Tom Kempton

Tom Kempton

From Lucca Tower I'm a postdoc at the University of St Andrews working with Kenneth Falconer on various problems relating to dynamics on self-affine sets. This position is funded by the EPSRC.

Previously 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 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.

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.

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, Preprint 2015.
The Scenery Flow for Self-Affine Measures, Preprint 2015.
Planar self-affine sets with equal Hausdorff, box and affinity dimensions, with K. Falconer, Preprint 2015.
Sets of beta-expansions and the Hausdorff Measure of Slices through Fractals, to appear 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.

Numbers in Ergodic Theory:

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

Seminars & Teaching:

In 2015 I taught the module MT1002 at St Andrews, students should consult the student area on MMS.

In 2013 I taught the course Ergodic Theory, which is part of the masters program at Utrecht and also part of the Stochastics and Financial Mathematics masters. For details, please see the course page.

I also gave a masters course on topics in dynamical systems, information about the course including some material can be found here. In the academic year 2011-2012 I organised the Stochastics and Numerics seminar together with Inan Ates, details of the seminar can be found here.

Travel Plans:

Here is a list of upcoming conferences which I think sound interesting.
Tom Kempton
School of Mathematics and Statistics
North Haugh
St Andrews
KY16 9SS
United Kingdom
+44 (0)1334 463745