Andrei Zabolotskii

I am a mathematician working on friezes, SL₂-tilings and cluster algebras, as well as other topics. I am interested in combinatorial approaches to problems in geometry, number theory, topology, and algebra. I also like computational problems, mathematical visualisation, mathematical databases, and formalisation of proofs.

I am currently a last-year PhD student at the Open University (UK). My lead supervisor is Ian Short.

Curriculum vitae (pdf)
andrei.zabolotskii@open.ac.uk

Publications

Ian Short, Matty van Son, Andrei Zabolotskii, Frieze patterns and Farey complexes, Adv. Math. 472 (2025), 110269; arXiv:2312.12953 [math.CO].
Andrei Zabolotskii, Wildest SL₂-tilings, Examples and Counterexamples 8 (2025), 100206; arXiv:2508.09773 [math.CO].
Andrei Zabolotskii, Additive systems for ℤ are undecidable, J. Comb. Math. Comb. Comput. 130 (2026), 241–253; arXiv:2508.17285 [math.CO].
11 papers in theoretical physics throughout 2012–2020, listed at Google Scholar.

Preprints

Oleg Karpenkov, Ian Short, Matty van Son, Andrei Zabolotskii, Classifying integer tilings and hypertilings, arXiv:2601.21445 [math.CO].
Andrei Zabolotskii, Beyond the Laurent phenomenon, arXiv:2603.29073 [math.RA].
Sammy Benzaira, Ian Short, Matty van Son, Andrei Zabolotskii, Enumerating tame friezes over ℤ/nℤ, arXiv:2410.23400 [math.CO].
Andrei Zabolotskii, Coweight lattice A_n* and lattice simplices, arXiv:2003.10251 [math.CO].

Software

Triangulations and friezes – an interactive demonstration of the connections between triangulated polygons, paths in the Farey graph, friezes, and cluster variables in the cluster algebra of type A_n.
Visual Cluster Algebras – a portal with several applets related to cluster algebras and friezes. Founded and maintained by Antoine de Saint Germain, co-maintained by me.
sandpile – a command line tool to study and visualise the sandpile model.
See more on Github and in the tidbits section.

Presentations

Conference talks

A planned talk at the Clusters, deformations and positivity workshop, ICJ, Lyon, 2–4 September 2026
A planned talk at the Farey’s legacy in frieze patterns and discrete geometry workshop, ICMS, Edinburgh, 20–24 April 2026
Laurent-Shmaurent, integer friezes, and polygon folding — talk at the Frieze patterns in algebra, combinatorics and geometry conference, CIRM, 12–16 May 2025
Additive systems for ℤ are undecidable — talk at the Postgraduate Combinatorial Conference, The University of Glasgow, 30 April – 2 May 2025
Gallery of Farey graphs, and Wild SL₂-tilings — talk at the Continued Fractions and SL₂-tilings LMS Northern Regional Meeting and Workshop, Durham University, 25–28 March 2024

Seminar talks

Farey graph, friezes, and cluster algebras — talk for The Archimedeans, Cambridge, February 2026
Friezes, cluster algebras, and the poly phenomenon — talk at the Selected Topics in Mathematics seminar, University of Liverpool, November 2025
SL₂-tilings, friezes, and Farey graphs — talk at the Geometry and Topology seminar, Durham University, September 2025
Friezes — talk at the Geometry Seminar of ICMS, ICMS-Sofia (via online), August 2025

Research visits

Research visit to Durham University Department of Mathematical Sciences, hosted by Anna Felikson and Pavel Tumarkin (September–October 2025)
Planned research visit to University of Lyon 1, hosted by Alexander Thomas (September 2026)

Teaching and research project supervision

Co-supervisor (with Ian Short and Matty van Son) of an EPSRC Doctoral Training Partnership funded summer internship at the Open University (2024)
Supervisor of research projects in mathematics and lecturer at various programs for high school students, including:
- MIT PRIMES Yulia’s Dream, an MIT program for gifted students from Ukraine (2023–2024)
- STEM Learning Research Placements and Experiences, hosted at the Open University (2024)
- Slon summer school (2010–2019, also co-organiser), as well as several other summer schools
Part-time teacher at RSM Online, an extracurricular mathematics education program (2022–2026)
Co-author of problems and teaching materials for Yandex Lyceum, a programming course taken by tens of thousands of school students annually (2016–2017)

Collaborative projects contributions and outreach

I am an editor and a contributor to the On-Line Encyclopedia of Integer Sequences. I published an expository article about it: The On-Line Encyclopedia of Integer Sequences in 2021, Mat. Pros. Ser. 3 28, 199–212 (2021) (English translation available); and wrote a series of articles in the Kvant magazine about remarkable integer sequences.

I also made minor contributions to LMFDB, Erdős Problems, and other projects.

Miscellaneous tidbits

kolakoski_algorithms – an efficient implementation of the Kolakoski sequence.
Full-plane Apollonian circle packing shader.
Problem 92.2 in Irish Math. Soc. Bulletin (and its solution), related to the Lights Out puzzle.