Professor Benjamin Martin | The University of Aberdeen

Professor Benjamin Martin

Personal Chair

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Email Address: b.martin@abdn.ac.uk
Telephone Number: +44 (0)1224 272759
Office Address: Fraser Noble 155
School/Department: School of Natural and Computing Sciences

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Latest Publications

Essential tori in 3-manifolds not detected in any characteristic
2024 - Published
Garden, G. S., Martin, B., Tillmann, S.
Working Papers: Preprint Papers
- [OPEN ACCESS] https://pure.abdn.ac.uk/ws/files/299632057/2411.15680v1.pdf
Powers of commutators in linear algebraic groups
2024 - Published
Martin, B.
Proceedings of the Edinburgh Mathematical Society, vol. 67, pp. 830–837
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.1017/S0013091524000361
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/24472/2/Martin_PEMS_Powers_of_commutators_VOR.pdf
On overgroups of distinguished unipotent elements in reductive groups and finite groups of Lie type
2024 - Published
Bate, M., Böhm, S., Martin, B., Roehrle, G.
Working Papers: Preprint Papers
- [ONLINE] DOI: https://doi.org/10.48550/arXiv.2407.16379
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/24148/1/2407.16379v1.pdf
G-complete reducibility and saturation
2024 - Published
Bate, M., Böhm, S., Litterick, A., Martin, B., Roehrle, G.
Working Papers: Preprint Papers
- [ONLINE] DOI: https://doi.org/10.48550/arXiv.2401.16927
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/22731/1/2401.16927v1.pdf
Complete reducibility for Lie subalgebras and semisimplification
2023 - Published
Bate, M., Böhm, S., Martin, B., Roehrle, G., Voggesberger, L.
European Journal of Mathematics, vol. 9, 116
Contributions to Journals: Articles
- [ONLINE] http://arxiv.org/abs/2305.00841v1
- [ONLINE] DOI: https://doi.org/10.1007/s40879-023-00710-4
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/20734/1/2305.00841v1.pdf
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/20734/2/Bate_etal_EJM_Complete_Reducibility_For_VoR.pdf

View My Publications

Publications

Page 1 of 1 Results 1 to 21 of 21

Essential tori in 3-manifolds not detected in any characteristic
2024 - Published
Garden, G. S., Martin, B., Tillmann, S.
Working Papers: Preprint Papers
- [OPEN ACCESS] https://pure.abdn.ac.uk/ws/files/299632057/2411.15680v1.pdf
Powers of commutators in linear algebraic groups
2024 - Published
Martin, B.
Proceedings of the Edinburgh Mathematical Society, vol. 67, pp. 830–837
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.1017/S0013091524000361
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/24472/2/Martin_PEMS_Powers_of_commutators_VOR.pdf
On overgroups of distinguished unipotent elements in reductive groups and finite groups of Lie type
2024 - Published
Bate, M., Böhm, S., Martin, B., Roehrle, G.
Working Papers: Preprint Papers
- [ONLINE] DOI: https://doi.org/10.48550/arXiv.2407.16379
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/24148/1/2407.16379v1.pdf
G-complete reducibility and saturation
2024 - Published
Bate, M., Böhm, S., Litterick, A., Martin, B., Roehrle, G.
Working Papers: Preprint Papers
- [ONLINE] DOI: https://doi.org/10.48550/arXiv.2401.16927
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/22731/1/2401.16927v1.pdf
Complete reducibility for Lie subalgebras and semisimplification
2023 - Published
Bate, M., Böhm, S., Martin, B., Roehrle, G., Voggesberger, L.
European Journal of Mathematics, vol. 9, 116
Contributions to Journals: Articles
- [ONLINE] http://arxiv.org/abs/2305.00841v1
- [ONLINE] DOI: https://doi.org/10.1007/s40879-023-00710-4
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/20734/1/2305.00841v1.pdf
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/20734/2/Bate_etal_EJM_Complete_Reducibility_For_VoR.pdf
Edifices: Building-like spaces associated to linear algebraic groups
2023 - Published
Bate, M., Martin, B., Röhrle, G.
Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial, vol. 20, no. 2-3, pp. 79-134
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.2140/iig.2023.20.79
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/23107/1/Bate_etal_MSP_Edifices_Building_Like_AAM.pdf
- [ONLINE] View publication in Scopus
- [ONLINE] https://abdn.elsevierpure.com/en/publications/ff4ea118-6cd1-4064-b0d5-02f4197bc53e
Strong and uniform boundedness of groups
2023 - Published
Kedra, J., Libman, A., Martin, B.
Journal of Topology and Analysis, vol. 15, no. 3, pp. 707-739
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.1142/S1793525321500497
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/18668/1/Kedra_etal_JTA_Strong_And_Uniform_AAM.pdf
Algebraic groups and $G$-complete reducibility: a geometric approach
2022 - Published
Martin, B.
Working Papers: Preprint Papers
- [ONLINE] DOI: https://doi.org/10.48550/arXiv.2207.12169
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/19641/1/2207.12169v1.pdf
Uniform boundedness for algebraic groups and Lie groups
2022 - Published
Kędra, J., Libman, A., Martin, B.
Working Papers: Preprint Papers
- [ONLINE] DOI: https://doi.org/10.48550/arXiv.2202.13885
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/21382/1/2202.13885v1.pdf
- [ONLINE] http://arxiv.org/abs/2202.13885v1
Overgroups of regular unipotent elements in reductive groups
2022 - Published
Bate, M., Martin, B., Röhrle, G.
Forum of Mathematics, Sigma, vol. 10, e13
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.1017/fms.2021.82
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/18275/1/Bates_etal_FMS_Overgroups_Regular_Unipotent_VoR.pdf
- [ONLINE] View publication in Scopus
Semisimplification for Subgroups of Reductive Algebraic Groups
2020 - Published
Bate, M., Martin, B., Roehrle, G.
Forum of Mathematics, Sigma, vol. 8, pp. 1-10
Contributions to Journals: Articles
- [ONLINE] https://arxiv.org/abs/2004.08105
- [ONLINE] DOI: https://doi.org/10.1017/fms.2020.30
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/15895/1/Bate_etal_Semisimplification_for_subgroups_VOR.pdf
Orbit Closures and Invariants
2019 - Published
Bate, M., Geranios, H., Martin, B.
Mathematische Zeitschrift, vol. 293, no. 3-4, pp. 1121-1159
Contributions to Journals: Articles
- [ONLINE] https://arxiv.org/abs/1604.00924
- [ONLINE] DOI: https://doi.org/10.1007/s00209-019-02228-6
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/11836/2/Bate2019_MZ_OrbitClosuresAndInvariants_VoR.pdf
- [ONLINE] View publication in Scopus
- [ONLINE] View publication in Mendeley
- [ONLINE] https://abdn.pure.elsevier.com/en/en/researchoutput/orbit-closures-and-invariants(02bb85f2-4c0f-4c2a-8309-e82b90b356d0).html
On Unipotent Radicals of Pseudo-Reductive Groups
2019 - Published
Bate, M., Martin, B., Röhrle, G., Stewart, D. I.
The Michigan Mathematical Journal, vol. 68, no. 2, pp. 277-299
Contributions to Journals: Articles
- [ONLINE] https://arxiv.org/abs/1704.04385
- [ONLINE] DOI: https://doi.org/10.1307/mmj/1550480563
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/11518/3/MMJ5377.pdf
- [ONLINE] View publication in Mendeley
- [ONLINE] View publication in Scopus
A proof of the first Kac-Weisfeiler conjecture in large characteristics
2019 - Published
Martin, B., Stewart, D. I., Topley, L., Tikaradze, A.
Representation Theory, vol. 23, pp. 278-293
Contributions to Journals: Articles
- [ONLINE] http://arxiv.org/abs/1810.12632v1
- [ONLINE] DOI: https://doi.org/10.1090/ert/529
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/12662/2/1810.12632v1.pdf
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/12662/1/GenericKW1withAppendix_AAM.pdf
- [ONLINE] View publication in Scopus
Definable equivalence relations and zeta functions of groups
2018 - Published
Hrushovski, E., Martin, B., Rideau, S., Cluckers, R.
Journal of the European Mathematical Society, vol. 20, no. 10, pp. 2467-2537
Contributions to Journals: Articles
- [ONLINE] https://arxiv.org/abs/math/0701011
- [ONLINE] DOI: https://doi.org/10.4171/JEMS/817
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/12588/1/zeta_EIp.pdf
On a question of Külshammer for homomorphisms of algebraic groups
2018 - Published
Lond, D., Martin, B.
Journal of Algebra, vol. 497, pp. 164-198
Contributions to Journals: Articles
- [ONLINE] https://arxiv.org/abs/1610.09665
- [ONLINE] DOI: https://doi.org/10.1016/j.jalgebra.2017.08.031
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/11206/1/kulshammer.pdf
Cocharacter-closure and the rational Hilbert-Mumford Theorem
2017 - Published
Bate, M., Herpel, S., Martin, B., Roehrle, G.
Mathematische Zeitschrift, vol. 287, no. 1-2, pp. 39-72
Contributions to Journals: Articles
- [ONLINE] http://arxiv.org/abs/1411.7849v2
- [ONLINE] DOI: https://doi.org/10.1007/s00209-016-1816-5
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/5047/3/Cocharacter_closure_and_the_rational_Hilbert_Mumford_Theorem.pdf
On a question of Külshammer for representations of finite groups in reductive groups
2016 - Published
Bate, M., Martin, B., Rohrle, G.
Israel Journal of Mathematics, vol. 214, no. 1, pp. 463-470
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.1007/s11856-016-1337-2
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/8893/1/kuls.pdf
Cocharacter-closure and spherical buildings
2015 - Published
Bate, M., Herpel, S., Martin, B., Rohrle, G.
Pacific Journal of Mathematics, vol. 279, no. 1-2, pp. 65-85
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.2140/pjm.2015.279.65
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/5370/1/pjm_v279_n1_p04_p.pdf
Generic stabilisers for actions of reductive groups
2015 - Published
Martin, B.
Pacific Journal of Mathematics, vol. 279, no. 1-2, pp. 397-422
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.2140/pjm.2015.279.397
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/5371/1/pjm_v279_n1_p18_p.pdf
G-complete reducibility in non-connected groups
2015 - Published
Bate, M., Herpel, S., Martin, B., Rohrle, G.
Proceedings of the American Mathematical Society, vol. 143, no. 3, pp. 1085-1100
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.1090/S0002-9939-2014-12348-3
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/10965/1/nonconnected_proc_revised3.pdf
- [ONLINE] http://www.ams.org/publications/ctp.pdf

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Latest Publications

Essential tori in 3-manifolds not detected in any characteristic

Powers of commutators in linear algebraic groups

On overgroups of distinguished unipotent elements in reductive groups and finite groups of Lie type

G-complete reducibility and saturation

Complete reducibility for Lie subalgebras and semisimplification

Essential tori in 3-manifolds not detected in any characteristic

Powers of commutators in linear algebraic groups

On overgroups of distinguished unipotent elements in reductive groups and finite groups of Lie type

G-complete reducibility and saturation

Complete reducibility for Lie subalgebras and semisimplification

Edifices: Building-like spaces associated to linear algebraic groups

Strong and uniform boundedness of groups

Algebraic groups and $G$-complete reducibility: a geometric approach

Uniform boundedness for algebraic groups and Lie groups

Overgroups of regular unipotent elements in reductive groups

Semisimplification for Subgroups of Reductive Algebraic Groups

Orbit Closures and Invariants

On Unipotent Radicals of Pseudo-Reductive Groups

A proof of the first Kac-Weisfeiler conjecture in large characteristics

Definable equivalence relations and zeta functions of groups

On a question of Külshammer for homomorphisms of algebraic groups

Cocharacter-closure and the rational Hilbert-Mumford Theorem

On a question of Külshammer for representations of finite groups in reductive groups

Cocharacter-closure and spherical buildings

Generic stabilisers for actions of reductive groups

G-complete reducibility in non-connected groups

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