Tom Kempton

Tom Kempton

From Lucca Tower

About Me:

I'm a lecturer at the University of Manchester working in the dynamical systems group. My main interests lie in applications of thermodynamic formalism to problems in fractal geometry and number theory, and in particular in the study of Bernoulli convolutions and self-affine sets. Fringe interests include percolation and the graph reconstruction conjecture.

Previously I was an EPSRC funded postdoc at the University of St Andrews working with Kenneth Falconer on various problems relating to dynamics on self-affine sets. Before that I worked with Karma Dajani at the University of Utrecht. The main focus of my research there was the ergodic theory of dynamical systems relating to expansions of real numbers. In particular, I looked at how properties of the random beta-transformation can be used in the discussion of absolute continuity of Bernoulli convolutions.

I completed my PhD at the University of Warwick in March 2011 under the supervision of Mark Pollicott. My thesis was on thermodynamic formalism for symbolic dynamical systems.

I'm originally from Derby and have also lived in Coventry, Utrecht, Edinburgh and Manchester. I regularly take part in Parkrun and am currently struggling to learn the Greek language in time for my wedding to Aspa next year.

Publications and Preprints:

The following preprint versions of papers are not final, for finished versions follow the links to the websites of the relevant journals. Click here for my Google Scholar profile.

On the L^q Dimensions of Measures on Hueter-Lalley Type Self-Affine Sets, with J. Fraser, to appear in Proc. AMS.

The Dimension of Projections of Self- Affine Sets and Measures, with K. Falconer, Preprint 2015.

The Random Continued Fraction Transformation, with C. Kalle and E. Verbitskiy, to appear in Nonlinearity 2017.

The Scenery Flow for Self-Affine Measures, Preprint 2015.

Planar self-affine sets with equal Hausdorff, box and affinity dimensions, with K. Falconer, appeared here in ETDS, 2016 .

Sets of beta-expansions and the Hausdorff Measure of Slices through Fractals, appeared here in the Journal of the European Mathematical Society, 2016 .

Bernoulli Convolutions and 1D Dynamics, with T. Persson, appeared here in Nonlinearity, 2015 .

Self-Affine Sets with Positive Lebesgue Measure (with K. Dajani and K. Jiang), Indag. Math 2014.

Digit Frequencies and Bernoulli Convolutions, Indag. Math 2014.

On The Invariant Density of the Random Beta- Transformation, appeared here in Acta Mathematica Hungarica, 2013.

Counting Beta Expansions and the Absolute Continuity of Bernoulli Convolutions appeared here in Monatshefte für Mathematik, 2013.

Thermodynamic Formalism for Suspension Flows over Countable Markov Shifts, appeared here in Nonlinearity, 2011.

Zero Temperature Limits of Gibbs Equilibrium States for Countable Markov Shifts, appeared here in the Journal of Statistical Physics, 2011.

Factors of Gibbs Measures for Subshifts of Finite Type, appeared here in the Bulletin of the London Mathematical Society, 2011.

Factors of Gibbs Measures for Full Shifts, (with M. Pollicott), appeared in the proceedings of the BIRS Workshop on Hidden Markov Processes, 2011.

PhD Opportunities:

I'm keen to supervise PhD students, and if you think that you'd like to do a PhD at Manchester then please get in touch. The school has various sources of funding including a number of fully funded EPSRC scholarships. Please drop me an email if you think you might be interested.


In 2017 I am teaching Fracal Geometry. Students should consult blackboard for all of the course materials. My office hour is 10:30 to 11:30 on Wednesdays, and my office is 2.218. Please feel free to drop in and ask me any quesions about the course during my office hour or at other times.

Numbers in Ergodic Theory:

Together with Charlene Kalle I organised a series of one day meetings in the Netherlands on Ergodic theory. These were supported by grants from the NWO and from the STAR cluster.

Tom Kempton
School of Mathematics
The University of Manchester
M13 9PL
United Kingdom
Office number 2.218
0044 161 3063683