Personal Information
I am currently a postdoctoral research associate at Bielefeld University in Germany in Dr. Michael Baake's group. I was previously a visiting fellow at the Open University in Milton Keynes, UK in Dr. Reem Yassawi's group. I am currently supported by the German Academic Exchange Service (DAAD) through the Postdoctoral Researchers International Mobility Experience (PRIME) Programme. I completed my PhD (Dr. Math.) in June 2019 at Bielefeld University, under the supervision of Dr. Michael Baake and Dr. Franz Gähler. My PhD thesis is entitled "Lyapunov Exponents in the Spectral Theory of Primitive Inflation Systems". For this work, I was awarded the Dissertationspreis by the Universitätsgesellschaft Bielefeld for the best PhD dissertation for the Faculty of Mathematics in 2019. My research is focused on hierarchical dynamical systems, in particular, substitution dynamical systems and their generalisations. These include- Random substitutions
- Substitutions on infinite alphabets
- Regular sequences
- Multi-dimensional substitution shifts
- S-adic shifts
I mainly look at spectral (diffraction, spectral measures) and dynamical (mixing, extended symmetries, invariant measures) properties, and how they relate to the defining parameters and features of the system. This lies within interactions between dynamical systems, ergodic theory, number theory, and harmonic analysis. In particular, I am currently working on projects anchored on renormalisation and self-similarity as central themes in studying dynamical systems composed of either sequences, point sets, tilings, or measures.
Among my other topics of interest are other areas in mathematical physics, such as deformation quantisation and discrete Schrödinger operators.
When I am not doing Maths, most likely I am playing volleyball or playing the guitar.
For students, please go to the "Teaching" tab.
Recent and upcoming Talks and Conferences
- Aspects of Aperiodic Order
Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany, August 27-September 1, 2023
- 15th International Conference on Quasicrystals (ICQ15) (invited speaker)
Steinhardt Museum of Natural History, Tel Aviv University, Israel, June 18-23, 2023
- Arithmetic and Spectral Structures in Aperiodic Order (organiser)
Together with Dan Rust, I co-organised this two-day mini-workshop, which followed a dual-hybrid format with participants from Bielefeld University (Germany) and Open University (UK), and was held from September 22-23, 2022. - Almost Periodicity in Aperiodic Order (invited speaker)
Banff International Research Station, Canada, September 9-11,2022
