Dr Jim Belk

Lecturer in Pure Mathematics (Mathematics)

telephone: 01413306527
email: Jim.Belk@glasgow.ac.uk
pronouns: He/him/his

School of Mathematics & Statistics, Room 426, University of Glasgow

Biography

Personal Website: https://jimbelk.github.io/web/

Research interests

My research interests include geometric group theory, dynamical systems, and fractal geometry. Within group theory, I am especially interested in discrete groups of homeomorphisms such as Thompson's groups and self-similar groups, and associated questions about computability, finiteness properties, and embeddings. Within dynamical systems my main interest is complex dynamics, including Thurston equivalence of branched covers, connections to mapping class groups and Teichmüller theory, and the topology and quasiconformal geometry of Julia sets. I am also interested in dynamics of homeomorphisms more broadly, including symbolic dynamics, as well as homeomorphism groups of fractals.

Research groups

Publications

List by: Type | Date

Jump to: 2025 | 2024 | 2023 | 2022 | 2021 | 2020 | 2019 | 2017 | 2016 | 2015 | 2014 | 2010 | 2005

Number of items: 28.

2025

Belk, James ORCID: https://orcid.org/0000-0002-9392-3378, Hyde, James and Tatch Moore, Justin (2025) A piecewise linear homeomorphism of the circle preserving rational points and periodic under renormalization. Groups, Geometry, and Dynamics, (doi: 10.4171/ggd/938) (Early Online Publication)

Belk, James ORCID: https://orcid.org/0000-0002-9392-3378, Hyde, James and Moore, Justin Tatch (2025) A piecewise linear homeomorphim of the circle which is periodic under renormalization. Groups, Geometry, and Dynamics, (Accepted for Publication)

Belk, James ORCID: https://orcid.org/0000-0002-9392-3378 and Forrest, Bradley (2025) Quasisymmetries of finitely ramified Julia sets. Mathematische Annalen, (doi: 10.1007/s00208-025-03238-y) (Early Online Publication)

Belk, Jim ORCID: https://orcid.org/0000-0002-9392-3378, Bleak, Collin, Matucci, Francesco and Zaremsky, Matthew C.B. (2025) Hyperbolic groups satisfy the Boone-Higman conjecture. Duke Mathematical Journal, (Accepted for Publication)

Belk, Jim ORCID: https://orcid.org/0000-0002-9392-3378, Bleak, C., Quick, M. and Skipper, R. (2025) The Maximality of T in Thompson’s group V. Archiv der Mathematik, 125, pp. 1-7. (doi: 10.1007/s00013-025-02136-8)

Belk, James ORCID: https://orcid.org/0000-0002-9392-3378, Bleak, Collin, Matucci, Francesco and Zaremsky, Matthew C.B. (2025) Progress around the Boone-Higman conjecture. EMS Surveys in Mathematical Sciences, (doi: 10.4171/EMSS/101) (Early Online Publication)

Belk, James ORCID: https://orcid.org/0000-0002-9392-3378 and Matucci, Francesco (2025) Boone-Higman embeddings for contracting self-similar groups. Groups, Geometry, and Dynamics, (doi: 10.4171/GGD/898) (Early Online Publication)

Belk, James ORCID: https://orcid.org/0000-0002-9392-3378, Bleak, Collin, Quick, Martyn and Skipper, Rachel (2025) Type systems and maximal subgroups of Thompson’s group V. Transactions of the American Mathematical Society Series B, 12, pp. 417-469. (doi: 10.1090/btran/204)

2024

Belk, James, Elliott, Luke and Matucci, Francesco (2024) A short proof of Rubin’s theorem. Israel Journal of Mathematics, (doi: 10.1007/s11856-024-2700-3) (Early Online Publication)

2023

Belk, James and Matucci, Francesco (2023) Conjugator length in Thompson’s groups. Bulletin of the London Mathematical Society, 55(2), pp. 793-810. (doi: 10.1112/blms.12757)

2022

Belk, James ORCID: https://orcid.org/0000-0002-9392-3378, Lanier, Justin, Margalit, Dan and Winarski, Rebecca R. (2022) Recognizing topological polynomials by lifting trees. Duke Mathematical Journal, 171(17), pp. 3401-3480. (doi: 10.1215/00127094-2022-0043)

Belk, James, Hyde, James and Matucci, Francesco (2022) Embedding Q into a finitely presented group. Bulletin of the American Mathematical Society, 59, pp. 561-567. (doi: 10.1090/bull/1762)

Belk, James ORCID: https://orcid.org/0000-0002-9392-3378 and Zaremsky, Matthew C. B. (2022) Twisted Brin-Thompson groups. Geometry and Topology, 26(3), pp. 1189-1223. (doi: 10.2140/gt.2022.26.1189)

2021

Belk, James ORCID: https://orcid.org/0000-0002-9392-3378, Bleak, Collin and Matucci, Francesco (2021) Rational embeddings of hyperbolic groups. Journal of Combinatorial Algebra, 5(2), pp. 123-183. (doi: 10.4171/JCA/52)

2020

Belk, Jim ORCID: https://orcid.org/0000-0002-9392-3378, Bleak, Collin and Matucci, Francesco (2020) Embedding right-angled Artin groups into Brin–Thompson groups. Mathematical Proceedings of the Cambridge Philosophical Society, 169(2), pp. 225-229. (doi: 10.1017/s0305004119000112)

2019

Belk, Jim ORCID: https://orcid.org/0000-0002-9392-3378 and Forrest, Bradley (2019) Rearrangement groups of fractals. Transactions of the American Mathematical Society, 372(7), pp. 4509-4552. (doi: 10.1090/tran/7386)

Belk, James ORCID: https://orcid.org/0000-0002-9392-3378, Hyde, James and Matucci, Francesco (2019) On the asynchronous rational group. Groups, Geometry, and Dynamics, 13(4), pp. 1271-1284. (doi: 10.4171/ggd/523)

2017

Belk, James ORCID: https://orcid.org/0000-0002-9392-3378 and Bleak, Collin (2017) Some undecidability results for asynchronous transducers and the Brin-Thompson group 2V. Transactions of the American Mathematical Society, 369(5), pp. 3157-3172. (doi: 10.1090/tran/6963)

2016

Belk, James ORCID: https://orcid.org/0000-0002-9392-3378 and Matucci, Francesco (2016) Röver's simple group is of type F∞. Publicacions Matemàtiques, 60, pp. 501-524. (doi: 10.5565/publmat_60216_07)

2015

Belk, James ORCID: https://orcid.org/0000-0002-9392-3378 and Forrest, Bradley (2015) A Thompson group for the basilica. Groups, Geometry, and Dynamics, 9(4), pp. 975-1000. (doi: 10.4171/ggd/333)

Belk, James ORCID: https://orcid.org/0000-0002-9392-3378 and McGrail, Robert W. (2015) The word problem for finitely presented quandles is undecidable. In: de Paiva, V., de Queiroz, R., Moss, L., Leivant, D. and de Oliveira, A. (eds.) Logic, Language, Information, and Computation. Series: Lecture Notes in Computer Science (LNTCS) (9160). Springer Berlin Heidelberg, pp. 1-13. ISBN 9783662477090 (doi: 10.1007/978-3-662-47709-0_1)

2014

Hossain, Nabil, McGrail, Robert W., Belk, James ORCID: https://orcid.org/0000-0002-9392-3378 and Matucci, Francesco (2014) Deciding conjugacy in Thompson's group F in linear time. In: 2013 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, Timisoara, Romania, 23-26 September 2013, pp. 89-96. ISBN 9781479930364 (doi: 10.1109/synasc.2013.19)

Belk, James ORCID: https://orcid.org/0000-0002-9392-3378 and Matucci, Francesco (2014) Conjugacy and dynamics in Thompson’s groups. Geometriae Dedicata, 169(1), pp. 239-261. (doi: 10.1007/s10711-013-9853-2)

McGrail, Robert W., Belk, James ORCID: https://orcid.org/0000-0002-9392-3378, Garber, Solomon, Wood, Japheth and Fish, Benjamin (2014) CSPs and connectedness: P/NP dichotomy for idempotent, right quasigroups. In: 2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, Timisoara, Romania, 22-25 September 2014, pp. 367-374. ISBN 9781479984480 (doi: 10.1109/synasc.2014.56)

Belk, James ORCID: https://orcid.org/0000-0002-9392-3378, Hossain, Nabil, Matucci, Francesco and McGrail, Robert (2014) Implementation of a solution to the conjugacy problem in Thompson's group F. ACM Communications in Computer Algebra, 47(3/4), pp. 120-121. (doi: 10.1145/2576802.2576823)

2010

Belk, James ORCID: https://orcid.org/0000-0002-9392-3378 and Koch, Sarah (2010) Iterated monodromy for a two-dimensional map. In: Bonk, Mario, Gilman, Jane, Masur, Howard, Minsky, Yair and Wolf, Michael (eds.) In the Tradition of Ahlfors–Bers, V. Series: Contemporary mathematics (510). American Mathematical Society, pp. 1-11. ISBN 9780821847329