Anthony Henderson

I am a Senior Lecturer in the School of Mathematics and Statistics at the University of Sydney. Here is my curriculum vitae (pdf, 5 pages).

Postal address: Dr Anthony Henderson
School of Mathematics and Statistics F07
University of Sydney NSW 2006
Australia
Office: Room 805 Carslaw Building
Email: anthonyh[at]maths.usyd.edu.au
Phone: +61 2 9351 3881

Research Interests

I am a member of the Algebra research group. Broadly speaking, I am interested in representations of Lie-theoretic objects and related aspects of combinatorics and geometry. The papers and talks listed below can be categorized into three main themes. I currently hold two research grants from the Australian Research Council, on `The geometry of exotic nilpotent cones' and `Pyramids and decomposition numbers for the symmetric and general linear groups' (joint with A. Mathas).

Published Papers

  1. Fourier transform, parabolic induction, and nilpotent orbits, Transform. Groups 6 (2001), no. 4, pp. 353-370.
  2. Spherical functions of the symmetric space G(Fq²)/G(Fq), Represent. Theory 5 (2001), pp. 581-614.
  3. Two-row nilpotent orbits of cyclic quivers, Math. Z. 243 (2003), no. 1, pp. 127-143.
  4. Symmetric subgroup invariants in irreducible representations of GF, when G=GLn, J. Algebra 261 (2003), no. 1, pp. 102-144.
  5. Representations of wreath products on cohomology of De Concini-Procesi compactifications, Int. Math. Res. Not. 2004 (2004), no. 20, pp. 983-1021.
  6. Species over a finite field, J. Algebraic Combin. 21 (2005), no. 2, pp. 147-161.
  7. Bases for certain cohomology representations of the symmetric group, J. Algebraic Combin. 24 (2006), no. 4, pp. 361-390.
  8. Plethysm for wreath products and homology of sub-posets of Dowling lattices, Electron. J. Combin. 13 (2006), no. 1, Research Paper 87, 25 pp.
  9. Induced characters of the projective general linear group over a finite field, J. Algebra 307 (2007), no. 1, pp. 116-135.
  10. Nilpotent orbits of linear and cyclic quivers and Kazhdan-Lusztig polynomials of type A, Represent. Theory 11 (2007), pp. 95-121.
  11. with Eric Rains: The cohomology of real De Concini-Procesi models of Coxeter type, Int. Math. Res. Not. 2008 (2008), rnn001, 29 pp.
  12. The symmetric group representation on cohomology of the regular elements of a maximal torus of the special linear group, J. Aust. Math. Soc. 84 (2008), no. 1, pp. 85-98.
  13. with Pramod N. Achar: Orbit closures in the enhanced nilpotent cone, Adv. Math. 219 (2008), no. 1, pp. 27-62.
  14. with Gus Lehrer: The equivariant Euler characteristic of real Coxeter toric varieties, Bull. London Math. Soc. 41 (2009), no. 3, pp. 515-523.

Selected Talks

  1. Spherical functions of the symmetric space G(Fq²)/G(Fq), MIT Lie Groups Seminar, November 2000, pdf (15 pages).
  2. Spherical functions and character sheaves, University of Sydney Algebra Seminar, August 2001 (a revised version of my thesis defence), pdf (12 pages).
  3. Symmetric subgroup invariants in irreducible representations of GF, when G=GLn, Annual Meeting of the Australian Mathematical Society, September 2001, pdf (6 pages).
  4. Fourier transform and Kloosterman sums, University of Sydney Algebra Seminar, October 2002, pdf (14 pages).
  5. Species over a finite field, Australia/New Zealand Mathematics Convention, July 2003, pdf (6 pages, 2 pictures missing).
  6. Polynomial functors and representations of wreath products, University of Sydney Algebra Seminar, August 2003, pdf (14 pages).
  7. Representations of wreath products on cohomology of De Concini-Procesi compactifications, Lie Minisymposium, November 2003, pdf (12 pages, 4 pictures missing).
  8. The symmetric group representation on cohomology of the regular elements of a maximal torus of the special linear group, Annual Meeting of the Australian Mathematical Society, September 2004, pdf (8 pages, 19 counting overlays).
  9. Nilpotent orbits and Kazhdan-Lusztig polynomials of type A, Mathematical Physics and Lie Theory, December 2004, pdf (7 pages).
  10. Equalities of Kazhdan-Lusztig polynomials of type A, University of Sydney Algebra Seminar, March 2005, pdf (14 pages).
  11. Bases for certain cohomologies with local coefficients of a hyperplane complement, Annual Meeting of the Australian Mathematical Society, September 2005, pdf (9 pages, 24 counting overlays).
  12. Quiver varieties and zero weight spaces, AMSI Workshop on Lie Theory, Lattices, and Dynamics, November 2005, pdf (11 pages).
  13. Poset homology and the cohomology of real De Concini-Procesi models, University of Sydney Algebra Seminar, August 2006, pdf (17 pages, 53 counting overlays).
  14. The cohomology of the real De Concini-Procesi model of type Bn, Annual Meeting of the Australian Mathematical Society, September 2006, pdf (8 pages, 20 counting overlays).
  15. The cohomology of real De Concini-Procesi models of Coxeter type, Braids and their Ramifications, Cortona, May 2007, pdf (14 pages, 45 counting overlays).
  16. Orbit closures in the enhanced nilpotent cone, Shuffles, Descents, and Representations, Nice, September 2007, pdf (14 pages, 37 counting overlays).
  17. Enhancing the nilpotent cone, Australia/New Zealand Mathematics Convention, Christchurch, December 2008, pdf (10 pages, 26 counting overlays).
  18. Geometry of the exotic nilpotent cone, Algebraic Lie Theory Seminar, Isaac Newton Institute, Cambridge, June 2009, pdf (13 pages, 31 counting overlays).

Teaching

In May 2009, I was awarded a Faculty of Science Citation for Excellence in Teaching. I have lectured the following units of study. I also run the SUMS Problem Competition for undergraduates from around Australia.

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