# Dr Ian Morris

## Reader in Mathematics, Deputy Director of Postgraduate Research Studies

Email: i.morris@qmul.ac.uk

Telephone: 020 7882 5447

Room Number: Room MB-516

Website: http://www.maths.qmul.ac.uk/~imorris/

## Profile

Dr. Ian Morris is a Reader in Mathematics at Queen Mary, University of London. He previously held a permanent position at the University of Surrey from 2012 to 2020 (first as Lecturer, then as Senior Lecturer) and earlier held temporary positions as a postdoctoral research fellow at the University of Rome Tor Vergata, the University of Warwick, the University of Manchester and the Erwin Schrödinger Institute in Vienna.

His core area of expertise is ergodic theory and the great majority of his research is in some way concerned with applications of ergodic theory to other areas of mathematical analysis. Historically these have included self-affine structures in fractal geometry, joint spectral characteristics of sets of matrices, the analysis of number-theoretic algorithms, the metric geometry of measurable subsets of the plane, and optimisation problems in dynamical systems. His current interests include marginal instability phenomena for switched linear differential and difference equations, and the ergodic theory of non-conformal repellers, including self-affine sets and measures.

## Research

## Publications

- Totally ergodic matrix equilibrium states have the Bernoulli property. To appear in
*Communications in Mathematical Physics.* - A converse statement to Hutchinson's theorem and a dimension gap for self-affine measures (with Çağrı Sert). To appear in
*Journal of the European Mathematical Society.* - How long is the Chaos Game? (with Natalia Jurga). To appear in
*Bulletin of the London Mathematical Society.* - A strongly irreducible affine iterated function system with two invariant measures of maximal dimension (with Çağrı Sert). To appear in
*Ergodic Theory and Dynamical Systems.* - 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. - Prevalent uniqueness in ergodic optimisation.
*Proceedings of the American Mathematical Society*149 (2021) 1631-1639. - Domination, almost additivity and thermodynamical formalism for planar matrix cocycles (with Balázs Bárány and Antti Käenmäki).
*Israel Journal of Mathematics*239 (2020) 173-214. - Analyticity of the affinity dimension for planar iterated function systems with matrices which preserve a cone (with Natalia Jurga).
*Nonlinearity*33 (2020) 1572-1593. - Effective estimates on the top Lyapunov exponent for random matrix products (with Natalia Jurga).
*Nonlinearity*32 (2019) 4117-4146. - Characterization of dominated splittings for operator cocycles acting on Banach spaces (with Alex Blumenthal).
*Journal of Differential Equations*267 (2019) 3977-4013. - A necessary and sufficient condition for a matrix equilibrium state to be mixing.
*Ergodic Theory and Dynamical Systems*39 (2019) 2223-2234. - An explicit formula for the pressure of box-like affine iterated function systems.
*Journal of Fractal Geometry*6 (2019) 127-141. - 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. - Lyapunov-maximising measures for pairs of weighted shift operators.
*Ergodic Theory and Dynamical Systems*39 (2019) 225-247. - Some observations on Käenmäki measures.
*Annales Academiæ Scientiarum Fennicæ*43 (2018) 945-960. - Ergodic properties of matrix equilibrium states.
*Ergodic Theory and Dynamical Systems*38 (2018) 2295-2320. - 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. - 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. - Generic properties of the lower spectral radius for some low-rank pairs of matrices.
*Linear Algebra and its Applications*524 (2017) 35-60. - On Falconer's formula for the generalised Rényi dimension of a self-affine measure.
*Annales Academiæ Scientiarum Fennicæ*42 (2017) 227-238. - An inequality for the matrix pressure function and applications.
*Advances in Mathematics*302 (2016) 280-308. - A rigorous version of R. P. Brent's model for the binary Euclidean algorithm.
*Advances in Mathematics*290 (2016) 73-143. - Continuity properties of the lower spectral radius (with Jairo Bochi).
*Proceedings of the London Mathematical Society*110 (2015) 477-509 - A note on configurations in sets of positive density which occur at all large scales.
*Israel Journal of Mathematics*207 (2015) 719-738. - 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. - 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. - The generalised Berger-Wang formula and the spectral radius of linear cocycles.
*Journal of Functional Analysis*262 (2012) 811-824. - 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. - A rapidly-converging lower bound for the joint spectral radius via multiplicative ergodic theory.
*Advances in Mathematics*225 (2010) 3425-3445. - Criteria for the stability of the finiteness property and for the uniqueness of Barabanov norms.
*Linear Algebra and its Applications*443 (2010) 1301-1311. - Ergodic optimization for generic continuous functions.
*Discrete and Continuous Dynamical Systems*27 (2010) 383-388. - The Conze-Guivarc'h-Mañé lemma for intermittent maps of the circle.
*Ergodic Theory and Dynamical Systems*29 (2009) 1603-1611. - Lyapunov optimizing measures for C
^{1}expanding maps of the circle (with Oliver Jenkinson).*Ergodic Theory and Dynamical Systems*28 (2008) 1849-1860. - Approximating the maximum ergodic average via periodic orbits (with David Collier).
*Ergodic Theory and Dynamical Systems*28 (2008) 1081-1090. - Maximizing measures of generic Hölder continuous potentials have zero entropy.
*Nonlinearity*21 (2008) 993-1000. - A sufficient condition for the subordination principle in ergodic optimization.
*Bulletin of the London Mathematical Society*39 (2007) 214-220. - Entropy for zero-temperature limits of Gibbs-equilibrium states for countable-alphabet subshifts of finite type.
*Journal of Statistical Physics*126 (2007) 315-324.