Anthony Henderson

I am an Associate Professor in the School of Mathematics and Statistics at the University of Sydney. Here is my curriculum vitae (pdf, 8 pages).


Postal address: A/Prof Anthony Henderson
School of Mathematics and Statistics F07
University of Sydney NSW 2006
Australia
Office: Room 805 Carslaw Building
Email: anthony.henderson[at]sydney.edu.au


Research

I am a member of the Algebra research group. Broadly speaking, I am interested in geometric and combinatorial aspects of representation theory. The papers and talks listed below can be categorized into three main themes. In 2012, I was one of two recipients of the Australian Mathematical Society Medal, awarded annually to a member of the Society under the age of 40 for distinguished research in the mathematical sciences. I thereby became a Fellow of the Australian Mathematical Society.

In 2011, I was the inaugural winner of the Christopher Heyde Medal of the Australian Academy of Science.

I am currently the Elected Vice-President of the Australian Mathematical Society and an Associate Editor of the Journal of the Australian Mathematical Society.

Preprints

  1. with Pramod N. Achar, Daniel Juteau and Simon Riche: Modular generalized Springer correspondence I: the general linear group, to appear in J. Eur. Math. Soc. (JEMS), available at arXiv:1307.2702 or here (version 3, 29 pages).
  2. with Pramod N. Achar, Daniel Juteau and Simon Riche: Modular generalized Springer correspondence II: classical groups, to appear in J. Eur. Math. Soc. (JEMS), available at arXiv:1404.1096 or here (version 3, 52 pages).
  3. Singularities of nilpotent orbit closures, to appear in Proceedings of the 5th Japanese-Australian Workshop on Real and Complex Singularities, available at arXiv:1408.3888 or here (version 2, 30 pages).
  4. with Pramod N. Achar, Daniel Juteau and Simon Riche: Modular generalized Springer correspondence III: exceptional groups, available at arXiv:1507.00401 or here (version 2, 38 pages).
  5. with Pramod N. Achar, Daniel Juteau and Simon Riche: Constructible sheaves on nilpotent cones in rather good characteristic, available at arXiv:1507.06581 or here (26 pages).

Research Publications

  1. Fourier transform, parabolic induction, and nilpotent orbits, Transform. Groups 6 (2001), no. 4, 353-370.
  2. Spherical functions of the symmetric space G(F)/G(Fq), Represent. Theory 5 (2001), 581-614.
  3. Two-row nilpotent orbits of cyclic quivers, Math. Z. 243 (2003), no. 1, 127-143.
  4. Symmetric subgroup invariants in irreducible representations of GF, when G=GLn, J. Algebra 261 (2003), no. 1, 102-144.
  5. Representations of wreath products on cohomology of De Concini-Procesi compactifications, Int. Math. Res. Not. 2004 (2004), no. 20, 983-1021.
  6. Species over a finite field, J. Algebraic Combin. 21 (2005), no. 2, 147-161.
  7. Bases for certain cohomology representations of the symmetric group, J. Algebraic Combin. 24 (2006), no. 4, 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, 116-135.
  10. Nilpotent orbits of linear and cyclic quivers and Kazhdan-Lusztig polynomials of type A, Represent. Theory 11 (2007), 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, 85-98.
  13. with Pramod N. Achar: Orbit closures in the enhanced nilpotent cone, Adv. Math. 219 (2008), no. 1, 27-62. Note the corrigendum.
  14. with Gus Lehrer: The equivariant Euler characteristic of real Coxeter toric varieties, Bull. London Math. Soc. 41 (2009), no. 3, 515-523.
  15. Exterior powers of the reflection representation in the cohomology of Springer fibres, C. R. Math. Acad. Sci. Paris 348 (2010), no. 19-20, 1055-1058.
  16. with Pramod N. Achar and Eric Sommers: Pieces of nilpotent cones for classical groups, Represent. Theory 15 (2011), 584-616.
  17. with Pramod N. Achar and Benjamin F. Jones: Normality of orbit closures in the enhanced nilpotent cone, Nagoya Math. J. 203 (2011), 1-45.
  18. Enhancing the Jordan canonical form, Austral. Math. Soc. Gaz. 38 (2011), no. 4, 206-211.
  19. with Michelle L. Wachs: Unimodality of Eulerian quasisymmetric functions, J. Combin. Theory Ser. A 119 (2012), no. 1, 135-145.
  20. with Peter E. Trapa: The exotic Robinson-Schensted correspondence, J. Algebra 370 (2012), 32-45.
  21. Rational cohomology of the real Coxeter toric variety of type A, in Configuration Spaces: Geometry, Combinatorics, and Topology, Publications of the Scuola Normale Superiore, no. 14, A. Björner, F. Cohen, C. De Concini, C. Procesi and M. Salvetti (eds.), Pisa, 2012, 313-326, available from SNS and Birkhäuser.
  22. with Pramod N. Achar: Geometric Satake, Springer correspondence, and small representations, Selecta Math. (N.S.) 19 (2013), no. 4, 949-986.
  23. with Pramod N. Achar, Daniel Juteau and Simon Riche: Weyl group actions on the Springer sheaf, Proc. Lond. Math. Soc. 108 (2014), no. 6, 1501-1528.
  24. with Anthony Licata: Diagram automorphisms of quiver varieties, Adv. Math. 267 (2014), 225-276.
  25. with Pramod N. Achar and Simon Riche: Geometric Satake, Springer correspondence, and small representations II, Represent. Theory 19 (2015), 94-166.

Selected Recent Talks

  1. Geometric Satake, Springer correspondence, and small representations, Algebraic Groups and Representation Theory, Hong Kong, January 2013.
  2. A partial history of the Schur functor, my plenary lecture at the Australian Mathematical Society Annual Meeting, Sydney, September 2013.
  3. Character sheaves and modular generalized Springer correspondence, the first two parts of a 3-lecture series in the Winter School on Geometric Representation Theory, RIMS, Kyoto, January 2015.
  4. Geometric modular representation theory, the introduction to a lecture series I gave at the Centre for Geometry and its Applications, POSTECH, Pohang, February 2015. Here is a YouTube video of an earlier version of this talk, given at the University of Western Sydney, August 2013.
  5. Geometric representation theory, four lectures on canonical bases of quantized universal enveloping algebras, delivered at the AMSI Winter School on Algebra, Geometry and Physics, Brisbane, July 2015. See here for the preceding lectures given by Masoud Kamgarpour and Tony Licata.

Postdoctoral Supervision

From July 2013 to March 2015, I supervised the University of Sydney Postdoctoral Fellowship of Alan Stapledon.

Postgraduate Supervision

I supervise or have supervised the following postgraduate students. I have also supervised seven Honours projects and eight Vacation Scholarships. For information about available PhD projects, see my page in Research Supervisor Connect.


Undergraduate Teaching

In May 2009, I was awarded a Faculty of Science Citation for Excellence in Teaching. I have lectured the following units of study. My lecture notes on Lie algebras have been published as the undergraduate textbook `Representations of Lie Algebras: An Introduction Through gln', Australian Mathematical Society Lecture Series, no. 22, Cambridge University Press, Cambridge, 2012, available from CUP Australia, CUP America, Amazon, Amazon UK and Book Depository. See the reviews in MathSciNet, zbMATH, Choice (subscriptions required), and the Gazette of the Australian Mathematical Society.

I also run the SUMS Problem Competition for undergraduates from around Australia.


Some Links