Carl-Fredrik Nyberg Brodda

I am a mathematician and an informatician. My research interests lie primarily in combinatorial group and semigroup theory, but also include the history of mathematics, formal language theory, logic, and combinatorics. I have also dipped my toes into bioinformatics.

From February 2025, I am a CMC Fellow at the June E. Huh Centre for Mathematical Challenges at KIAS, Seoul (Korea).
From January 2024 to February 2025, I was a Research Fellow at the School of Mathematics at KIAS, Seoul (Korea).
From August 2023 to December 2023, I was a project research fellow, working on geometric group theory with Sang-hyun (Sam) Kim, at the Korean Institute for Advanced Study (KIAS) in Seoul, South Korea.
Between 2022-2023, I was an ATER (postdoc) at Université Gustave Eiffel, Paris. While there, I was working with Marie-Pierre Béal and Dominique Perrin.
Between 2021-2022, I worked as a Dame Kathleen Ollerenshaw Trust Research Associate (postdoc) at the University of Manchester, UK.
Between 2018-2021, I did a PhD at the University of East Anglia, UK,
under the supervision of Dr Robert (Bob) D. Gray.
Between 2017-2018, I did an MSc at the University of St Andrews, UK.
My dissertation was supervised by Dr Collin P. Bleak.
Between 2016-2017, I did a BSc at Uppsala University, Sweden.
My dissertation was supervised by Dr Cecilia Holmgren.

My arXiv page is here. My ResearchGate page is here.
My Google Scholar page is here. My PhD thesis is here.
I am active on MathOverflow; my page is here.

I am fluent in English, Swedish, and French (I have taught in all three languages). I read Russian & German.
I am Swedish, and 27.

(Me enjoying the beautiful Norfolk broads!)

Email:
cfnb@kias.re.kr

I currently (May 2025) live in Seoul, South Korea.
Prior to this, I lived in (and you maybe met me in):

Stockholm (Sweden)
Uppsala (Sweden)
St Andrews (UK)
Norwich (UK)
Manchester (UK)
Paris (France)

Conference Organizing

I've recently been involved in (co-)organizing a number of conferences and workshops.

[2024] Korea-France Workshop on Dynamical Group Theory (DGT II). 29 February 2024, held at KIAS (Seoul, Korea).
Co-organized with: Sang-hyun Kim (KIAS)
[2024] Semigroups, Groupoids, and C*-algebras, 1-5 July 2024, held at KIAS (Seoul, Korea).
Co-organized with: Sang-hyun Kim (KIAS) and Nóra Szakács (Manchester)
[2024] New Methods in Group Actions on Manifolds (DGT III), 13-16 August 2024, held at KIAS (Seoul, Korea).
Co-organized with: Sang-hyun Kim (KIAS) and Thomas Koberda (Virginia)
[2024] KIAS-Rice Workshop on Geometric Topology (DGT IV), 24-27 September 2024, held at KIAS (Seoul, Korea).
Co-organized with: Sang-hyun Kim (KIAS), Sanghoon Kwak (KIAS), and Alan Reid (Rice)
[2024] World of GroupCraft IV, 9 September 2024. Online 24 hour conference, held via Zoom.
Co-organized with: Alex Bishop, Gemma Crowe, Soumya Dey, Alex Margolis, and Kane Townsend.
[2024] KIAS Graduate Student Meeting in Pure Mathematics, 21 October 2024, held at KIAS (Seoul, Korea)
Co-organized with: Sang-hyun Kim (KIAS)
[2025] 2nd KIAS Graduate Student Meeting in Pure Mathematics, 23 May 2025, held at KIAS (Seoul, Korea)
Co-organized with: Sang-hyun Kim (KIAS)
[2025] 2K-GATE Workshop I, June 2025, held at KIAS (Seoul, Korea)
Co-organized with: Hyungryul Baik (KAIST), Wonyong Jang (KAIST), and Sang-hyun Kim (KIAS)
[2025] Developments in Language Theory (DLT 2025), held in Seoul, Korea in August 2025. Part of program committee.
[2025] KIAS Conference on Mapping Class Groups, October 2025, held at KIAS (Seoul, Korea)
Co-organized with: Sang-hyun Kim (KIAS), Sanghoon Kwak (Seoul National University), Eugen Rogozinnikov (KIAS), and David Xu (KIAS).

Publications and Preprints

If you wish to receive a copy of any of these articles -- please send me an email, and I'd be happy to provide a (signed, personalised) copy!

Publications (newest first):

M. Kambites, C.-F. Nyberg-Brodda, N. Szakács, R. Webb, The growth of free inverse monoids, 2025, J. Math. Inst. Jussieu (accepted).
C.-F. Nyberg-Brodda, "On congruence subgroups of SL2(ℤ[1/p]) generated by two parabolic elements", 2025, Math. Proc. Camb. Phil. Soc. (accepted)
C.-F. Nyberg-Brodda, On the growth and integral (co)homology of free regular star-monoids, 2025, Int. J. of Algebra & Computation (accepted)
C.-F. Nyberg-Brodda, "G. S. Tseytin's seven-relation semigroup with undecidable word problem", in Evgeny Danstin and Vladik Kreinovich (eds). "Legacy of Grigory Tseytin", Springer, Cham, Switzerland, to appear (2025).
I. Foniqi, R. D. Gray & C.-F. Nyberg-Brodda, "Membership problems for positive one-relator groups and one-relation monoids", Canadian J. of Math. (2024, accepted).
C.-F. Nyberg-Brodda, "The abelianization of SL2(ℤ[1/m])", Journal of Algebra 660, 2024, pp. 614-618.
C.-F. Nyberg-Brodda, "On the Dehn functions of a class of monadic one-relation monoids", C. Rendus Mathématique (accepted, 2023).
M. Pichler, A. Meindl, M. Romberger, A. Eckes-Shepard, C.-F. Nyberg-Brodda, C. Buhigas, S. Llaneza-Lago, G. Lehmann, A. Hopes, G. Meister, J. Medenbach, T. Mock, "Ribosome profiling in the model diatom Thalassiosira pseudonana", Current Protocols (accepted, 2023), doi:101002/cpz1.843.
C.-F. Nyberg-Brodda, "On the word problem for weakly compressible monoids", Communications in Algebra (accepted, 2023)
C.-F. Nyberg-Brodda, "On the word problem for free products of semigroups and monoids", Journal of Algebra 622, (2023), pp. 721-741.
C.-F. Nyberg-Brodda, "A word-hyperbolic special monoid with undecidable Diophantine problem", Israel J. of Mathematics (accepted).
C.-F. Nyberg-Brodda, "Multiplication tables and word-hyperbolicity in free products of semigroups, monoids, and groups", J. AustMath. Soc. (accepted).
C.-F. Nyberg-Brodda, "Non-finitely generated maximal subgroups of context-free monoids", Journal of Algebra 616, (2023), pp. 227-238.
C.-F. Nyberg-Brodda, "On one-relator groups and units of special one-relation inverse monoids", Int. J. of Alg. and Comp. 32:7, (2022). pp.1379-1401.
C.-F. Nyberg-Brodda, "On the word problem for special monoids", Semigroup Forum 105:1, (2022), pp. 295-327.
C.-F. Nyberg-Brodda, "The word problem for one-relation monoids: a survey", Semigroup Forum 103:2, (2021), pp. 297–355.
C.-F. Nyberg-Brodda, "The B. B. Newman Spelling Theorem", British J. for the History of Mathematics 36:2, (2021), pp. 117-131.

Preprints (newest first):

M. Linton, C.-F. Nyberg-Brodda, The theory of one-relator groups: history and recent progress, 2025, arXiv:2501.18306.
R. D. Gray, C.-F. Nyberg-Brodda, Membership problems in braid groups and Artin groups, 2024, arXiv:2409.11335.
V. Berthé, H. Goulet-Ouellet, C.-F. Nyberg-Brodda, D. Perrin, K. Petersen, Density of group languages in shift spaces, 2024, arXiv:2403.17892
C.-F. Nyberg-Brodda, "Tropical one-relation monoids", (2022), arxiv:2209.12612.
C.-F. Nyberg-Brodda, "On the Diophantine problem in some one-relator groups", (2022), arXiv:2208.07145.

Translations and Miscellaneous Work

I sometimes do English translations of old (primarily Russian) articles! If you have something you want translated, let me know.
Some articles are without links for copyright reasons. If you wish to receive a copy, drop me a line and I'll send you a pdf (non-commercial use only).

Note: I am an official translator (Russian to English) for the Transactions of the Moscow Mathematical Society. The translation is organised jointly by the London Mathematical Society and the American Mathematical Society. My work in this capacity does not constitute endorsement of the policies or actions of any government or other agencies. In particular, I condemn the barbaric 2022 Russian invasion of Ukraine in the strongest possible terms.

Three articles on one-relator groups by Wilhelm Magnus (2025), arXiv:2501.18248.
This is a translation of three separate articles, originally written in German:
- W. Magnus, "Über diskontinuierliche Gruppen mit einer definierenden Relation (Der Freiheitssatz)", J. für die reine und angewandte Mathematik, 163:3 (1930), pp. 141–165.
- W. Magnus, "Untersuchungen über einige unendliche diskontinuierliche Gruppen", Math. Ann. 105 (1931), pp. 52–74
- W. Magnus, Das Identitätsproblem für Gruppen mit einer definierenden Relation, Math. Ann. 106 (1932), pp. 295–307.

Six Ukrainian articles on semigroup theory by A. K. Sushkevich (2023), arXiv:2203.02996.
This translation was featured on the website of the Ukrainian Mathematical Community.
It contains a translation of six separate articles, originally written in Ukrainian:
- A. K. Sushkevich, "On extending a semigroup to a whole group", Scientific Notes of the Kharkiv Mathematical Society, 4:12 (1935), pp. 81–87.
- A. K. Sushkevich, "On some properties of a type of generalised groups", Scientific Notes of the Kharkiv State University, 2–3 (1935), pp. 23–25.
- A. K. Sushkevich, "Investigations in the field of generalised groups", Scientific Notes of the Kharkiv State University, 6–7 (1936), pp. 49–52.
- A. K. Sushkevich, "On groups of matrices of rank 1", J. Inst. Math. Akad. Nauk UkrSSR, 3 (1937), pp. 83–94.
- A. K. Sushkevich, "On some types of singular matrices", Scientific Notes of the Kharkiv State University, 10 (1951), pp. 5–16.
- A. K. Sushkevich, "Generalised groups of some types of infinite matrices", Note. Sci. Res. Inst. Khar. S. Univ. & Khar. M. Soc 16 (1939), pp. 115–120
The Adian--Rabin Theorem -- an English Translation, (2022), arXiv:2208.08560.
This contains a translation of six separate articles, originally written in Russian:
- A. A. Markov, "Impossibility of some algorithms in the theory of associative systems", Dokl. Akad. Nauk SSSR, 77:1, (1951), pp. 19-20.
- A. A. Markov, "Impossibility of algorithms for recognising some properties of associative systems", Dokl. Akad. Nauk SSSR, 77:6, 1951, pp. 953-956.
- S. I. Adian, "Algorithmic unsolvability of problems of recognition of certain properties of groups", Dokl. Akad. Nauk SSSR, 103:4 (1955), pp. 533-535.
- S. I. Adian, "Unsolvability of some algorithmic problems in the theory of groups", Proc. Moscow Math. Soc. 6, (1957), pp. 231-298.
- S. I. Adian, "Finitely presented groups and algorithms", Dokl. Akad. Nauk SSSR, 117:1, (1957), pp. 9-12.
- S. I. Adian, "On algorithmic problems in effectively complete classes of groups", Dokl. Akad. Nauk SSSR, 123:1, (1958), pp. 13-16.

A translation of G. S. Makanin's 1966 Ph.D. thesis "On the Identity Problem for Finitely Presented Groups and Semigroups" (2021), arXiv:2102.00745.
A. S. Schwartz, "The volume invariant of coverings", Dokl. Akad. Nauk SSSR 105:1, (1955).
L. M. Shneerson, "Identities in semigroups with one defining relation", Log. Algebra Comput Math. Ivanovo Pedagog. Inst. 1:(1-2), pp. 139--156 (1972)
L. M. Shneerson, "Identities in semigroups with one defining relation. II", Log. Algebra Comput Math. Ivanovo Pedagog. Inst. 1:(3-4), pp. 112--124 (1972)
G. S. Tseitin, "An associative calculus with an unsolvable equivalence problem", Trudy Mat. Inst. Steklov 52, pp. 172--189 (1958)

Upcoming Talks (to be updated)

This semester, I'll be giving talks and/or seminars in the following locations:

24-Sep-2024 KIAS-Rice Workshop on Dynamical Group Theory (Dynamical Group Theory IV) held at KIAS, Seoul (Korea).

Where you might have seen me talk (to be updated)

Here are some past talks of mine:

06-Sep-2024 Semi(group) languages Invited speaker. CIAA 2024 (Akita, Japan)
June 2024
23-Apr-2024 The freeness problem for parabolic subgroups of SL(2,C) Seoul National University Exchange Seminar
09-Apr-2024 The freeness problem for parabolic subgroups of SL(2,C) KAIST Topology Seminar (Daejeon, Korea)
19-Mar-2024 Some decision problems in combinatorial (semi)group theory Seoul National University Exchange Seminar
29-Feb-2024 The freeness problem for parabolic subgroups of SL(2,C) Korea-France Workshop on Dynamical Group Theory (KIAS)
19-Feb-2024 The freeness problem for parabolic subgroups of SL(2,C) 4th EACGT (RIMS, Kyoto, Japan)
14-Feb-2024 The Freeness problem for parabolic subgroups of SL(2,C) Groups, Rings, Languages (RIMS, Kyoto, Japan)
26-Sep-2023 Decision problems in Baumslag-Solitar-like monoids Korea-Chile Workshop on Dynamical Group Theory (Incheon, South Korea)
20-Jul-2023 Membership problems for one-relator groups Virtual Seminar on Geometry and Topology (KIAS, South Korea)
06-Jul-2023 The Dehn function of some one-relation monoids Virtual Seminar on Geometry and Topology (KIAS, South Korea)
03-Jul-2023 One relation: the story so far TCA2023 (Pocinho, Portugal)
01-Jun-2023 The word problem for one-relator inverse monoids. III. Geometric Group Theory Series (Zoom), Steklov Math Inst. (Moscow, Russia)
25-May-2023 The word problem for one-relator inverse monoids. II. Geometric Group Theory Series (Zoom), Steklov Math Inst. (Moscow, Russia)
18-May-2023 The word problem for one-relator inverse monoids. I. Geometric Group Theory Series (Zoom), Steklov Math Inst. (Moscow, Russia)
18-Apr-2023 Hyperbolic and one-relator groups Séminaire de Math-Info, Université Gustave Eiffel (Paris, France)
05-Apr-2023 Monadic rewriting systems and the word problem Séminaire de Proofs & Algorithms, École Polytechnique (Paris, France)
13-Mar-2023 Language-theoretic methods in semigroup theory Séminaire de Combinatoire, École Polytechnique (Paris, France)
24-Feb-2023 The Dehn function of some one-relation monoids "Semigroups, Automata & Languages", CMUP. Zoom. (Porto, Portugal).
15-Feb-2023 Language-theoretic methods in semigroup theory Invited speaker. "Groups, Rings, Languages" (RIMS). Kyoto, Japan.
16-Dec-2022 Language-theoretic methods in semigroup theory IRIF automata seminar, Université Paris-Cité (Paris, France).
05-Dec-2022 The Dehn function of some one-relation monoids Logic Online Seminar. Zoom, Steklov Math. Institute (Moscow, Russia).
21-Nov-2022 The Dehn function of some one-relation monoids Algebra & Logic Seminar. Zoom, Univ. NOVA (Lisbon, Portugal).
24-Oct-2022 A century-old problem in mathematical logic IMJ-PRG Séminaire Générale de Logique (Paris, France).
24-Jun-2022 Free products and word-hyperbolic monoids 32nd NBSAN (York, UK)
21-Jun-2022 Decision problems in word-hyperbolic monoids Invited speaker. Topics in Geometric Semigroup Theory (York, UK).
08-Jun-2022 The word problem in semigroup theory Akita University Mathematical Sciences Seminar (Akita, Japan)
17-May-2022 The word problem for special semigroups University of Manchester Algebra Seminar. (Manchester, UK)

Era of online talks (due to COVID-19)

16-Feb-2022 Congruential languages and special rewriting systems "Groups, Rings, Languages" (RIMS Kyoto Workshop). Zoom.
07-Dec-2021 Le problème du mot pour les monoïdes à un relateur Séminaire d'Informatique, Université Gustave Eiffel (Paris, France).
14-Oct-2021 One-relation monoids and virtually free groups University of St Andrews Pure Colloquium. Zoom.
24-Jun-2021 Context-free graphs in context LMS Virtual Graduate Student Meeting. Zoom. Award for Best Talk
15-July-2021 The Muller-Schupp theorem for special monoids. British Early Career Mathematicians' Colloquium. Zoom.
04-Jun-2021 The Muller-Schupp theorem for special monoids. Invited speaker. Zassenhaus Groups & Friends Conference. Zoom.
11-Feb-2021 The Muller-Schupp theorem for special monoids. Newcastle University Algebra Seminar. Zoom.
08-Feb-2021 The Muller-Schupp theorem for special monoids. Algebra & Logic Seminar, Univ. NOVA de Lisboa. Zoom.
03-Feb-2021 Geometry and the word problem for special monoids York Semigroup Seminar. Zoom.
01-Feb-2021 Combinatorial semigroup theory. University of East Anglia Pure Maths Seminar. Zoom.
16-Nov-2020 The B. B. Newman Spelling Theorem. LMS Virtual Graduate Student Meeting. Zoom. Award for Best Talk
16-Sep-2020 The word problem for special monoids. eNBSAN (=e-North British Semigroups & Applications Network). Zoom.

Era of pre-pandemic talks

29-Nov-2019 Special semigroups and monadic monoids. LMS (= London Mathematical Soc.) Graduate Student Meeting. (London, UK).
28-Jun-2019 Decision problems for groups and semigroups. LMS Graduate Student Meeting. (London, UK). Award for Best Talk