Matty van Son

Matty van Son

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Current work

I am a Postdoctoral Research Associate at The Open University, working with Professor Ian Short. I am working on a project entitled "The Farey Framework", investigating the connections between SL\(_2\)-tilings and the Farey complex. This work is closely connected to Conway Coxeter friezes and the theory of cluster algebras. I co-organise the Selected Topics in Mathematics seminar through the University of Liverpool My working group at the Open University, with Ian Short and Andrei Zabolotskii
My research is funded by EPSRC grant EP/W002817/1.
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: Perron identity for arbitrary broken lines (2019). ( read online ) ( doi ) ( arXiv ) Palindromic sequences of the Markov spectrum (2019). ( read online ) ( doi ) ( arXiv ) Generalised Markov numbers (2020). ( read ) ( doi ) ( arXiv ) Preprints: Uniqueness conjectures for extended Markov numbers (2020). ( read ) ( arXiv ) Frieze patterns and Farey complexes (2024). ( read ) ( arXiv ) Geometry of multidimensional Farey summation algorithm and frieze patterns (2024). ( 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 coorganise 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: matty.van-son (at) open.ac.uk m.van-son (at) liverpool.ac.uk
School of Mathematics & Statistics The Open University Milton Keynes MK7 6AA United Kingdom