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.

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.

More people share my name than you might expect:

- Ian Matthew Morris is Willard Professor of Classics at Stanford University and, among other things, wrote the popular history book “Why the West Rules — For Now” which I quite enjoyed reading. Occasionally people email me to ask questions about it.
- Ian David Morris is also a historian, this time specialising in early Islamic history. He has worked at the University of St. Andrews and at the Spanish National Research Council.
- Ian David Morris was a professor at Hull-York Medical School, where I understand that he specialised in the study of DNA damage. At one point he and I were simultaneously based at the University of Manchester, where I occasionally received his mail.
- Ian D. Morris was a rabbi at Sinai Synagogue in Leeds. I believe that he is the author of a dissertation on the use of humour in Midrash Rabbah, the authorship of which has occasionally been attributed to me by automated search engines despite the fact that at the time he wrote it, I was five years old. At some point I will probably attempt to read it.
- Ifor Morris, formerly of Bangor University in Wales, was the author of several publications dealing with graph theory and related matters.

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.

- Jonah Varney has been my PhD student since September 2018. His work is concerned with marginally unstable discrete linear inclusions and fibre-bunched linear cocycles.

- Natalia Jurga worked with me as a postdoctoral research associate supported by my Leverhulme Trust grant from April 2018 to April 2020. She is currently a postdoctoral research associate at St. Andrews (where she is part of an EPSRC-funded project led by Prof. Jonathan Fraser) and was recently awarded a Leverhulme Trust Fellowship.

- Argyrios Christodoulou has been working with me as a postdoctoral research associate supported by my Leverhulme Trust grant since November 2019.

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:

- Fast approximation of the p-radius, matrix pressure or generalised Lyapunov exponent for positive and dominated matrices.
- Submitted. arXiv)
- Fast approximation of the affinity dimension for dominated affine iterated function systems.
- Submitted. (arXiv) (Mathematica code)
- A short proof that the number of division steps in the Euclidean algorithm is normally distributed.
- Preprint. (arXiv)
- Totally ergodic matrix equilibrium states have the Bernoulli property.
*Communications in Mathematical Physics*, to appear. (arXiv)- A converse statement to Hutchinson's theorem and a dimension gap for self-affine measures (with Çağrı Sert).
*Journal of the European Mathematical Society*, to appear. (arXiv)- How long is the Chaos Game? (with Natalia Jurga)
*Bulletin of the London Mathematical Society*, to appear. (arXiv)- A strongly irreducible affine iterated function system with two invariant measures of maximal dimension (with Çağrı Sert).
*Ergodic Theory and Dynamical Systems*, to appear. (arXiv)- L
^{q}-spectra of self-affine measures: closed forms, counterexamples and split binomial sums (with Jonathan Fraser, Lawrence Lee and Han Yu). *Nonlinearity*34 (2021) 6331-6357.(arXiv)- Prevalent uniqueness in ergodic optimisation.
*Proceedings of the American Mathematical Society*149 (2021) 1631-1639. (arXiv)- Domination, almost additivity and thermodynamical formalism for planar matrix cocycles (with Balázs Bárány and Antti Käenmäki).
*Israel Journal of Mathematics*239 (2020) 173-214. (arXiv)- Analyticity of the affinity dimension for planar iterated function systems with matrices which preserve a cone (with Natalia Jurga).
*Nonlinearity*33 (2020) 1572-1593. (arXiv)- Effective estimates on the top Lyapunov exponent for random matrix products (with Natalia Jurga).
*Nonlinearity*32 (2019) 4117-4146. (arXiv)- Characterization of dominated splittings for operator cocycles acting on Banach spaces (with Alex Blumenthal).
*Journal of Differential Equations*267 (2019) 3977-4013. (arXiv)- A necessary and sufficient condition for a matrix equilibrium state to be mixing.
*Ergodic Theory and Dynamical Systems*39 (2019) 2223-2234. (arXiv)- An explicit formula for the pressure of box-like affine iterated function systems.
*Journal of Fractal Geometry*6 (2019) 127-141. (arXiv)- On equality of Hausdorff and affinity dimensions, via self-affine measures on positive subsystems (with Pablo Shmerkin).
*Transactions of the American Mathematical Society*371 (2019) 1547-1582. (arXiv)- Lyapunov-maximising measures for pairs of weighted shift operators.
*Ergodic Theory and Dynamical Systems*39 (2019) 225-247. (arXiv)- Some observations on Käenmäki measures.
*Annales Academiæ Scientiarum Fennicæ*43 (2018) 945-960. (arXiv)- Ergodic properties of matrix equilibrium states.
*Ergodic Theory and Dynamical Systems*38 (2018) 2295-2320. (arXiv)- Equilibrium states of generalised singular value potentials and applications to affine iterated function systems (with Jairo Bochi).
*Geometric and Functional Analysis*28 (2018) 995-1028. (arXiv)- Structure of equilibrium states on self-affine sets and strict monotonicity of affinity dimension (with Antti Käenmäki).
*Proceedings of the London Mathematical Society*116 (2018) 929-956. (arXiv)- Generic properties of the lower spectral radius for some low-rank pairs of matrices.
*Linear Algebra and its Applications*524 (2017) 35-60. (arXiv)- On Falconer's formula for the generalised Rényi dimension of a self-affine measure.
*Annales Academiæ Scientiarum Fennicæ*42 (2017) 227-238. (arXiv)- An inequality for the matrix pressure function and applications.
*Advances in Mathematics*302 (2016) 280-308. (arXiv)- A rigorous version of R. P. Brent's model for the binary Euclidean algorithm.
*Advances in Mathematics*290 (2016) 73-143. (arXiv) - Continuity properties of the lower spectral radius (with Jairo Bochi).
*Proceedings of the London Mathematical Society*110 (2015) 477-509. (arXiv) - A note on configurations in sets of positive density which occur at all large scales.
*Israel Journal of Mathematics*207 (2015) 719-738. (arXiv) - Extremal sequences of polynomial complexity (with Kevin G. Hare and Nikita Sidorov).
*Mathematical Proceedings of the Cambridge Philosophical Society*155 (2013) 191-205. - 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) - 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. - A new sufficient condition for the uniqueness of Barabanov norms.
*SIAM Journal on Matrix Analysis and Applications*33 (2012) 317-324. (pdf) - The generalised Berger-Wang formula and the spectral radius of linear
cocycles.
*Journal of Functional Analysis*262 (2012) 811-824. (pdf) - 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) - A rapidly-converging lower bound for the joint spectral radius via
multiplicative ergodic theory.
*Advances in Mathematics*225 (2010) 3425-3445. (pdf) - 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) - Ergodic optimization for generic continuous functions.
*Discrete and Continuous Dynamical Systems*27 (2010) 383-388. (pdf) - The Conze-Guivarc'h-Mañé lemma for intermittent maps of the circle.
*Ergodic Theory and Dynamical Systems*29 (2009) 1603-1611 (pdf) - Lyapunov optimizing measures for C
^{1}expanding maps of the circle (with Oliver Jenkinson).*Ergodic Theory and Dynamical Systems*28 (2008) 1849-1860 (pdf) - Approximating the maximum ergodic average via periodic orbits (with David
Collier).
*Ergodic Theory and Dynamical Systems*28 (2008) 1081-1090 (pdf) - Maximizing measures of generic Hölder continuous potentials have zero
entropy.
*Nonlinearity*21 (2008) 993-1000 (pdf) - A sufficient condition for the subordination principle in ergodic optimization.

*Bulletin of the London Mathematical Society*39 (2007) 214-220 (pdf) - 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)