Publications

Papers

2010

Bate M.E, Herpel S, Martin B, Röhrle G.Complete reducibility and semisimple modules. Submitted. arXiv

Martin B. Compactifications of a representation variety. Submitted.

Bate M.E, Martin B, Röhrle G, Tange R. The strong Centre Conjecture: an invariant theory approach. Submitted arXiv

Gillard A.B, Martin B. Dark matter, Elko fields, and Weinberg's quantum field theory formalism. Submitted. arXiv

Martin B, Orr E. Evolving A-type neural networks. Submitted.

Bate M.E, Martin B, Röhrle G, Tange R. Complete reducibility and conjugacy classes of tuples in algebraic groups and Lie algebras. To appear in Math. Zeit. arXiv

Bate M.E, Martin B, Röhrle G, Tange R. Complete reducibility and separability. Trans. Amer. Math. Soc. no.8, 362:4283-4311 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. arXiv

Bate M.E, Martin B, Röhrle G, Tange R. Complete reducibility and separable field extensions.C. R. Math Acad. Sci. Paris no. 9-10, 348:495-497 arXiv

2009

Martin B. On the Diophantine equation x!=ym^α.New Zealand J. Math. 39:65-66

Bate M.E, Martin B, Röhrle G, Tange R. Closed orbits and uniform S-instability in geometric invariant theory. Submitted. arXiv

Bate M.E, Martin B, Röhrle G. On Tits' Centre Conjecture for fixed point subcomplexes. C. R. Acad. Sci. Paris. Ser. I 347:353-356. ScienceDirect | arXiv

2008

Bate M.E, Martin B, Röhrle G. Complete reducibility and commuting subgroups. J. Reine Angew. Math. 621:213-235. Reference Global | arXiv

2007

2006

Butler P, Gillard A, Gresnigt N, Joyce W, Martin B, Renaud P. In Symmetry, Spectroscopy and SCHUR: Proceedings of the Professor Brian G. Wybourne Commemorative Meeting, Torun, Poland, 39-48

2005

Bate M.E, Martin B, Röhrle G. A geometric approach to complete reducibility. Invent. Math. 161:177-218. 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. 128:541-557. Project Euclid

2004

Lubotzky A, Martin B. Polynomial representation growth and the congruence subgroup problem. Israel J. Math. 144:293-316. SpringerLink

2003

Martin B. A normal subgroup of a strongly reductive subgroup is strongly reductive. J. Algebra 265, no. 2:669-674. ScienceDirect

Martin B. Reductive subgroups of reductive groups in nonzero characteristic. J. Algebra 262, no. 2:265-286. ScienceDirect

2001

Martin B, Neeman A. The map V→V//G need not be separable. Math. Res. Lett. 8, no. 5-6:813-817.

Martin B. A foliation of the space of conjugacy classes of representations of a surface group. Geom. Dedicata 86, 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, 1:231-249. ScienceDirect

1999

Martin B. Etale slices for representation varieties in characteristic p. Indag. Math. (N.S.) 10, no. 4:555-564. ScienceDirect

Preprints, etc.

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

Carbone L, Martin B. Deformations of lattices in SL₂ over non-Archimedean local fields. In preparation.

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

Hrushovski E, Martin B. Zeta functions from definable equivalence relations. Preprint. arXiv

Martin B. An SL₂(k) character variety whose dimension jumps in characteristic 2. Preprint.

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

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