exponent for random matrix products (with Natalia Jurga).
  17. Nonlinearity 32 (2019) 4117-4146. (arXiv)
  18. Characterization of dominated splittings for operator cocycles acting on Banach spaces (with Alex Blumenthal).
  19. Journal of Differential Equations 267 (2019) 3977-4013. (arXiv)
  20. A necessary and sufficient condition for a matrix equilibrium state to be mixing.
  21. Ergodic Theory and Dynamical Systems 39 (2019) 2223-2234. (arXiv)
  22. An explicit formula for the pressure of box-like affine iterated function systems.
  23. Journal of Fractal Geometry 6 (2019) 127-141. (arXiv)
  24. On equality of Hausdorff and affinity dimensions, via self-affine measures on positive subsystems (with Pablo Shmerkin).
  25. Transactions of the American Mathematical Society 371 (2019) 1547-1582. (arXiv)
  26. Lyapunov-maximising measures for pairs of weighted shift operators.
  27. Ergodic Theory and Dynamical Systems 39 (2019) 225-247. (arXiv)
  28. Some observations on Käenmäki measures.
  29. Annales Academiæ Scientiarum Fennicæ 43 (2018) 945-960. (arXiv)
  30. Ergodic properties of matrix equilibrium states.
  31. Ergodic Theory and Dynamical Systems 38 (2018) 2295-2320. (arXiv)
  32. Equilibrium states of generalised singular value potentials and applications to affine iterated function systems (with Jairo Bochi).
  33. Geometric and Functional Analysis 28 (2018) 995-1028. (arXiv)
  34. Structure of equilibrium states on self-affine sets and strict monotonicity of affinity dimension (with Antti Käenmäki).
  35. Proceedings of the London Mathematical Society 116 (2018) 929-956. (arXiv)
  36. Generic properties of the lower spectral radius for some low-rank pairs of matrices.
  37. Linear Algebra and its Applications 524 (2017) 35-60. (arXiv)
  38. On Falconer's formula for the generalised Rényi dimension of a self-affine measure.
  39. Annales Academiæ Scientiarum Fennicæ 42 (2017) 227-238. (arXiv)
  40. An inequality for the matrix pressure function and applications.
  41. Advances in Mathematics 302 (2016) 280-308. (arXiv)
  42. A rigorous version of R. P. Brent's model for the binary Euclidean algorithm.
    Advances in Mathematics 290 (2016) 73-143. (arXiv)
  43. Continuity properties of the lower spectral radius (with Jairo Bochi).
    Proceedings of the London Mathematical Society 110 (2015) 477-509. (arXiv)
  44. A note on configurations in sets of positive density which occur at all large scales.
    Israel Journal of Mathematics 207 (2015) 719-738. (arXiv)
  45. Extremal sequences of polynomial complexity (with Kevin G. Hare and Nikita Sidorov).
    Mathematical Proceedings of the Cambridge Philosophical Society 155 (2013) 191-205.
  46. 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)
  47. 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.
  48. A new sufficient condition for the uniqueness of Barabanov norms.
    SIAM Journal on Matrix Analysis and Applications 33 (2012) 317-324. (pdf)
  49. The generalised Berger-Wang formula and the spectral radius of linear cocycles.
    Journal of Functional Analysis 262 (2012) 811-824. (pdf)
  50. 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)
  51. A rapidly-converging lower bound for the joint spectral radius via multiplicative ergodic theory.
    Advances in Mathematics 225 (2010) 3425-3445. (pdf)
  52. 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)
  53. Ergodic optimization for generic continuous functions.
    Discrete and Continuous Dynamical Systems 27 (2010) 383-388. (pdf)
  54. The Conze-Guivarc'h-Mañé lemma for intermittent maps of the circle.
    Ergodic Theory and Dynamical Systems 29 (2009) 1603-1611 (pdf)
  55. Lyapunov optimizing measures for C1 expanding maps of the circle (with Oliver Jenkinson).
    Ergodic Theory and Dynamical Systems 28 (2008) 1849-1860 (pdf)
  56. Approximating the maximum ergodic average via periodic orbits (with David Collier).
    Ergodic Theory and Dynamical Systems 28 (2008) 1081-1090 (pdf)
  57. Maximizing measures of generic Hölder continuous potentials have zero entropy.
    Nonlinearity 21 (2008) 993-1000 (pdf)
  58. A sufficient condition for the subordination principle in ergodic optimization.
    Bulletin of the London Mathematical Society 39 (2007) 214-220 (pdf)
  59. 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)