Publications

Papers

2018

Martin B., Stewart D., Topley L. Smoothness of stabilisers in generic characteristic. Preprint. arXiv

Martin B., Stewart D., Topley L. A proof of the first Kac–Weisfeiler conjecture in large characteristics. Submitted. arXiv

Kedra J., Libman A., Martin B. Strong and uniform boundedness of groups. Submitted. arXiv

Bate M.E., Geranios H., Martin B. Orbit closures and invariants. To appear in Math. Zeit. arXiv

Bate M.E., Martin B., Röhrle G., Stewart, D. On unipotent radicals of pseudo-reductive groups. To appear in Michigan Math. J. arXiv

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), 39–72Open 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.

Bate M.E., Martin B., Röhrle G. The strong Centre Conjecture II: reduction to Type A. In preparation.

Gillard A.B., Martin B. Spin-half quantum fields and non-standard Wigner classes. In preparation.

Martin B. Conjugacy classes of maximal subgroups of a reductive algebraic group. In preparation.

Martin B. Polynomial representation growth and alternating quotients. In preparation.

Carbone L., Martin B. A Teichmüller theory for lattices in PSL2 over non-Archimedean local fields. In preparation.

Martin B. Nonabelian 1-cocycles. Unpublished note.

Martin B. Varieties of representations of surface groups. PhD thesis.

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