Dr Simon Baker MMath PhD

Dr Simon Baker

School of Mathematics

Contact details

School of Mathematics
Watson Building
University of Birmingham
B15 2TT

Simon Baker is a lecturer in the School of Mathematics working within the Dynamical Systems and Topology research group.

Simon is interested in topics from Ergodic Theory, Fractal Geometry, and Number Theory. Specific areas include beta expansions, Diophantine approximation, and iterated function systems. He regularly gives invited talks at events held in the UK and abroad.

Personal webpage: https://simonbakermaths.wordpress.com/


  • PhD in Pure Mathematics, University of Manchester, 2014.
  • MMath in Mathematics, University of Warwick, 2010.


Simon graduated from the University of Warwick in 2010 and went on to complete a PhD in Pure Mathematics at the University of Manchester under the supervision of Prof. Richard Sharp and Dr Nikita Sidorov.

After completing his PhD, he was a Research Associate working with Dr Karma Dajani at the University of Utrecht. He then returned to Manchester for a year to take up an EPSRC Doctoral Prize fellowship. This was followed by a year in Reading where he was a Richard Rado Postdoctoral Fellow. Ten years after first arriving at Warwick he then returned as a Research Associate working under the supervision of Prof. Mark Pollicott.

He has been a lecturer in the School of Mathematics at the University of Birmingham since September 2019.


Semester 1

LC Real Analysis & the Calculus (Jinan)

Semester 2

LC Probability & Statistics (Jinan)

Postgraduate supervision

Simon is keen to supervise students who are interested in topics from Ergodic Theory and Fractal Geometry.


Simon’s research interests include Ergodic Theory, Fractal Geometry, and Number Theory. He is interested in applying ideas from Diophantine approximation to the study of overlapping iterated function systems. In particular, he is interested in whether suitable analogues of a well-known theorem due to Khintchine hold generically.  

Other activities

Associate Fellow of the Higher Education Academy.


Recent publications


Aistleitner, C, Baker, S, Technau, N & Yesha , N 2022, 'Gap statistics and higher correlations for geometric progressions modulo one', Mathematische Annalen. https://doi.org/10.1007/s00208-022-02362-3

Baker, S 2022, 'Iterated function systems with super-exponentially close cylinders II', Proceedings of the American Mathematical Society, vol. 150, no. 1, pp. 245-256. https://doi.org/10.1090/proc/15644

Algom, A, Baker, S & Shmerkin, P 2022, 'On normal numbers and self-similar measures', Advances in Mathematics, vol. 399, 108276. https://doi.org/10.1016/j.aim.2022.108276

Baker, S & Troscheit, S 2021, 'Analogues of Khintchine's theorem for random attractors', Transactions of the American Mathematical Society. https://doi.org/10.1090/tran/8537

Baker, S 2021, 'Equidistribution results for self-similar measures', International Mathematics Research Notices. https://doi.org/10.1093/imrn/rnab056

Baker, S 2021, 'New dimension bounds for αβ sets', Journal of Number Theory. https://doi.org/10.1016/j.jnt.2021.04.018

Baker, S 2020, 'Equidistribution results for sequences of polynomials', Journal of Number Theory. https://doi.org/10.1016/j.jnt.2020.01.003

Baker, S 2020, 'Iterated function systems with super-exponentially close cylinders', Advances in Mathematics. https://doi.org/https://arxiv.org/pdf/1909.04343.pdf

Baker, S & Jurga, N 2020, 'Maximising Bernoulli measures and dimension gaps for countable branched systems', Ergodic Theory and Dynamical Systems. https://doi.org/10.1017/etds.2020.41

Baker, S & Kong, D 2020, 'On the complexity of the set of codings for self-similar sets and a variation on the construction of Champernowne', Advances in Mathematics, vol. 360, 106934, pp. 1-29. https://doi.org/10.1016/j.aim.2019.106934

Baker, S & Aistleitner, C 2020, 'On the pair correlations of powers of real numbers', Israel Journal of Mathematics. https://doi.org/https://arxiv.org/pdf/1910.01437.pdf

Baker, S 2020, 'Overlapping iterated function systems from the perspective of Metric Number Theory', Memoirs of the American Mathematical Society. https://doi.org/https://arxiv.org/pdf/1901.07875.pdf

Baker, S & Farmer, M 2020, 'Quantitative recurrence properties for self-conformal sets', Proceedings of the American Mathematical Society.

Baker, S & Kong, D 2020, 'Two bifurcation sets arising from the beta transformation with a hole at 0', Indagationes Mathematicae, vol. 31, no. 3, pp. 436-449. https://doi.org/10.1016/j.indag.2020.03.001

Allen, D & Baker, S 2019, 'A general mass transference principle', Selecta Mathematica, New Series, vol. 25, no. 3, 39. https://doi.org/10.1007/s00029-019-0484-9

View all publications in research portal

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