Papers
2022
Martin, B. Powers of commutators in linear algebraic groups. Submitted. arXiv
Bate M.E., Martin B., Röhrle G. Edifices: building-like spaces associated to linear algebraic groups. Submitted.
Bate M.E., Martin B., Röhrle G. Overgroups of regular unipotent elements in reductive groups. Forum Math. Sigma 10 (2022), Paper No. e13, 13 pp. Open access link. arXiv
2021
Kedra J., Libman A., Martin B. Strong and uniform boundedness of groups. J. Topology and Analysis (2021), doi.org/10.1142/S1793525321500497. arXiv
2020
Bate M.E., Martin B., Röhrle G. Semisimplification for subgroups of reductive algebraic groups. Forum Math. Sigma 8 (2020), Paper No. e43, 10 pp. Open access link. arXiv
2019
Martin B., Stewart D., Topley L. A proof of the first Kac–Weisfeiler conjecture in large characteristics. With an appendix by Akaki Tikaradze. Represent. Th. 23 (2019), 278–293. Open access link
Bate M.E., Geranios H., Martin B. Orbit closures and invariants. Math. Zeit. 293 (2019), 1121–1159. Open access link. arXiv
Bate M.E., Martin B., Röhrle G., Stewart, D. On unipotent radicals of pseudo-reductive groups. Michigan Math. J. 68 (2019), 277–299. arXiv
2018
Hrushovski E., Martin B., Rideau S. Definable equivalence relations and zeta functions of groups. With an appendix by Raf Cluckers. J. Eur. Math. Soc. 20 (2018), 2467–2537. arXiv
Lond D., Martin B. On a question of Külshammer for homomorphisms of algebraic groups. J. Algebra 497 (2018), 164–198. arXiv
2017
Bate M.E., Herpel S., Martin B., Röhrle G. Cocharacter-closure and the rational Hilbert-Mumford Theorem. Math. Zeit. 287 (2017), 39–72. Open access link
2016
Bate M.E., Martin B., Röhrle G. On a question of Külshammer for representations of finite groups in reductive groups. Israel J. Math. 214 (2016), 463–470. arXiv
2015
Bate M.E., Herpel S., Martin B., Röhrle G. Cocharacter-closure and spherical buildings. Pacific J. Math. 279 (2015), 65-85. arXiv
Martin B. Generic stabilisers for actions of reductive groups. Pacific J. Math. 279 (2015), 397–422. arxiv
2014
Bate M.E., Herpel S., Martin B., Röhrle G. G-complete reducibility in non-connected groups. Proc. Amer. Math. Soc. 143 (2014), 1085–1100. arXiv
2013
Martin, B., Schillewaert J., Steinke G., & Struyve K. On metrically complete Bruhat-Tits buildings. Advances in Geom. 13 (2013), 497–510. arXiv
Bate M.E., Martin B., Röhrle G., Tange R. Closed orbits and uniform S-instability in geometric invariant theory. Trans. Amer. Math. Soc. 365 (2013), 3643–3673. arXiv
2012
Bate M.E., Martin B., Röhrle G. The strong Centre Conjecture: an invariant theory approach. J. Algebra 372 (2012), 505–530. arXiv
Gillard A.B., Martin B. Dark matter, Elko fields, and Weinberg’s quantum field theory formalism. Reports on Math. Phys. 69 (2012), 113–129. arXiv
Orr E., Martin B. Evolving A-type neural networks. Evolutionary Intelligence (Turing Centennial volume) 5 (2012), 3–22. arXiv
2011
Bate M.E., Martin B., Röhrle G., Tange R. Complete reducibility and conjugacy classes of tuples in algebraic groups and Lie algebras. Math. Zeit. 269 (2011), 809–832. arXiv
Bate M.E., Herpel S., Martin B., Röhrle G. G-complete reducibility and semisimple modules. Bull. London Math. Soc. 43 (2011), no. 6, 1069–1078. arXiv
Martin B. Compactifications of a representation variety. J. Group Theory 14 (2011), no. 6, 947–963.
2010
Bate M.E., Martin B., Röhrle G., Tange R. Complete reducibility and separability. Trans. Amer. Math. Soc. 362 (2010), no. 8, 4283–4311. arXiv
Gillard A.B., Martin B. Quantum fields, dark matter and non-standard Wigner classes. Proceedings of the 7th International Heidelberg Conference, Dark Matter in Astrophysics and Particle Physics, Dark 2009, 451–456, 2009. arXiv
Bate M.E., Martin B., Röhrle G., Tange R. Complete reducibility and separable field extensions.C. R. Math Acad. Sci. Paris 348 (2010), no. 9–10, 495-497. arXiv
2009
Martin B. On the Diophantine equation x!=ymα. New Zealand J. Math. 39 (2009), 65–66.
Bate M.E., Martin B., Röhrle G. On Tits’ Centre Conjecture for fixed point subcomplexes. C. R. Acad. Sci. Paris. Ser. I 347 (2009), 353–356. ScienceDirect | arXiv
2008
Bate M.E., Martin B., Röhrle G. Complete reducibility and commuting subgroups. J. Reine Angew. Math. 621 (2008), 213–235. Reference Global | arXiv
2006
Butler P., Gillard A., Gresnigt N., Joyce W., Martin B., Renaud P. Physics with a real Clifford algebra. In Symmetry, Spectroscopy and SCHUR: Proceedings of the Professor Brian G. Wybourne Commemorative Meeting, Torun, Poland, 39–48, 2006.
2005
Bate M.E., Martin B., Röhrle G. A geometric approach to complete reducibility. Invent. Math. 161 (2005), 177–218. SpringerLink | arXiv
Liebeck M., Martin B., Shalev A. On conjugacy classes of maximal subgroups of finite simple groups, and a related zeta function. Duke Math. J. 128 (2005), 541–557. Project Euclid
2004
Lubotzky A., Martin B. Polynomial representation growth and the congruence subgroup problem. Israel J. Math. 144 (2004), 293–316. SpringerLink
2003
Martin B. A normal subgroup of a strongly reductive subgroup is strongly reductive. J. Algebra 265 (2003), no. 2, 669–674. ScienceDirect
Martin B. Reductive subgroups of reductive groups in nonzero characteristic. J. Algebra 262 (2003) no. 2, 265–286. ScienceDirect
2001
Martin B., Neeman A. The map V→V//G need not be separable. Math. Res. Lett. 8 (2001), no. 5-6, 813–817.
Martin B. A foliation of the space of conjugacy classes of representations of a surface group. Geom. Dedicata 86 (2001), no.1-3, 19–27. SpringerLink
2000
Martin B. Restrictions of representations of a surface group to a pair of free subgroups. J. Algebra 225 (2000), no. 1, 231–249. ScienceDirect
1999
Martin B. Etale slices for representation varieties in characteristic p. Indag. Math. (N.S.) 10 (1999), no. 4, 555–564. ScienceDirect
Preprints, etc.
Martin, B. Algebraic groups and G-complete reducibility: a geometric approach. Unpublished notes (2022). arXiv
Martin B., Stewart D., Topley L. Smoothness of stabilisers in generic characteristic. Preprint. arXiv
Litterick, A., Martin, B. Rigid representations of triangle groups. Preprint. arXiv
Bate M.E., Martin B., Röhrle G. The strong Centre Conjecture II: reduction to Type A. In preparation.
Carbone L., Martin B. A Teichmüller theory for lattices in PSL2 over non-Archimedean local fields. In preparation.
Barton B., Martin B. How to implement semi-authentic mathematical experiences. Learning in undergraduate mathematics: the outcome spectrum (LUMOS). “How to” guide 2. Ako Aotearoa (2017). Link
Martin B. Nonabelian 1-cocycles. Unpublished note.
Martin B. Varieties of representations of surface groups. PhD thesis.
Ben Martin 