Matty van Son

Home • Research • Seminar & conferences • Apps & links • Contact
Current work
I am a mathematician. I work mostly in discrete geometry. Some of my research interests include multidimensional continued fractions, Conway-Coxeter frieze patterns, and Markov numbers. I am currently on the job market.
Employment history
[2021-] I currently hold an Honorary position at the University of Liverpool, through which I have been co-organising the online seminar Selected Topics in Mathematics.
[2022-2025] Most recently I worked as a Postdoctoral Research Associate at The Open University, working with Professor Ian Short. We worked on a project entitled "The Farey Framework", investigating the connections between SL\(_2\)-tilings and the Farey complex. This work was closely connected to Conway Coxeter friezes and the theory of cluster algebras. My research was funded by EPSRC grant EP/W002817/1.
[2021-2022] Previously I worked as a Postdoctoral Research Assistant at TU Wien with Professor Christian Müller. We worked on a project entitled "Discrete sufraces with prescribed mean curvature", funded by the Austrian Science Fund (FWF) P 29981.
Background
My CV (pdf).
I completed my PhD on Markov numbers in 2021 under the supervision of O. Karpenkov. My thesis is available as a pdf here.
I obtained my undergraduate degree from NUI Maynooth (now Maynooth University).
Research Interests
I am currently working on problems in the intersection of number theory, combinatorics, and lattice and hyperbolic geometries: these include questions on frieze patterns, SL\(_2\)-tilings, and multidimensional continued fractions.
Publications and Preprints
Publications:
  1. Frieze patterns and Farey complexes (2025). ( read ) ( doi ) ( arXiv )
  2. Generalised Markov numbers (2020). ( read ) ( doi ) ( arXiv )
  3. Palindromic sequences of the Markov spectrum (2019). ( read online ) ( doi ) ( arXiv )
  4. Perron identity for arbitrary broken lines (2019). ( read online ) ( doi ) ( arXiv )
Preprints:
  1. Enumerating tame friezes over \(\mathbb{Z}/n\mathbb{Z}\) (2024). ( read ) ( arXiv )
  2. Geometry of multidimensional Farey summation algorithm and frieze patterns (2024). ( read ) ( arXiv )
  3. Uniqueness conjectures for extended Markov numbers (2020). ( read ) ( arXiv )
Errata
Errata for the text Generalised Markov numbers (JNT, 2020) are available here .
Seminar
I hold an honorary research position at the University of Liverpool through which I co-organise a seminar entitled:
Selected Topics in Mathematics – Online Edition
My contact address for all things relating to the seminar is:
m.van-son (at) liverpool.ac.uk
Convergents calculator
Here is a small app for calculating the convergents of negative continued fractions.
Links
  • Andrei Zabolotskii's excellent app on friezes
  • A nice reference page for learning friezes by Anna Felikson
  • Here is an app on cluster algebras by Antoine de Saint Germain
Contact details
Here are my current contact details:
m.van-son (at) liverpool.ac.uk
Department of Mathematical Sciences
University of Liverpool
Liverpool
L69 7ZL
United Kingdom