Dr R. James Shank

Mathematics, Statistics & Act. Sci.
University of Kent
Canterbury, Kent, CT2 7FS, UK

Office: Room 253, Sibson Building
Telephone Number: 01227 82 3770
SMSAS Fax: 01227 82 7932
e-mail: R.J.Shank@kent.ac.uk

I completed my Ph.D. in homotopy theory at the University of Toronto in 1989. My supervisor was Professor Paul Selick. My current research interests are related to the invariant theory of finite groups. My collaborators include Eddy Campbell, Peter Fleischmann, Ian Hughes, Müfit Sezer, Gregor Kemper and David Wehlau.


The SMSAS has regular mathematics seminars.

See Moodle for online teaching material


Publications

  • H.E.A. Campbell, J.Chuai, R.J. Shank and D.L. Wehlau, Finite subgroups of fields, arXiv:1610.03709 (2016).

  • T. Pierron and R.J. Shank, Rings of invariants for the three dimensional modular representations of elementary abelian p-groups of rank four, Involve, a Journal of Mathematics 9-4 (2016) 551-581 (dx.doi.org/10.2140/involve.2016.9.551, arXiv:1410.5227).

  • M. Sezer and R.J. Shank, Rings of invariants for modular representations of the Klein four group, Transactions of the American Mathematical Society 368 (2016) no. 8, 5655-5673 (dx.doi.org/10.1090/tran/6516, arXiv:1309.7812).

  • H.E.A. Campbell, R.J. Shank and D.L. Wehlau, Rings of invariants for modular representations of elementary abelian p-groups, Transformation Groups 18 (2013) no. 1, 1-22 (doi:10.1007/s00031-013-9207-z, arXiv:1112.0230).

  • A. Hobson and R.J. Shank, The invariants of the third symmetric power representation of SL2( Fp), Journal of Algebra 333 (2011) no. 1, 241-257 (doi:10.1016/j.jalgebra.2011.02.023, arXiv:1006.0116).

  • A. Hobson and R.J. Shank, The invariants of the second symmetric power representation of SL2( Fq), Journal of Pure and Applied Algebra 215 (2011) no. 10, 2481-2485 (doi:10.1016/j.jpaa.2011.02.006, arXiv:1002.4318).

  • H.E.A. Campbell, R.J. Shank and D.L. Wehlau, Vector invariants for the two dimensional modular representation of a cyclic group of prime order, Advances in Mathematics 225 (2010) no. 2, 1069-1094 (doi:10.1016/j.aim.2010.03.018, arXiv:0901.2811).

  • R.J. Shank and D.L. Wehlau, Decomposing symmetric powers of certain modular representations of cyclic groups , in H.E.A. Campbell et al. (editors), Symmetry and Spaces: in Honor of Gerry Schwarz , Progress in Mathematics, volume 278, 169-196, Birkhäuser, 2010.

  • P. Fleischmann, M. Sezer, R.J. Shank and C.F. Woodcock, The Noether numbers for cyclic groups of prime order , Advances in Mathematics 207 (2006) no.1, 149-155.

  • M. Sezer and R.J. Shank, On the coinvariants of modular representations of cyclic groups of prime order , Journal of Pure and Applied Algebra 205 (2006) no. 1, 210-225.

  • M. Sezer and R.J. Shank, Coinvariants for modular representations of cyclic groups of prime order , arXiv:math.AC/0409107, IMS Technical Report UKC/IMS/04/29, September 2004, 29 pages (This is an extended version of the JPAA paper).

  • P. Fleischmann, G. Kemper and R.J. Shank, Depth and Cohomological Connectivity in Modular Invariant Theory, Transactions of the American Mathematical Society 357 (2005) no. 9, 3605-3621.

  • P. Fleischmann, G. Kemper and R.J. Shank, On the Depth of Cohomology Modules , Quarterly Journal of Mathematics 55 (2004) no. 2, 167-184.

  • R.J. Shank, Classical covariants and modular invariants , in H.E.A. Campbell and D.L. Wehlau (eds), Invariant Theory in All Characteristics, CRM Proceedings and Lecture Notes 35 , 241-249, AMS, 2004.

  • P. Fleischmann and R.J. Shank, The relative trace ideal and the depth of modular rings of invariants, Archiv der Mathematik 80 (2003) no. 4, 347-353.

  • R.J. Shank and D.L. Wehlau, Computing modular invariants of p-groups, Journal of Symbolic Computation 34 (2002) no. 5, 307-327.

  • R.J. Shank and D.L. Wehlau, Noether numbers for subrepresentations of cyclic groups of prime order , Bulletin of the London Mathematical Society 34 (2002) no. 4, 438-450.

  • H.E.A. Campbell, I.P. Hughes, G. Kemper, R.J. Shank and D.L. Wehlau, Depth of modular invariant rings, Transformation Groups 5 (2000) no. 1, 21-34.

  • R.J. Shank and D.L. Wehlau, On the depth of the invariants of the symmetric power representations of SL2(Fp), Journal of Algebra 218 (1999) no. 2, 642-653.

  • R.J. Shank and D.L. Wehlau, The transfer in modular invariant theory, Journal of Pure and Applied Algebra 142 (1999) no. 1, 63-77.

  • H.E.A. Campbell, A.V. Geramita, I.P. Hughes, R.J. Shank and D.L. Wehlau, Non-Cohen-Macaulay vector invariants and a Noether bound for a Gorenstein ring of invariants, Canadian Mathematical Bulletin 42 (1999) no. 2, 155-161.

  • R.J. Shank, S.A.G.B.I. bases for rings of formal modular seminvariants, Commentarii Mathematici Helvetici 73 (1998) no. 4, 548-565.

  • H.E.A. Campbell, I.P. Hughes, R.J. Shank and D.L. Wehlau, Bases for rings of coinvariants, Transformation Groups 1 (1996) no. 4, 307-336.

  • R.J. Shank, Lannes' T functor on Hopf algebras over the Steenrod algebra with applications to Carlsson modules and twisted algebras, Math. Z. 211 (1992) 341-350.

  • J.C. Harris and R.J. Shank, Lannes' T functor on summands of H*(B(Z/p)r), Transactions of the A.M.S. 333 (1992) 579-606.

  • J.C. Harris and R.J. Shank, Lannes' division functors on summands of H*(B(Z/p)r), Lecture Notes in Mathematics 1509, 120-133, Springer-Verlag, 1992.

  • J.C. Harris, T.J. Hunter and R.J. Shank, Steenrod algebra module maps from H*(B(Z/p)n) to H*(B(Z/p)s), Proceedings of the A.M.S. 112 (1991) 245-257.

    Notes: Preliminary notes on rigid reflection groups, (1995) 1-6.