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 Hausdorff Dimension of Bernoulli Convolutions, with S. Akiyama, D.J. Feng and T. Persson, preprint 2018.
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, appeared
here
in Annales Academiae Scientiarum Fennicae, 2017.
The Random Continued Fraction Transformation,
with C. Kalle and E. Verbitskiy, appeared
here 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.
Teaching:
During the spring semester 2018 I will be teaching Fracal Geometry. Students should consult blackboard for all of the course materials. My office hour is 12:00 to 13:00 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
Manchester
M13 9PL
United Kingdom
Office number 2.218
thomas.kempton@manchester.ac.uk
0044 161 3063683
